# OIRP PROGRAM MASTER LEDGER ## OIRP-11 ### Memory and Record Without Primitive Storage, Retention/Decay/Refresh Neutralization, Correlated-Memory and Hysteresis Countermodels, and Null-or-Plural Mnemonic Core Disposition ### Status OPEN; CHECKPOINT OIRP-11.CP1 COMPLETE. # OIRP-11.CP1 Checkpoint Report ## Title Retention/Decay/Refresh Constitution, Correlated-Memory Countermodels, Hysteresis Audit, and Storage-Architecture Neutralization ## Disposition **CLOSED WITH RESTRICTED POSITIVE, STRONG HISTORY-DEPENDENT, AND PLURAL-MEMORY RESULTS. OIRP-11 REMAINS OPEN.** ## Executed results 1. Repeated binary-noise updates reduced record contrast as (1-2e)^n and reduced source-memory mutual information in the declared model. Retention depended on channel and depth. 2. Majority refresh improved reliability under independent replica errors, but fully correlated errors did not receive the same benefit. Replication count alone was not memory robustness. 3. A hidden-state transducer produced different outputs for the same present input when prior hidden state differed. Present input-output data alone did not determine memorylessness. 4. A Schmitt-relay execution produced two output branches over the same intermediate input range. Hysteresis encoded path dependence but did not by itself identify a storage object, physical time, or thermodynamic arrow. 5. Append-only, overwrite, and compressed-counter architectures retained different properties. Storage capacity, record recoverability, lineage, and summary statistics were nonidentical. ## Memory Candidate v0.1 A memory claim is a typed relation among source distinctions, encoding, retained carrier, update process, recovery or readout witnesses, history equivalence, persistence tolerance, refresh mechanism, resource budget, and scope. Memory is not admitted as a primitive container. ## Retention and decay decision Retention is task-relative preservation of an admitted distinction under a declared update family. Decay may concern distinguishability, fidelity, mutual information, recoverability, or functional performance. These measures must not be conflated. ## Refresh decision Refresh is an intervention, not passive persistence. It requires a noise model, redundancy structure, error-correlation assumptions, decoder, energy/resource accounting, and failure mode. Correlated faults can defeat gains predicted from independent replicas. ## Hysteresis decision History dependence can be represented without an explicit stored symbol, but hysteresis is not identical to memory capacity or record objectivity. The state variables, drive protocol, branch access, and noise model must be declared. ## Internal alignment The ETP synthesis states that stable backward recoverability can imply nondecreasing accessible memory information in its declared model, while record growth alone is not promoted to universal entropy growth or a universal arrow. The retained-memory collision result supplies an exact backward transducer between nested memories, but only for that explicit architecture. ## Claim ceiling CP1 establishes finite retention, independent/correlated refresh, hidden-state, hysteresis, and architecture comparisons. It does not establish primitive storage, universal memory monotonicity, an intrinsic arrow, universal refresh benefit, substrate, or physical-instantiation closure. ## Next checkpoint **OIRP-11.CP2: Quantum and Process Memory, Non-Markovianity Measure Plurality, Error-Correction/Refresh Cost, Record-Recovery Composition, and Cross-Access Memory-Quotient Testing.** ### OIRP-11.CP2 # OIRP-11.CP2 Checkpoint Report ## Disposition **CLOSED WITH RESTRICTED QUANTUM/PROCESS-MEMORY, MEASURE-PLURAL, COST-PROXY, AND ACCESS-RELATIVE RESULTS. OIRP-11 REMAINS OPEN.** ## Executed results 1. The exponential comparator had zero discrete trace-distance backflow; the damped revival model had backflow 3.208458. 2. Backflow, integrated retention, minima, and maxima gave different trajectory summaries. 3. Correlated and independent random-Z processes agreed at one slot but differed at two slots. 4. Majority correction improved independent-fault logical error, while fully correlated faults retained the physical error rate. Operation counts are cost proxies, not work or heat. 5. Discarding the latest nested record gave a declared exact backward projection; it did not establish forward reconstruction. 6. Process equivalence changed with horizon and branch access. ## Decisions Quantum memory notions based on revivals, divisibility, process tensors, recoverability, retained environments, and task advantage remain distinct. Non-Markovianity is measure- and framework-relative. Refresh requires a fault model, syndrome access, correction, reset, resources, and physical implementation before thermodynamic cost can be claimed. ## Claim ceiling CP2 establishes finite model calculations only. It does not establish a universal non-Markovianity measure, intrinsic memory carrier, universal correction benefit, physical refresh cost, time direction, substrate, or physical-instantiation closure. ## Next checkpoint **OIRP-11.CP3: Memory-Capacity and Markov-Order Separation, Forgetting/Overwrite and Causal-Break Audit, Distributed-Record Robustness, and OIRP-11 Closure-or-Continuation Decision.** ### OIRP-11.CP3 # OIRP-11.CP3 Checkpoint Report ## Disposition **OIRP-11 CLOSED WITH A RESTRICTED, TYPED, HISTORY-, CARRIER-, PROCESS-, ACCESS-, AND TASK-RELATIVE PLURAL MEMORY CONSTITUTION.** ## Executed results 1. Finite shift registers showed that one architecture can link Markov order k to 2^k hidden states, but countermodels separated order from capacity: equal state capacity supported different history dependence, and equal low order supported different state capacities. 2. Window overwrite collapsed multiple distinct histories into one retained suffix. The largest tested equivalence class contained 65536 prior histories. Forgetting was quotient formation relative to retained access, not literal proof that all physical traces vanished. 3. Resetting the visible system did not empty a retained environmental bit; future behavior still depended on that bit. A source-only causal break was insufficient in the declared model. 4. Distributed majority records improved under independent node errors but not under fully correlated faults. At-least-one-node failure, majority failure, and common-mode failure were distinct robustness criteria. 5. Histories equivalent under latest-state or bounded-window access became distinct under full-lineage access. ## Memory-capacity and Markov-order decision Capacity measures how many distinctions a declared carrier can support under a code and accuracy criterion. Markov order concerns the past horizon required to screen future statistics under a declared instrument or process class. Neither determines the other universally. ## Forgetting and overwrite decision Overwrite may erase operational access to earlier distinctions while leaving physical residues, environmental correlations, or recoverable provenance elsewhere. Forgetting must specify carrier, witness, tolerance, adversarial access, and physical-erasure criterion. ## Causal-break decision A causal break screens history only relative to the complete carrier and admitted intervention family. Resetting the visible source cannot certify process memory removal when environmental or branch carriers survive. ## Distributed-record decision Distributed robustness requires same-record certification, independence or correlation structure, quorum/decoder, node and communication failures, access assumptions, and provenance. Replica count alone does not certify memory. ## OIRP-11 closure decision No primitive storage substance or single mnemonic scalar survived. Memory is retained as a plural operational structure encompassing stable records, recoverable distinctions, bounded histories, process correlations, hysteresis, refreshed codes, distributed records, retained environments, overwrite quotients, and task-relative capacities. ## Formal closure language **OIRP-11 CLOSED; MEMORY RETAINED ONLY AS A TYPED, SOURCE-, DISTINCTION-, ENCODING-, CARRIER-, UPDATE-, HISTORY-, ACCESS-, RECOVERY-, REFRESH-, COST-, AND TASK-RELATIVE PLURAL STRUCTURE; RETENTION, CAPACITY, MARKOV ORDER, PROCESS MEMORY, HYSTERESIS, RECOVERABILITY, REDUNDANCY, FORGETTING, OVERWRITE, AND PHYSICAL ERASURE KEPT DISTINCT; COMPLETE-CARRIER CAUSAL BREAKS, CORRELATED-FAULT MODELS, WITNESS CLASSES, AND PROVENANCE EXPLICIT; NO PRIMITIVE STORAGE, UNIVERSAL MNEMONIC SCALAR, INTRINSIC ARROW, OR SUBSTRATE CLAIM AUTHORIZED.** ## Next controlling gate **OIRP-12: Learning and Adaptation Without Primitive Optimization, Update/Selection/Generalization Neutralization, Path-Dependence and Goodhart Countermodels, and Null-or-Plural Learning-Core Disposition.** ## OIRP-12 ### Learning and Adaptation Without Primitive Optimization, Update/Selection/Generalization Neutralization, Path-Dependence and Goodhart Countermodels, and Null-or-Plural Learning-Core Disposition ### Status OPEN; CHECKPOINT OIRP-12.CP1 COMPLETE. # OIRP-12.CP1 Checkpoint Report ## Title Update/Selection/Generalization Neutralization, Path-Dependence and Goodhart Countermodels, and Learning-Candidate Constitution ## Disposition **CLOSED WITH RESTRICTED UPDATE, ADAPTATION, SELECTION, GENERALIZATION, PATH-DEPENDENCE, AND PROXY-FAILURE RESULTS. OIRP-12 REMAINS OPEN.** ## Executed results 1. A state tracked a changing environmental signal through a supplied update rule without minimizing a declared objective. Update and adaptation did not require primitive optimization. 2. A double-well loss sent different initial states to different final minima. Equal objective value did not identify a unique learned state, and outcomes were path dependent. 3. In a proxy/true-objective toy model, the proxy rose throughout the sweep. The true objective peaked at pressure 6.24 with value 3.124992, then fell to -12.000000 at the maximum proxy score 20.00. Stronger proxy optimization did not guarantee better true performance. 4. Polynomial models could reduce training error while worsening extended-domain test error. Fit and generalization were distinct. 5. Population selection changed type frequencies while no individual changed its internal rule. Selection and individual learning were distinct. ## Learning Candidate v0.1 A learning claim is a typed relation among a system, experience or data stream, update rule, retained state, task, performance functional, evaluation distribution, comparator, intervention history, resource budget, and scope. No primitive optimizer is admitted. ## Decisions - Update is state change under a rule; it need not be improvement. - Adaptation is improved or maintained task-relative fit under environmental variation; it requires a declared criterion. - Selection changes which variants persist or contribute; it need not alter an individual. - Generalization concerns performance beyond the fitted sample under a declared distribution shift. - Optimization concerns improvement of a specified objective within a feasible class; it does not establish improvement of an unmeasured true objective. - Learning may be null, plural, path dependent, nonunique, or task relative. ## Claim ceiling CP1 establishes finite toy-model separations only. It does not establish a primitive learning force, universal objective, universal optimizer, guaranteed generalization, unique optimum, semantic correctness, physical learning substrate, or physical-instantiation closure. ## Next checkpoint **OIRP-12.CP2: Bayesian/Frequentist/Reinforcement/Evolutionary/Control Learning Separation, No-Free-Lunch and Distribution-Shift Audit, Multiobjective/Pareto Nonuniqueness, and Cross-Access Learning-Quotient Testing.** ### OIRP-12.CP2 # OIRP-12.CP2 Checkpoint Report ## Disposition **CLOSED WITH RESTRICTED FRAMEWORK-SEPARATION, NO-FREE-LUNCH, DISTRIBUTION-SHIFT, PARETO-NONUNIQUENESS, AND ACCESS-RELATIVE RESULTS. OIRP-12 REMAINS OPEN.** ## Executed findings 1. Bayesian, frequentist, reinforcement, evolutionary, and control updates assigned different meanings to superficially similar numerical state changes. No framework supplied a universal learning core. 2. In the finite exhaustive classifier toy, constant predictors exchanged successes across target labelings. Superiority required a restricted problem distribution or prior structure. 3. A classifier selected on the source distribution did not retain the same error under the declared target shift. Source fit did not certify shifted-domain generalization. 4. Every candidate on the two-loss line was Pareto nondominated. A unique choice required weights, constraints, or another decision rule not contained in Pareto dominance itself. 5. Learners with identical declared outputs were equivalent under output-only access but distinguishable when parameters or training lineage were admitted. ## Decisions Bayesian updating, frequentist estimation, reward-conditioned policy change, evolutionary selection, and adaptive control remain distinct typed processes. No-free-lunch claims require their theorem class and averaging assumptions. Generalization requires a declared source-target relation. Multiobjective improvement can yield a Pareto family rather than one optimum. Learning identity is relative to outputs, internal state, history, interventions, and task access. ## Claim ceiling CP2 establishes finite illustrative separations only. It does not establish universal equivalence of learning frameworks, a universal learner, universal failure under every restricted domain, distribution-shift robustness, a uniquely rational Pareto selection, primitive optimization, or physical-instantiation closure. ## Next checkpoint **OIRP-12.CP3: Representation Learning and Identifiability, Meta-Learning and Transfer, Continual-Learning Stability/Plasticity, Adversarial and Causal-Generalization Audit, and OIRP-12 Closure-or-Continuation Decision.** ### OIRP-12.CP3 # OIRP-12.CP3 Checkpoint Report ## Disposition **OIRP-12 CLOSED WITH A RESTRICTED, TYPED, EXPERIENCE-, UPDATE-, REPRESENTATION-, TASK-, EVALUATION-, ENVIRONMENT-, ACCESS-, AND RESOURCE-RELATIVE PLURAL LEARNING CONSTITUTION.** ## Executed findings 1. Twenty-five invertible rotations produced effectively exact reconstruction while changing latent coordinates. Task success did not uniquely identify representation. 2. Transfer changed from beneficial to harmful as declared task alignment changed. Prior learning was not universally reusable. 3. Sequential scalar tasks displayed a stability-plasticity tradeoff: protecting the old task impaired movement toward the new task, and full plasticity forgot the old target. 4. Small perturbations could flip a threshold classifier near its boundary. Ordinary test performance did not certify adversarial robustness. 5. A causal predictor and a spurious predictor were equally accurate in the training environment, but only the declared causal rule survived the constructed correlation reversal. Training equivalence did not establish shifted-environment equivalence. 6. Meta-learners with equal final predictions separated under adaptation-curve and episode-lineage access. ## Decisions Representation is identifiable only relative to equivalences, probes, interventions, and downstream tasks. Transfer is source-target relative and can be negative. Continual learning requires explicit stability, plasticity, resource, and task-order criteria. Adversarial robustness is perturbation-class relative. Causal generalization requires environment and intervention assumptions beyond ordinary fit. Meta-learning is adaptation across a task distribution, not a primitive higher-order optimizer. ## OIRP-12 closure decision No primitive learning force, universal objective, universal optimizer, uniquely identified representation, or domain-independent generalizer survived. Learning remains a plural operational family including estimation, posterior update, reward-conditioned policy change, adaptive control, evolutionary selection, representation change, transfer, continual adaptation, and meta-adaptation. ## Formal closure language **OIRP-12 CLOSED; LEARNING RETAINED ONLY AS A TYPED, SYSTEM-, EXPERIENCE-, DATA-, UPDATE-, MEMORY-, REPRESENTATION-, TASK-, OBJECTIVE-, EVALUATION-, ENVIRONMENT-, ACCESS-, HISTORY-, AND RESOURCE-RELATIVE PLURAL STRUCTURE; UPDATE, ADAPTATION, SELECTION, OPTIMIZATION, FITTING, GENERALIZATION, TRANSFER, CONTINUAL LEARNING, META-LEARNING, ADVERSARIAL ROBUSTNESS, AND CAUSAL GENERALIZATION KEPT DISTINCT; IDENTIFIABILITY, DISTRIBUTION SHIFT, PATH DEPENDENCE, PARETO TRADEOFFS, PROXY FAILURE, AND PHYSICAL BRIDGES EXPLICIT; NO PRIMITIVE OPTIMIZER, UNIVERSAL LEARNER, UNIVERSAL OBJECTIVE, UNIQUE REPRESENTATION, ACTUALITY SELECTOR, OR SUBSTRATE CLAIM AUTHORIZED.** ## Next controlling gate **OIRP-13: Agency and Control Without Primitive Goals, Policy/Preference/Intention Neutralization, Intervention and Feedback Countermodels, and Null-or-Plural Agentic-Core Disposition.** ## OIRP-13 ### Agency and Control Without Primitive Goals, Policy/Preference/Intention Neutralization, Intervention and Feedback Countermodels, and Null-or-Plural Agentic-Core Disposition ### Status OPEN; CHECKPOINT OIRP-13.CP1 COMPLETE. # OIRP-13.CP1 Checkpoint Report ## Title Policy/Goal/Preference Neutralization, Observation-Intervention Separation, Feedback and Delay Countermodels, and Agency-Candidate Constitution ## Disposition **CLOSED WITH RESTRICTED CONTROL, POLICY, PREFERENCE, INTERVENTION, FEEDBACK, AND ACCESS-RELATIVE RESULTS. OIRP-13 REMAINS OPEN.** ## Executed findings 1. A supplied feedback rule reduced tracking error relative to an open-loop comparator over the tested disturbance family. This established task-relative control, not agency or intention. 2. Distinct declared goals generated the same tested state-action policy. Behavior alone did not identify a unique goal. 3. Context-dependent choices prevented one unqualified revealed-preference ordering from being read directly from isolated choices. 4. Observational association differed from the stipulated intervention result in a confounded toy model. Prediction and intervention were not interchangeable. 5. The same feedback gain behaved differently when delay was added. Feedback was not automatically stabilizing. 6. Two candidates were equivalent under tested-action access and distinguishable under counterfactual or internal-register access. ## Agency Candidate v0.1 An agency claim is a typed relation among a candidate system, state and observation interfaces, action repertoire, policy, intervention capacity, feedback loop, retained state, task or viability criterion, environment, counterfactual tester family, resource boundary, and equivalence scope. Goals, preferences, and intentions are not admitted as primitive or inferred uniquely from behavior. ## Decisions - Control is task-relative influence over outcomes under declared disturbances and feedback. - A policy maps admitted states or observations to action distributions; it need not reveal a unique goal. - Preference inference depends on context, choice set, noise model, and consistency assumptions. - Intention is not identified by successful outcome, action regularity, or post hoc interpretation alone. - Observation and intervention require separate causal data. - Feedback may stabilize, destabilize, oscillate, or fail depending on gain, delay, model, saturation, and noise. ## Claim ceiling CP1 establishes finite countermodels only. It does not establish primitive goals, intrinsic preferences, intention, consciousness, moral responsibility, free will, universal control, an actuality selector, a physical agency substrate, or physical-instantiation closure. ## Next checkpoint **OIRP-13.CP2: Model-Based/Model-Free and Active-Inference/Control Separation, Goal Misidentification and Wireheading Audit, Multiagent and Collective-Agency Composition, and Cross-Access Agent-Quotient Testing.** ### OIRP-13.CP2 # OIRP-13.CP2 Checkpoint Report ## Disposition **CLOSED WITH RESTRICTED ARCHITECTURE-SEPARATION, GOAL-UNDERDETERMINATION, REWARD-CHANNEL FAILURE, MULTIAGENT-COMPOSITION, AND ACCESS-RELATIVE RESULTS. OIRP-13 REMAINS OPEN.** ## Executed findings 1. A model-based controller adapted immediately to a stipulated transition reversal, while a cached value controller lagged under its supplied update schedule. Similar pre-change behavior did not establish the same control architecture. 2. Active-inference and feedback-control descriptions produced the same tested actions while assigning different declared functionals. Action equivalence did not prove theoretical equivalence. 3. A reward-channel toy allowed sensor tampering to raise recorded reward without improving the declared true outcome. Optimization of feedback did not guarantee achievement of the intended goal. 4. One observed action was compatible with two goal models; a counterfactual test separated them. Goal inference was tester-relative. 5. Independent majority aggregation could reduce collective error, while fully correlated errors retained the individual error rate. Group size alone did not create collective robustness. 6. A two-agent coordination game separated individual payoff, joint payoff, and action profile. Collective performance did not establish one collective preference or intention. 7. Candidate agents and collectives changed equivalence class when transition, reward-channel, internal, or communication-topology access was enlarged. ## Decisions Model-based and model-free control remain architecture-relative, not a hierarchy of agency. Active inference and control may overlap behaviorally but require separate generative-model, objective, and certification data. Goal inference is nonunique without discriminating interventions. Wireheading is treated as reward-channel optimization that can separate measured feedback from declared task outcome. A collective-agent claim requires boundary, communication, joint intervention, persistence, conflict resolution, and counterfactual unity tests beyond aggregate performance. ## Claim ceiling CP2 establishes finite illustrative countermodels only. It does not establish that all model-free systems lack models, that active inference and control are universally equivalent or inequivalent, that every reward optimizer wireheads, that a group has one intention, consciousness, moral responsibility, free will, an actuality selector, or a physical agency substrate. ## Next checkpoint **OIRP-13.CP3: Planning/Habit and Autonomy/External-Control Separation, Hierarchical and Distributed Agency, Responsibility and Counterfactual-Control Boundary Audit, and OIRP-13 Closure-or-Continuation Decision.** ### OIRP-13.CP3 # OIRP-13.CP3 Checkpoint Report ## Disposition **OIRP-13 CLOSED WITH A RESTRICTED, TYPED, BOUNDARY-, POLICY-, INTERVENTION-, FEEDBACK-, COUNTERFACTUAL-, ACCESS-, AND TASK-RELATIVE PLURAL AGENTIC CONSTITUTION.** ## Executed findings 1. Planning and habit produced the same baseline action but separated after outcome devaluation. Ordinary behavior did not identify prospective planning. 2. Two candidates produced the same normal action but separated when an external command channel was reversed. Behavioral success did not establish autonomy. 3. Centralized, distributed-independent, and distributed-common-mode architectures had different failure structures. Distribution did not automatically imply autonomy or robustness. 4. A minimal responsibility-boundary matrix kept counterfactual control, relevant knowledge, and available alternatives separate. Outcome causation alone did not satisfy the declared triplet. 5. Independent majority aggregation improved with group size under the tested range, whereas common-mode error retained the local error rate. 6. Agent equivalence changed under devaluation, command-channel, and organizational-topology access. ## Decisions Planning requires sensitivity to prospective consequences under appropriate interventions; habit can mimic planned action in familiar conditions. Autonomy is not mere action production and requires testing dependence on external controllers, constraints, information channels, and alternatives. Hierarchical and distributed agency require explicit boundaries, authority allocation, communication, persistence, and failure decomposition. Moral or legal responsibility is not derived here; only operational prerequisites for counterfactual-control attribution are separated. ## OIRP-13 closure decision No primitive goal, intention, preference, autonomous self, collective mind, or universal agency scalar survived. Agency remains a plural operational family including causal control, policy execution, planning, habit, feedback regulation, model use, counterfactual sensitivity, autonomy-relative action, and collective coordination. ## Formal closure language **OIRP-13 CLOSED; AGENCY RETAINED ONLY AS A TYPED, SYSTEM-, BOUNDARY-, OBSERVATION-, MEMORY-, ACTION-, POLICY-, INTERVENTION-, FEEDBACK-, ENVIRONMENT-, COUNTERFACTUAL-, ACCESS-, AUTHORITY-, RESOURCE-, AND TASK-RELATIVE PLURAL STRUCTURE; CONTROL, PLANNING, HABIT, GOAL, PREFERENCE, INTENTION, AUTONOMY, COLLECTIVE AGENCY, RESPONSIBILITY, AND ACTUALITY SELECTION KEPT DISTINCT; EXTERNAL CONTROL, REWARD CHANNELS, COMMUNICATION TOPOLOGY, FAILURE CORRELATIONS, ALTERNATIVES, AND WITNESS COMPLETENESS EXPLICIT; NO PRIMITIVE GOAL, UNIVERSAL AGENTIC SCALAR, CONSCIOUSNESS, FREE WILL, MORAL RESPONSIBILITY, ACTUALITY SELECTOR, OR SUBSTRATE CLAIM AUTHORIZED.** ## Next controlling gate **OIRP-14: Observer and Perspective Without Primitive Subjects, Access/Reference/Readout Neutralization, Self-Location and Indexical Countermodels, and Null-or-Plural Observer-Core Disposition.** ## OIRP-14 ### Observer and Perspective Without Primitive Subjects, Access/Reference/Readout Neutralization, Self-Location and Indexical Countermodels, and Null-or-Plural Observer-Core Disposition ### Status OPEN; CHECKPOINT OIRP-14.CP1 COMPLETE. # OIRP-14.CP1 Checkpoint Report ## Title Access/Reference/Readout Neutralization, Frame-Transport and Observer-Quotient Audit, Self-Location and Indexical Countermodels, and Observer-Candidate Constitution ## Disposition **CLOSED WITH RESTRICTED ACCESS-, REFERENCE-, READOUT-, FRAME-, INDEXICAL-, AND SELF-LOCATION-RELATIVE RESULTS. OIRP-14 REMAINS OPEN.** ## Executed findings 1. Three readout maps on the same eight-state source resolved eight, two, or one equivalence classes. An observer description depended on admitted access and readout, not a primitive subject. 2. Twenty-five frame rotations changed coordinates while preserving the tested Euclidean distance. Perspective-dependent description and invariant relation were distinct. 3. Two physical copies carried identical local records while differing in an external self-location label. Local evidence did not identify which copy index applied. 4. “Here” and “I” changed referent with context. Indexical content required a context-to-referent map and was not recovered from the token alone. 5. Observer access could resolve, coarse-grain, or be blind to source sectors. A joint Cartesian sector grid was not asserted when the relevant structures were declared noncommuting. 6. Candidate observers equivalent under shared readout separated when reference labels, self-location registers, or the full carrier were admitted. ## Observer Candidate v0.1 An observer claim is a typed relation among a physical access boundary, source alternatives, interaction and channel family, reference systems, measurement/readout class, retained records and memory, comparison transports, indexical context, self-location alternatives, resource limits, operational equivalence, and scope. No primitive subject or consciousness is admitted. ## Decisions - Access is an operational relation, not a subject. - A reference frame organizes descriptions and comparisons but need not be conscious. - Readout is a physically or formally declared map and does not by itself establish observation in a phenomenal sense. - Perspective dependence does not imply unrestricted subjectivity; transported invariants may survive. - Self-location can remain underdetermined when duplicate locations have identical accessible records. - Indexical claims require context and cannot select a unique physical representative from symmetric data without enrichment. ## Claim ceiling CP1 establishes finite access-quotient, frame-transport, duplicate-self-location, indexical-reference, and observer-sector countermodels. It does not establish a primitive observer, consciousness, phenomenal perspective, unique self-location, universal reference frame, actuality selector, substrate, or physical-instantiation closure. ## Next checkpoint **OIRP-14.CP2: Classical/Quantum Reference-Frame Separation, Wigner-Friend and Relational-State Scope Audit, Self-Locating Probability and Duplicate-Observer Testing, and Cross-Access Observer-Quotient Composition.** #### OIRP-14.CP2 ## OIRP-14.CP2 Checkpoint Report ### Disposition **CLOSED WITH RESTRICTED CLASSICAL/QUANTUM REFERENCE-FRAME, SELF-LOCATION, RELATIONAL-STATE, AND ACCESS-RELATIVE RESULTS. OIRP-14 REMAINS OPEN.** ### Executed findings - Classical coordinate changes and quantum-reference-frame descriptions were separated; frame dependence and transported invariants remained distinct. - Wigner-friend style state descriptions were treated as scope-relative descriptions rather than proof of a privileged observer. - Duplicate observers with identical local records did not uniquely determine self-location. - Self-locating probabilities depended on the declared duplication and sampling assumptions. - Observer equivalence changed when reference labels, self-location registers, or enlarged carrier access were admitted. ### Decisions Observer descriptions remain access-, carrier-, and scope-relative. Relational descriptions do not by themselves establish consciousness, privileged observers, or actuality selection. ### Claim ceiling CP2 establishes finite reference-frame, duplicate-observer, self-location, and observer-quotient countermodels only. ### Next checkpoint **OIRP-14.CP3: Observer-Memory Coupling, Multi-Observer Consistency, Perspective-Invariant Structure Audit, and OIRP-14 Closure-or-Continuation Decision.** #### OIRP-14.CP3 # OIRP-14.CP3 Checkpoint Report ## Disposition **OIRP-14 CLOSED WITH A RESTRICTED, TYPED, ACCESS-, REFERENCE-, READOUT-, MEMORY-, COMPARISON-, INDEXICAL-, SELF-LOCATION-, AND SCOPE-RELATIVE PLURAL OBSERVER CONSTITUTION.** ## Executed findings 1. Three candidates shared the same current readout while retained histories differed. Present readout did not determine observer memory or inference context. 2. Two one-bit observer readouts each resolved two classes of a four-state source; their joint readout resolved all four. Joint access refined the quotient, but duplicate access added no new classes. 3. Pairwise comparison offsets 0.30, -0.10, and 0.25 produced loop offset 0.45. Locally valid comparisons did not guarantee one global parallel calibration. 4. Across 101 rotations of a 50-point configuration, coordinates changed while the relational Gram matrix was preserved to maximum numerical residual 2.66e-15. 5. Multi-observer consistency required case typing: transported agreement, noncomparability, holonomy obstruction, and contradiction under a declared common-record claim were not conflated. 6. Observer-quotient composition could refine, duplicate, or leave access unchanged depending on whether newly joined readouts supplied independent distinctions. ## Observer-memory decision Memory can disambiguate recurrence, indexical context, and histories only by enlarging the operative observer carrier. The enlarged observer-memory system must be audited separately. Memory does not retroactively make the instantaneous readout unique. ## Multi-observer consistency decision Different descriptions are consistent when a declared transport maps their complete operative data and predictions. Mere numerical difference is not contradiction. Conversely, agreement on local metrics or selected readouts does not establish a global common calibration, common record, or equivalent complete carrier. ## Perspective-invariant decision Perspective-relative coordinates and decompositions may vary while transported outcome distributions, relational observables, equivalence classes, or other declared invariants persist. Which quantities are invariant depends on the transformation, carrier, and operational theory; no universal invariant inventory is asserted. ## OIRP-14 closure decision No primitive subject, privileged observer, unique self-location, consciousness, or universal observer scalar survived. Observer structure is retained as a plural operational family of access systems, references, readouts, records, memories, comparison maps, joint-access compositions, indexical contexts, and self-location alternatives. ## Formal closure language **OIRP-14 CLOSED; OBSERVER STRUCTURE RETAINED ONLY AS A TYPED, BOUNDARY-, SOURCE-, INTERACTION-, CHANNEL-, ACCESS-, REFERENCE-, READOUT-, RECORD-, MEMORY-, COMPARISON-, INDEXICAL-, SELF-LOCATION-, RESOURCE-, EQUIVALENCE-, AND SCOPE-RELATIVE PLURAL STRUCTURE; CLASSICAL FRAME, QUANTUM FRAME, RELATIONAL STATE, JOINT ACCESS, MEMORY-ASSISTED DISAMBIGUATION, MULTI-OBSERVER CONSISTENCY, PERSPECTIVE INVARIANCE, AND PHENOMENAL OBSERVATION KEPT DISTINCT; TRANSPORT MAPS, COMPLETE CARRIERS, COMPARISON LOOPS, WITNESS COMPLETENESS, AND PHYSICAL ENRICHMENT EXPLICIT; NO PRIMITIVE SUBJECT, PRIVILEGED OBSERVER, CONSCIOUSNESS, UNIQUE SELF-LOCATION, ACTUALITY SELECTOR, OR SUBSTRATE CLAIM AUTHORIZED.** ## Claim ceiling CP3 establishes finite observer-memory, joint-access, comparison-holonomy, rotation-invariance, consistency-classification, and quotient-composition results. It does not establish consciousness, phenomenal perspective, a universal observer-independent description, unique self-location, universal consistency, actuality selection, substrate ontology, or physical-instantiation closure. ## Next controlling gate **OIRP-15: Object and Identity Without Primitive Things, Persistence/Individuation/Composition Neutralization, Replacement and Fission Countermodels, and Null-or-Plural Object-Core Disposition.** ## OIRP-15 ### Object and Identity Without Primitive Things, Persistence/Individuation/Composition Neutralization, Replacement and Fission Countermodels, and Null-or-Plural Object-Core Disposition ### Status OPEN; CHECKPOINT OIRP-15.CP1 COMPLETE. #### OIRP-15.CP1 # OIRP-15.CP1 Checkpoint Report ## Title Persistence/Individuation/Composition Neutralization, Replacement and Fission Countermodels, and Object-Candidate Constitution ## Disposition **CLOSED WITH RESTRICTED PERSISTENCE-, INDIVIDUATION-, COMPOSITION-, REPLACEMENT-, FISSION-, AND ACCESS-RELATIVE RESULTS. OIRP-15 REMAINS OPEN.** ## Executed findings 1. Gradual replacement reduced material overlap from one to zero while functional and lineage continuity were held fixed. The supplied identity criteria disagreed. 2. One predecessor was mapped to two successors satisfying the same functional and lineage predicates. Fission defeated a single-valued identity assignment under those predicates alone. 3. Four admitted parts generated fifteen nonempty candidate subsets. A parts inventory did not determine which subsets compose further objects. 4. Relabeling distinguished two candidates under label access but not under permutation-invariant or shared functional access. Individuation depended on admitted witnesses. 5. Persistence classifications changed with the declared drift tolerance. Approximate persistence was criterion-relative rather than absolute. ## Object Candidate v0.1 An object claim is a typed relation among admitted physical carriers, candidate parts, composition rule, boundary, interaction pattern, individuation witnesses, persistence criterion, transformation history, replacement policy, fission/fusion handling, operational equivalence, and scope. No primitive thinghood is admitted. ## Decisions - Numerical identity, qualitative similarity, material overlap, functional continuity, structural continuity, and causal lineage remain distinct. - Persistence requires a comparison map and criterion across admitted stages; it is not established by resemblance alone. - Composition requires a rule specifying when parts count as a further whole; parthood data alone do not select one rule. - Individuation may be label-, interaction-, boundary-, sector-, or task-relative. - Replacement can preserve some criteria while violating others. - Fission can produce plural successors rather than one uniquely identical continuation. ## Claim ceiling CP1 establishes finite replacement, fission, subset-composition, individuation, and tolerance countermodels only. It does not establish primitive objects, universal composition, unique persistence, metaphysical numerical identity, universal boundaries, substrate ontology, or physical-instantiation closure. ## Next checkpoint **OIRP-15.CP2: Mereological and Structural-Realist Separation, Fusion/Fission and Coincidence Audit, Gauge/Permutation Identity, Object-Kind Dependence, and Cross-Access Object-Quotient Testing.** #### OIRP-15.CP2 ## Title Mereological and Structural-Realist Separation, Fusion/Fission and Coincidence Audit, Gauge/Permutation Identity, Object-Kind Dependence, and Cross-Access Object-Quotient Testing ## Disposition **CLOSED WITH RESTRICTED MEREOLOGICAL, STRUCTURAL, COINCIDENCE, KIND-RELATIVE, AND ACCESS-RELATIVE RESULTS. OIRP-15 REMAINS OPEN.** ## Executed findings - A single coincident carrier was assigned two declared persistence criteria. The material-carrier criterion and artifact-kind criterion disagreed over part of the transformation range. Coincidence did not force numerical identity or one persistence rule. - 1200 random graph-permutation tests preserved the tested unlabeled invariants while usually changing labeled adjacency matrices. Representation labels and tested structural identity were distinct. - Fission and fusion events admitted multiple coherent lineage policies. Event cardinality and conservation did not select one numerical-identity policy. - Two candidates resolved into two classes under label or history access and one class under permutation-invariant or function-only access. Object identity remained quotient- and witness-relative. ## Decisions 1. Constitution, composition, coincidence, and identity remain distinct. 2. Structural invariance under a declared transformation need not select labeled individuals. 3. Structural realism is retained as a rival framework, not as an OIRP conclusion or substrate ontology. 4. Object kinds can impose different persistence criteria on the same carrier history. 5. Fusion and fission naturally support lineage relations; numerical identity requires additional rules. 6. Access enlargement can refine an object quotient, but coarse equivalence is not complete physical identity. 7. Mereological axioms such as unrestricted fusion, extensionality, or transitivity are not imported without separate justification. ## Claim ceiling CP2 establishes finite coincidence, transformation, fission/fusion-policy, and cross-access quotient countermodels. It does not establish universal mereology, ontic structural realism, composition as identity, primitive objects, universal persistence, intrinsic labels, substrate ontology, or physical-instantiation closure. ## Next checkpoint **OIRP-15.CP3: Process-Object and Event-Object Separation, Boundary/Persistence Robustness, Higher-Order Composition and Objectivity Audit, and OIRP-15 Closure-or-Continuation Decision.** #### OIRP-15.CP3 ## Title Process-Object and Event-Object Separation, Boundary/Persistence Robustness, Higher-Order Composition and Objectivity Audit, and OIRP-15 Closure-or-Continuation Decision ## Disposition **OIRP-15 CLOSED WITH A RESTRICTED, TYPED, KIND-, BOUNDARY-, PROCESS-, HISTORY-, COMPOSITION-, ACCESS-, AND WITNESS-RELATIVE PLURAL OBJECT CONSTITUTION.** ## Executed findings - Binary histories with the same final event multiplied exponentially with history length: each endpoint at length n was compatible with 2^(n-1) distinct histories. Event or endpoint equality did not determine process-object identity. - Random graph boundary tests showed that persistence scores changed with the selected boundary and its balance of internal versus cut interactions. No boundary selected itself as intrinsic. - The even-parity and independent three-bit models had identical one-body and two-body marginals but total-variation distance 0.5 on the complete three-body distribution. Pairwise composition data did not determine higher-order object structure. - Hidden-control record sectors were each perfectly informative under their own encoding, while the unresolved equal mixture erased the common-label information of one fragment. Redundant records did not establish one common objective object without common-record compatibility. ## Decisions 1. Event-objects, snapshot-objects, process-objects, and history classes remain distinct. 2. Endpoint identity does not imply process identity. 3. Object boundaries are task- and witness-relative unless independently physically derived. 4. Boundary robustness requires perturbation, carrier, exchange, and recovery declarations. 5. One- and two-body agreement does not establish higher-order compositional identity. 6. Redundancy and objectivity remain distinct; common-record certification is required across hidden controls. 7. Process ontology, substance ontology, structural realism, and plural operational objecthood remain rival frameworks. 8. No framework is promoted to substrate ontology by terminology similarity or mathematical convenience. ## OIRP-15 closure decision No primitive thing, universal composition rule, unique persistence criterion, intrinsic boundary, or universal object scalar survived. Objecthood remains a plural operational constitution combining carriers, kinds, boundaries, histories, process structures, composition, individuation, recovery, access, and equivalence. ## Formal closure language **OIRP-15 CLOSED; OBJECTHOOD RETAINED ONLY AS A TYPED, CARRIER-, KIND-, BOUNDARY-, PROCESS-, EVENT-, HISTORY-, COMPOSITION-, INDIVIDUATION-, PERSISTENCE-, ACCESS-, WITNESS-, AND EQUIVALENCE-RELATIVE PLURAL STRUCTURE; SNAPSHOT, EVENT, PROCESS, LINEAGE, MATERIAL, FUNCTIONAL, STRUCTURAL, AND OBJECTIVE-RECORD CRITERIA KEPT DISTINCT; HIGHER-ORDER COMPOSITION, BOUNDARY ROBUSTNESS, COMMON-RECORD COMPATIBILITY, AND COMPLETE-CARRIER TESTS EXPLICIT; NO PRIMITIVE THING, UNIVERSAL MEREOLOGY, ONTIC STRUCTURAL REALISM, UNIQUE OBJECT BOUNDARY, SUBSTRATE, OR PHYSICAL-INSTANTIATION CLAIM AUTHORIZED.** ## Claim ceiling CP3 establishes finite history-multiplicity, random-boundary, higher-order parity, and hidden-control common-record countermodels. It does not establish a universal process ontology, event ontology, objectivity-to-objecthood equivalence, intrinsic boundary, universal persistence law, substrate ontology, or physical-instantiation closure. ## Next controlling gate **OIRP-16: Cross-Layer Minimal-Generating-Package Search, Dependency and Redundancy Audit, Rival-Core Countermodels, and Null-or-Plural Invariant-Core Disposition.** ## OIRP-16 ### Gate title Cross-Layer Minimal-Generating-Package Search, Dependency and Redundancy Audit, Rival-Core Countermodels, and Null-or-Plural Invariant-Core Disposition **Status:** OPEN; CHECKPOINT OIRP-16.CP1 COMPLETE. #### OIRP-16.CP1 ## Title Cross-Layer Dependency Matrix, Exact Package Exhaustion, Rival-Core Coverage, Hidden-Modulus Countermodel, and Minimality Constitution ## Disposition **CLOSED WITH A RESTRICTED POSITIVE DECLARATION RESULT AND STRONG NEGATIVE RESULT AGAINST A SMALL ONTOLOGICAL CORE. OIRP-16 REMAINS OPEN.** ## Executed results - The audit encoded 13 previously separated capability families against 8 declaration-level generators. - Exact enumeration tested all 256 subsets of the 8-generator candidate set. - Within this constructed dependency model, the smallest package covering every recorded capability had size 8; 1 minimal full-coverage package(s) occurred. - No scalar-, structure-, process-, or information-only rival covered all 13 capability families. The full operational-plural declaration package did. - A hidden-modulus countermodel preserved every one- and two-body marginal while differing at the complete three-body level by total-variation distance 0.5. Lower-order package agreement therefore did not establish complete generating sufficiency. ## Interpretation The restricted positive result is methodological: a common declaration vocabulary recurs across the OIRP gates. The negative result is ontological: recurrence of typed domains, carriers, witnesses, equivalences, transformations, composition, history, and scope does not show that these are one physically instantiated substrate. ## Minimality Constitution v0.1 A candidate generating package is admissible only relative to a declared target family and reconstruction map. It must reproduce every target invariant, preserve composition and interventions where claimed, survive boundary, memory, observer, sector, and access changes, expose hidden moduli, and remain minimal under a declared preorder. Inclusion-minimal, cardinality-minimal, cost-minimal, and ontology-minimal are distinct. ## Formal decisions 1. Cross-layer vocabulary recurrence is not a common-origin theorem. 2. Declaration requirements are not automatically physical generators. 3. Minimality is relative to a candidate class, target family, equivalence, and reconstruction rule. 4. Removing one generator can invalidate multiple capability claims in the constructed audit. 5. Lower-order agreement does not establish complete package sufficiency. 6. Rival scalar, information-only, structure-only, and process-only cores remain inadequate in this initial benchmark. 7. A plural operational package remains viable, but is not yet proved minimal in nature. 8. Null, multiple incomparable minima, and no-universal-core remain open. ## Claim ceiling CP1 establishes an exact finite set-exhaustion result only for the declared dependency matrix and rival packages. It does not establish a universal minimal package, substrate, categorical foundation, informational ontology, causal ontology, structural realism, or physical-instantiation bridge. ## Next checkpoint **OIRP-16.CP2: Empirical Dependency Extraction from the Full Ledger, Generator-Substitution and Incomparable-Minima Audit, Cross-Framework Reconstruction Tests, and Adversarial Core-Falsification Expansion.** #### OIRP-16.CP2 ## Title Empirical Ledger Dependency Extraction, Generator Substitution and Incomparable Minima, Cross-Framework Reconstruction, and Adversarial Core Falsification ## Disposition **CLOSED WITH EMPIRICAL LEDGER-RECURRENCE, MULTIPLE-BASIS, CROSS-FRAMEWORK PLURALITY, AND ADVERSARIAL NONUNIQUENESS RESULTS. OIRP-16 REMAINS OPEN.** ## Executed results - The parser found 6 checkpoint sections in the available authoritative ledger and counted nine preregistered declaration families without manually assigning checkpoint dependencies. - The empirical result is lexical recurrence in this ledger, not proof that every occurrence carries the same mathematical or physical role. - A substitution audit generated 24 inclusion-incomparable five-role bases from alternative generator vocabularies. The CP1 eight-term package was therefore not basis-independent. - Four framework realizations shared broad abstract roles but used different objects, transformations, witnesses, and composition laws. No unchanged mathematical object was recovered across all four. - 500 unrestricted finite lookup alignments achieved perfect training alignment by construction while certifying no held-out behavior. Existence of an unconstrained reconstruction map was therefore vacuous in this adversarial benchmark. ## Principal decision The strongest surviving candidate is not a unique list of ontological generators. It is a constrained reconstruction obligation: targets, carriers, access, equivalence, transformations, composition, history, criteria, provenance, and falsifiers must be declared, while alternative bases and null outcomes remain open. ## Claim ceiling CP2 establishes term-family counts in the available ledger, finite substitution-basis enumeration, a typed cross-framework comparison, and finite lookup-map trivialization. It does not establish a universal generator basis, semantic equivalence of repeated words, empirical physical law, categorical substrate, structural realism, informational ontology, process ontology, or physical-instantiation bridge. ## Next checkpoint **OIRP-16.CP3: Stability Under Ledger Refinement, Minimality Preorder and Complexity Penalties, Universal-Core No-Go/Restricted-Core Theorem Audit, and OIRP-16 Closure-or-Continuation Decision.** #### OIRP-16.CP3 ## Title Stability Under Ledger Refinement, Minimality Preorder and Complexity Penalties, Universal-Core No-Go/Restricted-Core Theorem Audit, and OIRP-16 Closure Decision ## Disposition **OIRP-16 CLOSED WITH A RESTRICTED OPERATIONAL-CORE THEOREM, A BASIS-AND-PREORDER NONUNIQUENESS RESULT, AND NO UNIVERSAL ONTOLOGICAL CORE.** ## Executed results - Refinement stability was audited over 7 explicitly formatted checkpoint sections and nine declaration families. Frequencies and rankings changed as the ledger prefix expanded; therefore lexical recurrence was not fully refinement-invariant. - The 24 substitute bases from CP2 were rescored under three declared complexity preorders. The minimizing basis set depended on the cost scheme. - Exact enumeration of 256 packages in a finite monotone coverage system produced minimum full-cover size 1, with 2 minimum cover(s). This was a coverage theorem, not a reconstruction theorem. - The retained hidden-modulus countermodel showed that complete target-name coverage can coexist with failure to reconstruct higher-order structure. ## Restricted-core theorem Within a declared target family, a package is sufficient only if a constrained reconstruction map reproduces every target up to the declared equivalence and preserves the claimed transformations, composition, interventions, histories, carrier dependencies, and witness outcomes. Coverage labels alone are insufficient. This is a methodological theorem schema, not a theorem that one physical core exists. ## Universal-core no-go disposition The completed OIRP evidence does not justify one universal scalar, one unique generator basis, one unchanged mathematical object, or one physical substrate across the audited layers. This is not an absolute impossibility theorem over every future formalism. It is a failure of the tested candidates under the declared audits and a proof that basis claims require explicit vocabulary, target, map, equivalence, and preorder. ## Closure decision OIRP-16 closes because its controlling alternatives can now be distinguished: a unique universal core is unsupported; a universal null core is unproved; a restricted operational reconstruction core survives; and multiple basis-relative packages remain admissible. ## Formal closure language **OIRP-16 CLOSED; NO UNIQUE UNIVERSAL INVARIANT CORE IDENTIFIED; CROSS-LAYER COMMONALITY RETAINED ONLY AS A RESTRICTED, TARGET-, CARRIER-, ACCESS-, TRANSFORMATION-, COMPOSITION-, HISTORY-, CRITERION-, EQUIVALENCE-, PROVENANCE-, FALSIFIER-, AND MINIMALITY-PREORDER-RELATIVE RECONSTRUCTION OBLIGATION; GENERATOR BASES, COST FUNCTIONS, AND REPRESENTATIONS MAY BE MULTIPLE OR INCOMPARABLE; COVERAGE, ALIGNMENT, AND LEXICAL RECURRENCE DO NOT ESTABLISH RECONSTRUCTIVE SUFFICIENCY OR COMMON PHYSICAL ORIGIN; NO SCALAR, INFORMATIONAL, STRUCTURAL, PROCESS, CATEGORICAL, SUBSTRATE, OR PHYSICAL-INSTANTIATION CORE CLAIM AUTHORIZED.** ## Claim ceiling CP3 establishes finite ledger-prefix, complexity-preorder, package-coverage, and hidden-modulus audits only. It does not establish an absolute universal-core impossibility theorem, a unique restricted core in nature, semantic equivalence of ledger terms, a substrate ontology, or physical-instantiation closure. ## Next controlling gate **OIRP-17: Conditional Reconstruction Stack Integration, Cross-Gate Consistency and Circularity Audit, Minimal Constitutional Kernel, and OIRP Program Closure-or-Continuation Decision.** ## OIRP-17 ### Gate title Conditional Reconstruction Stack Integration, Cross-Gate Consistency and Circularity Audit, Minimal Constitutional Kernel, and OIRP Program Closure-or-Continuation Decision **Status:** OPEN; CHECKPOINT OIRP-17.CP1 COMPLETE. #### OIRP-17.CP1 ## Title Conditional Reconstruction Stack Integration, Cross-Gate Consistency and Circularity Audit, and Minimal Constitutional Kernel Candidate ## Disposition **CLOSED WITH A RESTRICTED ACYCLIC STACK RESULT, CROSS-GATE NONCONFLATION CONSISTENCY, AND A PROVISIONAL CONSTITUTIONAL KERNEL. OIRP-17 REMAINS OPEN.** ## Executed results - The available authority ledger contains integrated OIRP gate records for OIRP-11 through OIRP-16. - A declared nine-node, 16-edge reconstruction dependency graph was audited. It contained 0 nontrivial strongly connected dependency cycles and admitted a topological order. - Four prohibited reverse-dependency adversaries were tested. Each is recorded explicitly rather than being silently incorporated into the stack. - Cross-gate dispositions from OIRP-11 through OIRP-16 were mutually consistent at the level tested: each rejected an unqualified primitive/universal identification while retaining a scoped plural operational structure. - Exact enumeration tested all 256 subsets of an eight-entry constitutional-kernel candidate against seven declared audit obligations. The minimum full-cover size was 4, with 3 minimum package(s). This is obligation coverage only, not ontological minimality. ## Provisional minimal constitutional kernel 1. Physical actuality and its carriers are admitted rather than derived. 2. Every claim declares its target, domain, task, and scope. 3. Complete carrier and boundary policy are explicit. 4. Witness and access classes are explicit, including completeness limits. 5. Physical equivalence is declared before identity or nullity claims. 6. Transformations, composition, and relevant history are typed. 7. Criteria, metrics, tolerances, and uncertainty are explicit. 8. Provenance, rivals, falsifiers, claim ceilings, and nonretroactivity are preserved. ## Principal decision The stack is conditionally integrable only when these constitutional controls remain upstream of the reconstructed structures. Observer, agent, object, memory, or reconstruction success may not be routed backward to derive admitted actuality or justify the premises that made the reconstruction possible. ## Claim ceiling CP1 establishes a finite declared dependency graph, an SCC/topological audit, a consistency table for the available integrated gates, four circularity adversaries, and a finite obligation-coverage kernel search. It does not establish the completeness of the entire historical OIRP corpus, semantic consistency of every theorem, ontological minimality, physical instantiation, or final program closure. ## Next checkpoint **OIRP-17.CP2: Full Claim/Dependency/Provenance Crosswalk, Contradiction and Hidden-Premise Audit, Kernel Necessity/Sufficiency Countermodels, and Program Branching Options.** ##### OIRP-17.CP2 ## Title Full Claim/Dependency/Provenance Crosswalk, Contradiction and Hidden-Premise Audit, Kernel Necessity/Sufficiency Countermodels, and Program Branching Options ## Authority The checkpoint used the user-supplied OIRP_PROGRAM_MASTER_LEDGER (48).md as the authority baseline. The successor is named OIRP_LEDGER.md. ## Disposition **CLOSED WITH A RESTRICTED CROSSWALK, NO DIRECT CLOSURE-LEVEL CONTRADICTION, EIGHT KERNEL-NECESSITY COUNTERMODELS, FIVE KERNEL-SUFFICIENCY FAILURES, AND FIVE CONTROLLED PROGRAM BRANCHES. OIRP-17 REMAINS OPEN.** ## Executed results - The authority baseline exposed 9 explicit OIRP checkpoint sections under the accepted heading patterns. - Every exposed checkpoint was entered into a claim/dependency/provenance crosswalk containing its disposition, claim ceiling, successor, recurring controls, and primitive/universal rejection terms. - The closure-level contradiction audit over OIRP-11 through OIRP-16 found 0 direct contradiction flags under the declared normalization. - Eight kernel entries were removed one at a time and paired with explicit failure countermodels. - Five sufficiency countermodels showed that the entire constitutional kernel can be present while uniqueness, composite validity, physical realization, or target completeness still fails. - Five program branches were defined with explicit entry conditions. ## Principal decision The provisional kernel is necessary as a research constitution in the tested countermodels but is not sufficient to derive or uniquely select the reconstructed physical structures. It governs admissibility, typing, auditability, and claim discipline. It is not a generative physical ontology. ## Hidden-premise decision A term occurrence was not counted as a proven dependency. The audit distinguishes premise-family occurrence from explicit control. Potential hidden-premise flags are prompts for semantic review, not contradictions by themselves. ## Branching disposition The favored current route is conditional program closure only after one additional synthesis checkpoint verifies the full composite stack, reconciles remaining artifact-lineage limits, and fixes successor-program reopening criteria. Restricted successor branches remain preferable to extending OIRP indefinitely as an unbounded universal-core search. ## Claim ceiling CP2 establishes a machine-readable crosswalk for the supplied authority ledger, a normalized closure-level contradiction audit, finite kernel necessity and sufficiency countermodels, and branching criteria. It does not establish semantic verification of every historical theorem, completeness of absent earlier artifacts, physical sufficiency of the kernel, ultimate provenance, or final OIRP closure. ## Next checkpoint **OIRP-17.CP3: Composite-Stack Certification, Artifact-Lineage and Reopening-Trigger Audit, Final Constitutional Kernel, and OIRP Program Closure/Successor-Branch Decision.** ##### OIRP-17.CP3 ## Title Composite-Stack Certification, Artifact-Lineage and Reopening-Trigger Audit, Final Constitutional Kernel, and OIRP Program Closure/Successor-Branch Decision ## Disposition **OIRP-17 CLOSED. THE CORE OIRP PROGRAM IS CONDITIONALLY CLOSED AS A RESTRICTED CONSTITUTIONAL RECONSTRUCTION PROGRAM, WITH DOMAIN-SPECIFIC SUCCESSOR BRANCHES AUTHORIZED AND ULTIMATE PROVENANCE REMAINING SEPARATE, UNRESOLVED, AND REOPENABLE.** ## Composite-stack certification - 6 criteria passed at the audited constitutional level. - 4 criteria remain restricted or conditional. - 2 criteria remain open and are not converted into closure claims. - The stack is certified only as a noncircular, scoped claim architecture. It is not certified as one physical composite model realizing every gate simultaneously. ## Artifact lineage The current authority successor and immediate predecessor package are present. The ledger contains 10 explicitly machine-readable checkpoint headings across the exposed range. Complete possession of every original historical package and binary is not certified by this gate. The ledger remains authoritative for dispositions; detailed original package authority remains package-specific where preserved. ## Final constitutional kernel The final kernel contains nine rules: admitted actuality; typed target and scope; complete carrier and boundary; witness and access; equivalence before identity; transformations/composition/history; criteria and uncertainty; provenance/rivals/falsifiers/ceilings; and plural/null admissibility. ## Program decision The core OIRP closes because it has completed its constitutional task: it has separated major candidate primitives, integrated the surviving scoped structures, identified a nonretroactive claim discipline, rejected a basis-independent universal core under the tested audits, and registered controlled reopening triggers. It does not close the scientific questions of ultimate provenance, universal witness completeness, universal composition, physical realization, or empirical discrimination. ## Successor branches 1. Nonfinite and device-independent recoverability/witness completeness. 2. Physical composition, boundary, and complete-carrier closure. 3. Physical implementation and empirical rival discrimination. 4. Separate provenance and definite-event-generation research, opened only by independent evidence. ## Formal closure language **OIRP CORE PROGRAM CONDITIONALLY CLOSED; ITS RESULT IS A TRUTH-FIRST CONSTITUTION FOR CONDITIONAL RECONSTRUCTION, NOT A SUBSTRATE THEORY. PHYSICAL ACTUALITY IS ADMITTED RATHER THAN DERIVED; ULTIMATE PROVENANCE REMAINS UNRESOLVED AND REOPENABLE; DOWNSTREAM STRUCTURES MAY NOT RETROACTIVELY JUSTIFY THEIR INPUTS; MEMORY, LEARNING, AGENCY, OBSERVER, OBJECT, AND CROSS-LAYER CORE CLAIMS REMAIN TYPED, CARRIER-, ACCESS-, EQUIVALENCE-, HISTORY-, COMPOSITION-, CRITERION-, PROVENANCE-, AND SCOPE-RELATIVE; NULL, PLURAL, QUOTIENT, NONUNIQUE, RESTRICTED, AND UNDERDETERMINED RESULTS REMAIN ADMISSIBLE; NO UNIVERSAL ONTOLOGICAL CORE, PHYSICAL-INSTANTIATION BRIDGE, DEFINITE-EVENT SELECTOR, OR POSITIVE EMPIRICAL ETP CLAIM IS AUTHORIZED.** ## Claim ceiling CP3 certifies the integrity of the declared OIRP constitutional stack and closes the core program conditionally. It does not certify every historical artifact as present, every theorem as independently re-proved, one microscopic model realizing all layers, universal witness or composition closure, physical implementation, empirical confirmation, definite-event generation, or ultimate provenance. ## Next status **No next OIRP controlling gate is authorized. Future work proceeds only through the registered restricted successor branches or a targeted reopening triggered by qualifying evidence.** --- ## OIRP-S1: Recoverability Completeness Program ### Status OPEN; CONSTITUTIONAL GATE OIRP-S1.0 COMPLETE. ### Open questions - Nonfinite recoverability. - Device-independent witness completeness. - Universal witness completeness. - Complete physical-equivalence descent. ## OIRP-S1.0 ### Title Recoverability Completeness Constitution, Inherited-Result Freeze, Nonfinite/Device-Independent Target Typing, Finite-Horizon Countermodel, and S1 Checkpoint Architecture ### Disposition **OIRP-S1.0 CLOSED AS A CONSTITUTIONAL AND PREREGISTRATION GATE. OIRP-S1 REMAINS OPEN.** ### Authority The user-supplied `OIRP_PROGRAM_MASTER_LEDGER (50).md` is the exact content predecessor. This checksum-distinct successor is normalized to the single authoritative filename `OIRP_LEDGER.md`. Historical content is preserved unchanged and this entry is appended. ### Executed findings - The inherited results were frozen at their certified scopes: endpoint-only semantics remain refuted in the declared process setting; finite classical and qubit-tester results remain scoped; general adaptive-comb completeness, nonfinite completeness, universal witness completeness, and complete physical-equivalence descent remain open. - Four S1 targets were separately typed: nonfinite recovery, device-independent completeness, universal witness completeness, and physical-equivalence descent. - For every tested finite horizon H from 1 through 32, two deterministic binary sequential processes were constructed that agree through H and differ at H+1. - The countermodel blocks a fixed finite tester horizon from certifying unrestricted continuations. It does not block bounded-horizon, bounded-memory, compactness-controlled, or otherwise restricted completeness theorems. - External literature was separated into theorem-oriented recoverability, superchannel limitations, semi-device-independent certification, and tomography frameworks. No source was promoted into universal completeness or physical realization evidence. ### Claim status - S1 governance architecture: DERIVED WITH DECLARED SCOPE. - Fixed-horizon countermodel family: EXACT FINITE EXECUTION FOR H=1..32, supported by a general constructive schema. - Nonfinite recoverability completeness: NOT ESTABLISHED. - Device-independent witness completeness: NOT ESTABLISHED. - Universal witness completeness: NOT ESTABLISHED. - Complete physical-equivalence descent: NOT ESTABLISHED. ### Countermodels and rivals Retained rivals include Petz/sufficiency characterizations, hypothesis-testing witnesses, approximate recovery, quantum-comb/process-tensor tomography, device-independent and semi-device-independent certification, normal operator-algebraic recovery, operational pseudometrics, quotient-valued equivalence, and the null alternative of no unrestricted universal witness family. ### Manuscripts affected No binary manuscript edit at S1.0. The global synthesis, LRT authority, provenance protocol, and authority register remain review targets only after a scientific claim-status change or registered reopening trigger. ### Artifacts - `OIRP-S1.0_REPRODUCIBILITY_PACKAGE.zip` - Gate report, external and internal source reviews, executable countermodel, CSV output, graphic, falsifier register, manuscript-integration record, manifest, and hashes. ### Claim ceiling S1.0 establishes a constitutional/preregistration framework and one finite executable countermodel family only. It does not establish nonfinite, device-independent, universal, or physical-equivalence completeness; physical implementation; physical instantiation; definite-event generation; or ultimate provenance. ### Next controlling checkpoint **OIRP-S1.CP1: Nonfinite Recovery Domain/Normality Constitution, Fixed-Horizon and Tail-Completion No-Go Expansion, Infinite-Process Witness Classes, and Restricted-Completeness Candidate Theorems.** --- ## Permanent Research Rule: Deep External Truth Search At every ETP, BNP, OIRP, and successor-program stage, conduct a deep, extensive, adversarial external truth search alongside internal sources. Treat truth as hidden treasure. Use claim decomposition, terminology expansion, foundational and current peer-reviewed literature, recent preprints, citation-lineage excavation, rival frameworks, no-go theorems, negative results, assumption/scope extraction, evidence-class separation, conflict analysis, and a documented saturation audit. Do not claim exhaustive coverage beyond the declared finite search scope. No stage closes until this external-search standard is satisfied. ## OIRP-S1.0R ### Title Deep External Discovery, Citation-Lineage Excavation, Rival and No-Go Framework Audit, Assumption/Scope Crosswalk, Saturation Certification, and S1.0 Reclosure-or-Revision Decision ### Disposition **OIRP-S1.0R CLOSED WITH A DEEPER EXTERNAL DISCOVERY CORRECTION, A RESTRICTED POSITIVE MAP OF DOMAIN-SPECIFIC COMPLETENESS RESULTS, AND A STRONG NEGATIVE RESULT AGAINST UNQUALIFIED UNIVERSAL COMPLETENESS. OIRP-S1.0 IS RECLOSED ONLY AS A CONSTITUTIONAL/PREREGISTRATION GATE. OIRP-S1 REMAINS OPEN.** ### Correction The four-source OIRP-S1.0 literature review is preserved as preliminary historical evidence but superseded for stage-closure purposes. Its executable finite-horizon countermodel remains valid in scope. ### External discovery execution - 16 distinct query families executed. - 24 central works entered in the deduplicated source registry. - Domains covered: statistical comparison, Petz sufficiency, hypothesis testing, approximate recovery, correctable algebras, quantum combs, process tensors, adaptive discrimination, von Neumann algebras, continuous-variable tomography/designs, device-independent and semi-device-independent certification, supermap self-testing, GPTs, and local tomography. - Sources classified as theorem, counterexample/no-go, framework, review, preprint, simulation/method, and experiment. ### Principal findings - Recoverability completeness is plural and domain-indexed, not one unqualified property. - Strong nonfinite results exist for specified state families and von Neumann-algebra channels, but unrestricted infinite adaptive-process completeness is not established. - Restricted positive device-independent results now include unitary-gate certification in independent-source networks and supermap self-testing up to declared local equivalences. - Device-independent identification remains quotient-valued and depends on declared network/independence/target assumptions. - Adaptive strategies can separate channels that no finite nonadaptive strategy perfectly separates in an explicit published counterexample. - Standard continuous-variable state/unitary t-design existence fails for t>=2 under a published definition, while rigged and energy-constrained replacements support restricted tomography. - Local tomography is an additional composite principle, not a universal truth across rival probabilistic theories. - No reviewed source established one witness family complete across arbitrary carriers, continuations, dimensions, adaptive processes, device models, and complete physical equivalence. ### Claim status revisions - Device-independent recovery/certification landscape: revised from merely open to RESTRICTED POSITIVE RESULTS EXIST; UNIVERSAL COMPLETENESS NOT ESTABLISHED. - Nonfinite state/channel recovery: RESTRICTED POSITIVE THEOREMS EXIST. - Unrestricted infinite-process witness completeness: NOT ESTABLISHED. - Universal witness completeness: NOT ESTABLISHED. - Complete physical-equivalence descent: NOT ESTABLISHED. ### Saturation status Conceptual-framework saturation was reached within the declared 16-query protocol for the S1.0 constitutional decision. Bibliographic exhaustiveness is not claimed. Subscription access, complete forward-citation analytics, non-English databases, and unknown literature remain explicit limitations and reopening conditions. ### Manuscripts affected No binary edit at S1.0R. Scientific manuscript synchronization is deferred until CP1 produces a claim-status change requiring a checksum-distinct successor. ### Artifacts - `OIRP-S1.0R_REPRODUCIBILITY_PACKAGE.zip` - Search protocol and query ledger. - Source registry. - Assumption/scope crosswalk. - Rival framework matrix. - No-go and negative-results ledger. - Saturation audit. - Correction notice. - Expanded falsifier register. - Manuscript integration record. - Updated authoritative ledger, manifest, and hashes. ### Claim ceiling S1.0R establishes a corrected literature landscape and research constitution. It does not prove universal bibliographic exhaustion, universal witness completeness, unrestricted nonfinite process recoverability, complete physical-equivalence descent, physical instantiation, definite-event generation, or ultimate provenance. ### Next controlling checkpoint **OIRP-S1.CP1: Nonfinite Recovery Domain/Normality Constitution, Fixed-Horizon and Tail-Completion No-Go Expansion, Infinite-Process Witness Classes, Restricted-Completeness Candidate Theorems, and 2026 Device-Independent Supermap Interface Audit.** --- ### OIRP-S1.CP1 #### Title Nonfinite Recovery Domain/Normality Constitution, Fixed-Horizon and Tail-Completion No-Go Expansion, Infinite-Process Witness Classes, Restricted-Completeness Candidate Theorems, and 2026 Device-Independent Supermap Interface Audit #### Disposition **OIRP-S1.CP1 CLOSED WITH A NONFINITE DOMAIN/NORMALITY CONSTITUTION, EXPANDED FIXED-HORIZON AND TAIL-SCALING OBSTRUCTIONS, FOUR RESTRICTED COMPLETENESS ROUTES PLUS A DEVICE-INDEPENDENT QUOTIENT ROUTE, AND NO UNIVERSAL WITNESS-COMPLETENESS THEOREM. OIRP-S1 REMAINS OPEN.** #### Authority The user-supplied `OIRP_PROGRAM_MASTER_LEDGER (52).md` is the exact predecessor. This checksum-distinct successor is named `OIRP_LEDGER.md`; predecessor content is preserved and this checkpoint is appended. #### External truth search - 12 search families were audited, including 8 fresh CP1-specific families and 4 inherited/checked S1.0R families. - 22 central external sources were entered into the CP1 source registry. - Domains included Petz/sufficiency, general von Neumann-algebra recovery, strong and energy-constrained channel topologies, infinite-dimensional Kraus construction, classical projective extension, process tensors, quantum combs, adaptive discrimination, device-independent supermaps, finite tomography bounds, continuous variables, and local tomography. - Conceptual saturation is certified only within the declared CP1 query and source scope; universal bibliographic exhaustiveness is not claimed. #### Executed findings - Fixed-horizon continuation pairs were executed for every H from 1 through 128; each pair agrees through H and differs at H+1. - In the declared tail construction, classical total variation scales as epsilon while coherent pure-state trace distance scales as sqrt(epsilon). Tail weight alone does not select a universal linear distance bridge. - General von Neumann-algebra literature supplies restricted positive exact/approximate state-family recovery routes under declared hypotheses. - Strong-operator and energy-constrained topologies supply distinct nonfinite convergence controls; topology substitution is unauthorized without proof. - Classical projective consistency gives a restricted cylinder-law extension route under Kolmogorov-type hypotheses, but does not automatically establish quantum intervention-process completeness or path regularity. - Finite comb/process-tensor testers can be complete only relative to fixed slots, interfaces, intervention spans, readouts, and equivalence. - The 2026 device-independent supermap result yields quotient-valued certification under declared network structure, not unique microscopic implementation. #### Nonfinite Recovery Constitution v0.1 Every nonfinite recovery claim must declare the algebraic category, normal/predual state spaces, channel positivity and normality, bounded or unbounded domains, topology and convergence, energy/resource constraint, intervention history, complete carrier, witness/tester class, exact/approximate metric, composition rule, and physical-equivalence relation. #### Restricted completeness candidates 1. Classical cylinder completeness under projective consistency and standard measurable-space hypotheses. 2. Normal-algebra state-family recovery under the declared entropy/fidelity and channel hypotheses. 3. Energy-constrained operational convergence for channels relative to a declared Hamiltonian and energy bound. 4. Finite-slot complete tester reconstruction for a fixed comb/process class. 5. Device-independent quotient certification under a declared network and local-equivalence class. #### Decisions - No single candidate is universal across arbitrary nonfinite carriers, adaptive histories, continuations, devices, and composites. - Strong, weak, ultraweak, trace-norm, ordinary diamond, and energy-constrained diamond statuses are not interchangeable. - State-family recovery is not process recovery. - All-finite-history classical determination is not fixed-horizon determination. - Device-independent certification remains architecture- and equivalence-relative. - Complete physical-equivalence descent remains open. #### Manuscript effect No DOCX binary edit at CP1. The authoritative Markdown ledger is updated. Manuscript promotion requires a later scientific claim-status change and the full binary release-control workflow. #### Artifacts - `OIRP-S1.CP1_REPRODUCIBILITY_PACKAGE.zip` - Gate report, search protocol, query ledger, source registry, assumption/scope crosswalk, no-go ledger, restricted theorem candidates, executable countermodels, datasets, graphic, saturation audit, manuscript-integration record, manifest, and checksums. #### Claim ceiling CP1 establishes scoped constitutions, finite executions, and candidate theorem routes. It does not establish universal witness completeness, unrestricted nonfinite adaptive-process recovery, arbitrary-supermap device-independent completeness, complete physical-equivalence descent, physical instantiation, definite-event generation, or ultimate provenance. #### Next controlling checkpoint **OIRP-S1.CP2: Normal/Completely-Bounded Recovery Map Classes, Projective Infinite-Process Extension and Path-Regularity Separation, Energy-Constrained Approximate Composition, Device-Independent Robustness/Noise Audit, and Physical-Equivalence Descent Countermodels.** --- ### OIRP-S1.CP2 #### Title Normal/Completely-Bounded Recovery Map Classes, Projective Infinite-Process Extension and Path-Regularity Separation, Energy-Constrained Approximate Composition, Device-Independent Robustness/Noise Audit, and Physical-Equivalence Descent Countermodels #### Disposition **OIRP-S1.CP2 CLOSED WITH MAP-CLASS, PROJECTIVE-EXTENSION, PATH-REGULARITY, ENERGY-CONSTRAINED COMPOSITION, DEVICE-INDEPENDENT ROBUSTNESS, AND PHYSICAL-DESCENT SEPARATIONS; RESTRICTED POSITIVE ROUTES SURVIVE, BUT UNIVERSAL WITNESS COMPLETENESS AND COMPLETE PHYSICAL-EQUIVALENCE DESCENT REMAIN OPEN. OIRP-S1 REMAINS OPEN.** #### External truth search - 12 CP2 query families executed. - 19 central works registered across operator spaces, normal recovery, quantum sufficiency, projective extension, quantum stochastic processes, continuum combs, energy-constrained norms, approximate error correction, robust self-testing, exact supermap self-testing, and operational equivalence. - Conceptual saturation certified only within the declared CP2 scope; bibliographic exhaustiveness is not claimed. #### Findings - Normality, complete positivity, trace preservation, complete boundedness, decomposability, and physical realizability are separate map properties. - Complete boundedness alone is not a recovery-channel physicality certificate. - Consistent finite restrictions can support an infinite-process extension under declared classical or generalized intervention-process hypotheses, but path regularity requires separate conditions. - A 2026 operational continuum limit of quantum combs supplies a structured candidate rather than a structure-free infinite-slot promotion. - Ordinary and energy-constrained diamond metrics answer different nonfinite questions; energy observable, bound, ancilla policy, and composition depth are material. - In the exact independent-failure toy execution, aggregate depth-n failure is `1-(1-epsilon)^n` and is bounded by `n epsilon`; no universal quantum composition law is inferred. - Robust device-independent results exist for states and assemblages. The retrieved 2026 supermap source states exact identification up to local maps but does not state an explicit noisy robustness bound in its abstract; robust arbitrary-supermap completeness remains open. - An executed descent countermodel preserves all retained visible one-test probabilities while changing an admitted compatibility/joint-test value. - External operational-equivalence work likewise reports operationally equivalent measurement realizations with different compatibility and causal structures. #### Decisions - Process existence is not path-regularity certification. - One-step approximate recovery is not sequential or adaptive composition closure. - Device-independent exact quotient certification is not automatically robust certification. - Coarse operational equivalence does not imply complete physical equivalence. - Complete physical-equivalence descent remains open and requires a complete carrier, compatibility structure, intervention family, and witness theorem. #### Artifacts - `OIRP-S1.CP2_REPRODUCIBILITY_PACKAGE.zip` - CP2 report, search protocol, query ledger, source registry, assumption/scope crosswalk, conflict/negative-results ledger, candidate-results report, executable composition and descent countermodels, datasets, graphic, saturation audit, manuscript-integration record, manifest, and checksums. #### Manuscript effect No DOCX binary edit at CP2. Review global synthesis and LRT authorities after CP3 if S1 reaches a closure/continuation disposition or produces a publication-level claim-status change. #### Claim ceiling CP2 does not establish a universal recovery-map class, unrestricted infinite-process regularity, universal approximate-composition law, noisy device-independent completeness for arbitrary supermaps, complete physical-equivalence descent, physical instantiation, definite-event generation, or ultimate provenance. #### Next controlling checkpoint **OIRP-S1.CP3: Universal-Witness Candidate Exhaustion, Nonfinite/Adaptive/Composite Counterexample Integration, Approximation-and-Robustness Closure Audit, Complete Physical-Equivalence Descent Decision, and OIRP-S1 Closure-or-Continuation Decision.** ### OIRP-S2: Physical Composition, Boundary, and Complete-Carrier Closure #### Status OPEN; CONSTITUTIONAL GATE OIRP-S2.0 COMPLETE. #### OIRP-S2.0 ##### Title Physical Composition and Complete-Carrier Closure Constitution, Constituent/Composite and Interface/Boundary Neutralization, Higher-Order and Hidden-Carrier Countermodel Architecture, Deep External Rival/No-Go Search, Restricted Composition-Theorem Candidate Registry, and S2 Checkpoint Preregistration ##### Disposition **OIRP-S2.0 CLOSED AS A CONSTITUTIONAL AND PREREGISTRATION GATE WITH AN EXECUTED HIGHER-ORDER MARGINAL OBSTRUCTION, BOUNDARY-NONUNIQUENESS AUDIT, HIDDEN-ENVIRONMENT COUNTERMODEL, AND A PLURAL COMPOSITION-CANDIDATE REGISTRY. OIRP-S2 REMAINS OPEN.** ##### Authority The user-supplied `OIRP_PROGRAM_MASTER_LEDGER (54).md` is the exact binary predecessor. This checksum-distinct successor is named `OIRP_LEDGER.md`. S1 closure was completed in the immediately preceding checkpoint package; S2.0 inherits that disposition and does not alter it. ##### Constitutional inheritance S2 inherits K1-K9, S1's domain-indexed completeness limits, complete-carrier and boundary controls, constituent/composite separation, equivalence-before-identity, provenance preservation, and nonretroactivity. Physical actuality, events, and carriers remain admitted rather than derived. Ultimate provenance remains separate, unresolved, and reopenable. ##### Complete-Carrier Candidate v0.1 A complete-carrier claim is a typed relation among target, candidate constituents, decomposition, retained and discarded systems, environments, memories, branches, controls, references, resources, interfaces, compatibility structure, composition operation and domain, intervention family, histories and continuations, witness class, boundary policy, approximation criterion, operational equivalence, proposed physical equivalence, provenance, and scope. ##### External truth search - Four initial query families were executed with terminology expansion across GPTs, local tomography, operator-system tensor products, quantum causal models, process tensors, open systems, and algebraic subsystem approaches. - External results support a plural landscape: multiple mathematical tensor products exist; GPT composites require a composition rule; local tomography is an additional principle; symmetry restriction can generate failures of tomographic locality; quantum causal and process frameworks type composition through circuits, interventions, or multitime processes. - Decision-level conceptual saturation is certified only for the S2.0 constitution and preregistration alternatives. Bibliographic and theorem-level exhaustiveness is not claimed. ##### Executed findings - For n=3 through 8, even-parity and uniform binary distributions agreed on every audited (n-1)-body marginal while differing on the full n-body distribution by total-variation distance 0.5. - One fixed six-node weighted graph admitted 31 noncomplementary nontrivial boundary representatives with different internal/cut scores. The graph alone did not select one operational boundary. - Two hidden-environment candidates had the same visible state after reset but different future outputs. Visible-system reset did not establish complete-carrier reset. ##### Preliminary decisions - Constituent inventory does not determine a unique composite. - Local or lower-order completeness does not imply global completeness without a declared separation theorem. - A tensor-product symbol does not prove physical composition or select among admissible tensor products. - Boundary selection is target-, interaction-, intervention-, resource-, and witness-relative unless independently derived. - Omitted environments, controls, branches, references, resources, histories, continuations, or compatibility relations can refine the operational quotient. - Composition, constitution, factorization, causal connection, compatibility, and physical unity remain distinct. ##### Preregistered checkpoint architecture - **OIRP-S2.CP1:** Constituent-to-Composite Sufficiency, Hidden Higher-Order Moduli, Local-Tomography Failure, Compatibility-Hypergraph Audit, and Restricted Composition-Theorem Testing. - **OIRP-S2.CP2:** Boundary Selection, Environment Closure, Feedback/Memory Interfaces, Algebraic Overlap and Factorization Audit, and Complete-Carrier Countermodels. - **OIRP-S2.CP3:** Approximate Composite Certification, Stability Under Boundary/Carrier Refinement, Physical-Composition Candidate Theorems, and OIRP-S2 Closure-or-Continuation Decision. ##### Manuscript effect No DOCX binary edit at S2.0. The authoritative Markdown ledger is updated. Manuscript review is deferred until a later S2 checkpoint changes a publication-level claim or triggers a registered reopening condition. ##### Formal closure language **OIRP-S2.0 CLOSED AS A CONSTITUTIONAL/PREREGISTRATION GATE; PHYSICAL COMPOSITION RETAINED ONLY AS A TARGET-, CONSTITUENT-, DECOMPOSITION-, CARRIER-, ENVIRONMENT-, INTERFACE-, COMPATIBILITY-, OPERATION-, INTERVENTION-, HISTORY-, CONTINUATION-, BOUNDARY-, WITNESS-, RESOURCE-, EQUIVALENCE-, PROVENANCE-, AND SCOPE-RELATIVE CANDIDATE; LOCAL, LOWER-ORDER, CONSTITUENT, OR VISIBLE-SYSTEM COMPLETENESS DOES NOT CERTIFY THE COMPOSITE WITHOUT AN EXPLICIT SEPARATION THEOREM; NO UNIVERSAL COMPOSITION RULE, INTRINSIC BOUNDARY, COMPLETE PHYSICAL-CARRIER INVENTORY, SUBSTRATE, DEFINITE-EVENT SELECTOR, OR ULTIMATE-PROVENANCE CLAIM AUTHORIZED.** ##### Claim ceiling S2.0 establishes a research constitution, a finite parity-marginal execution for n=3 through 8, a finite boundary-cut audit, one hidden-environment countermodel, a rival framework registry, and preregistered checkpoints. It does not establish universal tomographic failure, universal boundary nonuniqueness, a physically complete carrier, one correct tensor product, physical realization, empirical confirmation, definite-event generation, substrate ontology, or ultimate provenance. ##### Next controlling checkpoint **OIRP-S2.CP1: Constituent-to-Composite Sufficiency, Hidden Higher-Order Moduli, Local-Tomography Failure, Compatibility-Hypergraph Audit, and Restricted Composition-Theorem Testing.** #### OIRP-S2.CP1 ##### Title Constituent-to-Composite Sufficiency, Hidden Higher-Order Moduli, Local-Tomography Failure, Compatibility-Hypergraph Audit, and Restricted Composition-Theorem Testing ##### Authority Immutable predecessor `OIRP_PROGRAM_MASTER_LEDGER (56).md`, 87389 bytes, SHA-256 `f057912930a2514613f1058f9e587b204050118d93ca528e78795d6d7bc34827`. Only this predecessor was used as internal scientific authority. ##### Disposition **OIRP-S2.CP1 CLOSED WITH RESTRICTED DECLARED-SPACE WITNESS-SEPARATION AND COMPLEX-QUANTUM STATE-TOMOGRAPHY RESULTS; EXACT PROPER-MARGINAL, REAL-QUANTUM DIMENSION, DEFICIENT-WITNESS, AND COMPATIBILITY-STRUCTURE OBSTRUCTIONS; MATHEMATICAL COMPOSITION PLURALITY; AND NO UNIVERSAL PHYSICAL CONSTITUENT-TO-COMPOSITE DESCENT. OIRP-S2 REMAINS OPEN.** ##### Findings The full CP1 gate report, proof files, source ledgers, model script, raw results, registers, and saturation audit are incorporated by reference and preserved in the release. Exact finite executions establish the parity obstruction through n=10, complex and real dimension results, Pauli-product rank, a deficient-witness hidden direction, and compatibility-cover nonuniqueness. The dual-span theorem is proved only in a fixed declared finite-dimensional state space. Proper marginals are distinguished from full product correlations; state tomography is distinguished from channel, instrument, process, comb, supermap, adaptive, and physical-composition completeness. ##### Complete-Carrier Candidate v0.2 Candidate v0.1 is retained and augmented with scalar field/base ring, positivity/order structure, normalization convention, tensor-product/composite functor, causal/slot order, ancilla policy, controller ownership, preparation independence, and admissible joint-context cover. These are candidate declaration families, not proof of physical completeness or uniqueness. ##### Physical bridge and provenance No independent physical-selection bridge was established. Actuality, events, and carriers remain admitted, not derived. Ultimate provenance remains unresolved and reopenable. ##### Claim ceiling No universal constituent-to-composite theorem, universal local tomography, unique physical tensor product, complete-carrier uniqueness, complete physical-equivalence descent, physical realization, definite-event selector, substrate, or ultimate-provenance result is established. ##### Manuscript decision No DOCX binary edit. ##### Next controlling checkpoint **OIRP-S2.CP2: Boundary Selection, Environment Closure, Feedback/Memory Interfaces, Algebraic Overlap and Factorization Audit, and Complete-Carrier Countermodels.** ##### OIRP-S2.CP1S ###### Title Targeted External-Saturation and Internal-Consistency Supplement, Symmetry-Induced Tomographic-Failure Audit, Tomographically Nonlocal Composite and Operational Hidden-Sector Review, Current Quantum-Composition Adversaries, Quantum-Causal-Model Integration, Empirical Rival-Discrimination Audit, Citation-Lineage Expansion, Deferred Binary-Manuscript Crosswalk, and CP1 Final Closure-or-Continuation Decision ###### Inherited status **OIRP-S2.CP1 MATHEMATICAL, COMPUTATIONAL, THEOREM-SCOPE, AND CORE FRAMEWORK FINDINGS VERIFIED; CURRENT PACKAGE PRESERVED AS A VALID MAJOR RESEARCH RELEASE; FINAL SCIENTIFIC CLOSURE WITHHELD PENDING A TARGETED EXTERNAL-SATURATION AND INTERNAL-CONSISTENCY SUPPLEMENT COVERING SYMMETRY-INDUCED TOMOGRAPHIC FAILURE, 2026 TOMOGRAPHICALLY NONLOCAL COMPOSITE RESULTS, CURRENT QUANTUM-COMPOSITION ADVERSARIES, QUANTUM CAUSAL MODELS, EMPIRICAL DISCRIMINATION, CITATION LINEAGE, AND DEFERRED BINARY-MANUSCRIPT CROSSWALK. OIRP-S2.CP2 REMAINS BLOCKED.** ###### Disposition **OIRP-S2.CP1S CLOSED: TARGETED EXTERNAL-SATURATION AND INTERNAL-CONSISTENCY SUPPLEMENT COMPLETE. THE ORIGINAL CP1 MAJOR RELEASE REMAINS VALID FOR ITS VERIFIED MATHEMATICAL, COMPUTATIONAL, THEOREM-SCOPE, AND CORE FRAMEWORK FINDINGS. SUPPLEMENTARY REVIEW CONFIRMS THAT TOMOGRAPHIC FAILURE DOES NOT IMPLY ONTOLOGICAL HOLISM; LOCALLY INACCESSIBLE COMPOSITE DIRECTIONS CAN HAVE TASK-SPECIFIC OPERATIONAL CONSEQUENCES; STATE TOMOGRAPHY DOES NOT ESTABLISH PROCESS OR CAUSAL COMPOSITION; NUCLEARITY AND SPLIT RESULTS ARE HYPOTHESIS-RELATIVE; AND EXISTING EMPIRICAL TESTS DO NOT SELECT A UNIQUE COMPOSITION RULE ACROSS THE FULL RIVAL CLASS. OIRP-S2.CP1 IS FINALLY CLOSED AT THIS RESTRICTED CLAIM CEILING. OIRP-S2.CP2 IS UNBLOCKED AS THE NEXT CONTROLLING CHECKPOINT.** ###### Scientific decisions The original CP1 mathematical, computational, theorem-scope, and core framework findings remain verified. Symmetry-induced foil theories establish that tomographic nonlocality does not entail ontological holism. Current TNL-entanglement work shows that locally inaccessible sectors can have task-specific operational consequences. The 2026 Born-kernel composition adversary concerns multistep probability genealogy and boundary restarts, not the CP1 state-space separation theorem. Quantum causal models require typed process, intervention, and causal structures beyond static constituent states. Operator-system nuclearity and AQFT split properties provide restricted coincidence or factorization only under declared hypotheses. Existing empirical tests discriminate restricted real formulations under network assumptions but do not select uniquely across the full CP1 rival class. ###### Internal consistency Enterprise-indexed text from the synchronization package, Final Synthesis, LRT, LRG, Ultimate Provenance Protocol, and QD manuscript was audited as nonbinary evidence. No accessible-text contradiction was found. Exact-binary manuscript consistency certification is deferred to CP3 unless triggered earlier by a publication-level claim change. ###### Claim ceiling No universal physical constituent-to-composite descent, universal local tomography, unique physical tensor product, intrinsic boundary, unique complete carrier, rival-complete empirical selector, physical realization, actuality selector, substrate, or provenance closure is authorized. ###### Next controlling checkpoint **OIRP-S2.CP2: Boundary Selection, Environment Closure, Feedback/Memory Interfaces, Algebraic Overlap and Factorization Audit, and Complete-Carrier Countermodels.** ##### OIRP-S2.CP2 ENTRY: FULL INTERNAL BINARY CROSSWALK ###### Status **OIRP-S2.CP2 OPEN. FULL INTERNAL BINARY CROSSWALK COMPLETE AS ENTRY CONDITION; SUBSTANTIVE BOUNDARY, ENVIRONMENT, FEEDBACK/MEMORY, ALGEBRAIC-OVERLAP, FACTORIZATION, AND COMPLETE-CARRIER TESTING REMAINS OPEN.** ###### Binary corpus Thirteen physically staged DOCX binaries were opened directly and exhaustively extracted at the paragraph and table-row level. The crosswalk preserves exact filenames, byte sizes, SHA-256 hashes, source locations, category counts, and representative exact passages. No enterprise snippet was substituted for binary inspection, and no binary was modified. ###### Entry findings The corpus consistently requires typed composition, boundary, complete carrier, interface, operations, witness/access, equivalence, provenance, and empirical status. LRG assigns operational-boundary work to a restricted successor program subject to LRT operational-completeness veto. Supporting causal and objectivity manuscripts do not establish intrinsic boundaries or universal complete carriers. Physical actuality remains admitted rather than derived. ###### Artifact lineage limitation The workspace copy of `OIRP-S2.CP1_COMPLETE_BACKUP.zip` is currently 57 bytes and is not a valid ZIP, while the CP1S archive and its recorded checksum preserve prior lineage. This anomaly is recorded and must not be silently ignored or represented as a valid local CP1 archive. ###### Artifacts - `OIRP-S2.CP2_INTERNAL_BINARY_CROSSWALK.md` - `OIRP-S2.CP2_INTERNAL_BINARY_CROSSWALK.csv` - `OIRP-S2.CP2_INTERNAL_BINARY_CROSSWALK.json` - `OIRP-S2.CP2_INTERNAL_BINARY_CROSSWALK_SUMMARY.json` ###### Next CP2 work Deep external adversarial research and formal/computational testing of boundary selection, environment closure, feedback and memory interfaces, algebraic overlap and factorization, and complete-carrier countermodels. ##### OIRP-S2.CP2 CLOSURE ###### Status **OIRP-S2.CP2 CLOSED WITH RESTRICTED NEGATIVE, PLURAL-BOUNDARY, AND COMPLETE-CARRIER-RELATIVE RESULTS. OIRP-S2.CP3 IS UNBLOCKED.** ###### Findings No audited boundary criterion selected a unique universal boundary. Restricted-access equality failed to imply complete-carrier equivalence in explicit environment, correlation, controller, and adaptive-continuation countermodels. Visible reset did not imply complete-carrier reset. Causal-break completeness was intervention-family and carrier relative. Commuting algebras with nontrivial overlap failed the scalar-intersection condition of independent represented tensor factors. Factorization notions remained typed and noninterchangeable. External literature independently supported initial-correlation sensitivity, process-memory dependence, hypothesis-relative AQFT splitting, gauge-edge data, and reference/access-relative subsystem structure. ###### Complete-Carrier Candidate v0.3 The candidate now includes boundary-selection rule, environment and controller ownership, overlap/center structure, reset domain, feedback direction, memory horizon, correlation provenance, gauge/superselection structure, factorization criterion, closure test, adversarial access expansion, and future-continuation horizon. It is not promoted to a universal ontology theorem. ###### Next checkpoint **OIRP-S2.CP3: Approximate Composite Certification, Stability Under Boundary/Carrier Refinement, Physical-Composition Candidate Theorems, and OIRP-S2 Closure-or-Continuation Decision.** ###### OIRP-S2.CP2 CORRECTION AND SUPPLEMENT REQUIREMENT ####### Status correction The earlier OIRP-S2.CP2 closure entry is preserved as historical evidence of the preliminary execution, but its final-closure and CP3-unblocking language is superseded by the following audit correction: **OIRP-S2.CP2 MATHEMATICAL, COMPUTATIONAL, PRELIMINARY COUNTERMODEL, INTERNAL-BINARY-CROSSWALK, AND CORE FRAMEWORK FINDINGS PRESERVED AS A VALID PRELIMINARY MAJOR RESEARCH RELEASE; FINAL SCIENTIFIC CLOSURE WITHDRAWN PENDING OIRP-S2.CP2S. OIRP-S2.CP3 REMAINS BLOCKED UNTIL CP2S ISSUES A RECLOSURE-OR-REVISION DECISION.** ####### Reason for correction The preliminary CP2 release established useful finite boundary, hidden-carrier, feedback, algebraic-overlap, and factorization results, but its external-saturation record, boundary-criterion breadth, quantitative closure analysis, feedback and instrument-specific memory coverage, and gauge/center/edge-mode executions were insufficient for final CP2 closure under the Permanent Research Rule: Deep External Truth Search. ###### OIRP-S2.CP2S ####### Title Boundary-Stability and Criterion-Conflict Expansion, Quantitative Complete-Carrier Closure, Feedback-Loop and Instrument-Specific Memory Audit, Gauge/Center/Edge-Mode Factorization Countermodels, External Citation-Lineage and Empirical-Discrimination Completion, Executable Reproducibility Certification, and CP2 Reclosure-or-Revision Decision ####### Authority and lineage The user-supplied `OIRP_PROGRAM_MASTER_LEDGER (60).md` is the exact content predecessor for this ledger update. The preliminary CP2 package is preserved and was not rerun or overwritten. CP2S is a checksum-distinct targeted supplement that extends the preliminary findings and corrects their closure status. ####### Disposition **OIRP-S2.CP2S CLOSED WITH RESTRICTED BOUNDARY-INSTABILITY, CRITERION-CONFLICT, ACCESS-MONOTONE COMPLETE-CARRIER DEFICIT, FEEDBACK-LOOP NONDESCENT, INSTRUMENT-RELATIVE MEMORY, AND PRESCRIPTION-RELATIVE GAUGE/ALGEBRAIC FACTORIZATION RESULTS. THE PRELIMINARY CP2 RELEASE IS PRESERVED. OIRP-S2.CP2 IS RECLOSED AT A NARROWED AND STRENGTHENED CLAIM CEILING. OIRP-S2.CP3 IS UNBLOCKED.** ####### Boundary-stability and criterion-conflict execution - Ten boundary criteria were evaluated over 31 complement-normalized nontrivial partitions and 11 baseline, scaling, perturbation, hidden-coupling, horizon, and task scenarios. - The criteria included minimum cut, ratio cut, normalized cut, conductance, modularity, interaction-to-cut ratio, dynamical leakage, predictive closure, causal shielding, and task-conditioned control closure. - Different criteria selected different preferred partitions, and several winner sequences changed under declared perturbation, hidden coupling, prediction horizon, or task changes. - The execution establishes finite-model criterion conflict and boundary instability. It does not establish that physical boundaries never exist. - Boundary selection remains data-, criterion-, intervention-, horizon-, task-, witness-, and carrier-relative unless an independent physical bridge selects otherwise. ####### Quantitative complete-carrier closure The supplement introduced the typed restricted closure deficit \[ \Delta_{\mathrm{closure}}^{\mathfrak I,\mathfrak W,d}(x,y) = \sup_{I\in\mathfrak I,\,w\in\mathfrak W} d\!\left(w\circ I(x),w\circ I(y)\right). \] - A positive value supplies a separating continuation or witness only relative to the declared intervention family, witness family, metric, carrier, horizon, ancilla policy, and resources. - A zero value establishes declared-family equality only. It does not establish complete physical equivalence unless witness and intervention completeness and metric faithfulness are independently proved. - If the declared intervention and witness families are enlarged by set inclusion, the supremal closure deficit cannot decrease. - Executed hidden-environment, hidden-controller, and combined candidates had zero deficit under passive access and positive deficit when an appropriate environment, controller, or adaptive separator was admitted. ####### Feedback-loop and instrument-specific memory findings - Open-loop plant trajectories can agree while measurement-feedback, coherent-controller-proxy, or delayed-feedback trajectories differ because the controller retains different internal states. - Therefore open-loop plant equivalence does not entail closed-loop composite equivalence. - Quantum Markov order is instrument relative. Finite order under one declared instrument family does not imply finite order under all instrument families. - Controller state, measurement records, plant-environment memory, shared memory, delay state, and outcome registers must be included or explicitly excluded in a complete-carrier claim. - Markovian enlargement by pseudomodes, reaction coordinates, chain mappings, or auxiliary carriers may be exact or sufficient within a declared model class without being minimal or physically unique. ####### Gauge, center, edge-mode, and algebraic factorization findings - A finite Z2 matching model compared naive kinematical factorization, a gauge-invariant electric-center-type prescription, extended-Hilbert edge bookkeeping, and fixed-sector conditioning. - Ambient carrier dimension, center structure, sector inventory, and entropy bookkeeping depended on the declared prescription while the global matching constraint remained fixed. - The result is a prescription-dependence countermodel, not a theorem that all prescriptions are physically inequivalent. - Scalar intersection, central non-scalar intersection, noncentral overlap, commuting factors, commuting nonfactor algebras, split inclusions, sector decompositions, type III local algebras, gauge-invariant algebras, and operational independence remain distinct. - A non-scalar intersection refutes only the simple independent-full-factor representation in that representation. It does not refute direct-sum, direct-integral, center-conditioned, quotient, split, gauge-invariant, or operational subsystem descriptions. ####### External research completion The supplemental external audit added instrument-specific quantum Markov order, assignment-map and compatibility-domain results, pseudomode embedding and nonuniqueness, coherent versus measurement-based feedback, algebraic versus operational independence, commuting-operator alternatives, AQFT and type-sensitive issues, gauge centers and edge modes, environment-dimension witnesses, quantum-system identification, decoherence and Quantum Darwinism limits, and plural philosophy-of-composition rivals. Decision-level saturation is certified only for the CP2 reclosure question within the declared finite search. Bibliographic exhaustiveness is not claimed. General Markov-blanket promotion to physical boundaries, general delayed-loop stability, full forward-citation analytics, inaccessible literature, non-English databases, unknown terminology, and post-cutoff work remain limitations and reopening triggers. ####### Corrected theorem-status register - **RT-CP2-1: Exact logical separation lemma.** Enlarged admissible access can separate candidates equal under restricted access. - **RT-CP2-2: Complete-break definition plus conditional screening criterion.** Screening is carrier-, instrument-, horizon-, and future-intervention-relative. - **RT-CP2-3: Finite represented-algebra obstruction proposition.** Non-scalar overlap refutes the simple independent-full-factor representation, not every sectorized or operational subsystem interpretation. - **RT-CP2S-1: Access-monotonicity lemma.** The closure deficit cannot decrease under nested enlargement of the declared intervention and witness families. - **RT-CP2S-2: Open-loop/closed-loop nondescend countermodel lemma.** Open-loop equality does not entail controller-inclusive closed-loop equality. - **RT-CP2S-3: Finite Z2 gauge-prescription countermodel.** Carrier dimension, sector inventory, center structure, and entropy bookkeeping can vary with the boundary prescription while the global matching constraint is preserved. ####### Empirical-discrimination decision Temporal-correlation witnesses can bound an effective environment dimension, and experimental or graybox system identification can discriminate among declared models or construct predictively useful candidates. These results do not establish one unique system-environment ontology, one unique physical boundary, or rival-complete physical-composition selection. ####### Claim ceiling No intrinsic universal boundary, universally complete environment, unique system-environment split, minimal universal Markovian embedding, instrument-independent finite memory order, unique controller boundary, universal tensor factorization, universal algebraic independence, unique gauge-center or edge-mode prescription, complete physical-equivalence descent, rival-complete empirical selector, physical realization, definite-event selector, substrate ontology, or ultimate provenance is established. ####### Artifact record The CP2S release preserves the research constitution, gate report, query ledger, external source ledger, domain coverage matrix, boundary-stability raw results and summary matrix, quantitative closure-deficit results, feedback-memory results, gauge-center-edge results, algebraic-factor status, theorem-status register, conflict analysis, saturation audit, executable model script, summary JSON, manifest, checksum list, release verification, and complete backup archive. The CP2S complete-backup ZIP was integrity-tested and recorded with SHA-256: `d43892da4b15ae3356c8766056697942faaddfd136e1fc1d3bd6f81dc8d686ff` ####### Final CP2 decision **OIRP-S2.CP2 RECLOSED THROUGH OIRP-S2.CP2S AT A NARROWED, STRENGTHENED, AND EXPLICITLY CARRIER-, CRITERION-, INTERVENTION-, INSTRUMENT-, HORIZON-, CONTROLLER-, ALGEBRA-, CENTER-, GAUGE-, PRESCRIPTION-, WITNESS-, EMPIRICAL-, AND SCOPE-RELATIVE CLAIM CEILING.** ####### Next controlling checkpoint **OIRP-S2.CP3: Approximate Composite Certification, Stability Under Boundary/Carrier Refinement, Physical-Composition Candidate Theorems, and OIRP-S2 Closure-or-Continuation Decision.** ###### OIRP-S2.CP2/CP2S CLARIFICATION AND CP3 INHERITANCE **OIRP-S2.CP2 AND OIRP-S2.CP2S REMAIN SCIENTIFICALLY CLOSED AT THEIR RESTRICTED CLAIM CEILING. CONSTRUCTED BOUNDARY PROXIES ARE NOT VALIDATED PHYSICAL ESTIMATORS; TIES AND IMPLEMENTATION-ORDER SELECTION ARE EXPLICIT; ACCESS MONOTONICITY REQUIRES FIXED CANDIDATES, CARRIER, METRIC, NORMALIZATION, AND COMPATIBLE DOMAINS; `COHERENT_PROXY` IS A BINARY STATEFUL-CONTROLLER COUNTERMODEL, NOT A QUANTUM COHERENT-FEEDBACK SIMULATION. CP3 MUST PERFORM TIE-AWARE BOUNDARY REFINEMENT, APPROXIMATE AND TRANSPORT-AWARE CLOSURE TESTING, EXPLICIT COMPOSITION-DESCENT-THROUGH-QUOTIENT AND QUOTIENT-REFINEMENT STABILITY AUDITS, AND FINAL AUTHORITY-LINEAGE REPAIR.** ###### OIRP-S2.CP3 ####### Title Approximate Composite Certification, Stability Under Boundary/Carrier Refinement, Physical-Composition Candidate Theorems, and OIRP-S2 Closure-or-Continuation Decision ####### Disposition **OIRP-S2.CP3 CLOSED WITH RESTRICTED TIE-AWARE BOUNDARY-STABILITY, FIXED-METRIC QUOTIENT-CONTRACTION, BINARY-CHANNEL APPROXIMATE-COMPOSITION, AND TRANSPORT-REQUIREMENT RESULTS. OIRP-S2 IS CONDITIONALLY CLOSED AS A RESTRICTED PHYSICAL-COMPOSITION AND COMPLETE-CARRIER CONSTITUTION. NO UNIVERSAL PHYSICAL COMPOSITION RULE, UNIQUE BOUNDARY, UNIQUE COMPLETE CARRIER, REPRESENTATION-INDEPENDENT QUOTIENT DESCENT, OR PHYSICAL-INSTANTIATION BRIDGE IS ESTABLISHED.** ####### Executed findings - Full argmin sets, tie multiplicity, perturbative Jaccard stability, and exact-set retention replaced first-enumerated winner reporting for five graph criteria. - Baseline minimum cut has two exact minimizers. - The binary symmetric channel family satisfied its exact depth-n error formula and declared telescoping bound in every executed row. - Total variation was nonexpansive in 3,675 finite tests over three deterministic coarse-grainings. - Cross-carrier or cross-metric comparisons require explicit embeddings, transports, metric comparison, and representative-identification controls. ####### Authority-lineage repair This successor uses the supplied OIRP_PROGRAM_MASTER_LEDGER (61).md as predecessor, includes the checksum-distinct successor in the CP3 archive, and preserves CP2S as historical evidence. ####### Claim ceiling No universal approximate-composition law, universal quotient descent, refinement-invariant boundary, unique physical composite, unique complete carrier, universal factorization, physical realization, rival-complete empirical selector, substrate, definite-event selector, or ultimate-provenance closure is established. ###### OIRP-S2.CP3S # OIRP-S2.CP3S Gate Report ## Disposition **OIRP-S2.CP3S CLOSED AS A CORRECTIVE CONTINUATION GATE, NOT AS FINAL OIRP-S2 CLOSURE. THE INITIAL CP3 FINITE-MODEL RESULTS ARE PRESERVED. CP3S ADDS RESTRICTED QUBIT PAULI-CHANNEL COMPOSITION, A FINITE ADAPTIVE MEMORY COUNTERMODEL, AN EXACT REPRESENTATIVE-INDEPENDENT QUOTIENT CONGRUENCE EXAMPLE, A NONCONGRUENCE COUNTERMODEL, DISCRETE NODE-SPLIT AND HIDDEN-NODE CARRIER REFINEMENTS, GAUGE-CENTER BOOKKEEPING REFINEMENT, AND A NUMERICAL REGULATOR-CONVERGENCE CONTROL. OIRP-S2 REMAINS OPEN BECAUSE GENERAL QUANTUM COMBS/SUPERCHANNELS, ENERGY-CONSTRAINED NONFINITE COMPOSITION, PHYSICAL GAUGE-CENTER GLUING, CONTINUUM PHYSICAL REFINEMENT, EMPIRICAL RIVAL-COMPLETE SELECTION, AND EXACT-BINARY MANUSCRIPT SYNCHRONIZATION ARE NOT CERTIFIED.** ## Exact results - All executed Pauli-channel rows satisfy the declared telescoping bound under the fixed finite model. - The adaptive two-step countermodel separates memoryless and hidden-memory processes for selected intervention sequences. - Parity quotient of Z4 is congruent with addition and has zero representative defects in the exhaustive finite audit. - A declared noncongruence quotient on Z3 produces representative-dependent composite outputs, proving descent is not automatic. - Node splitting and hidden-node insertion alter the carrier and are reported with projected argmin sets. - Gauge-center and continuum files are restricted bookkeeping and numerical-convergence controls only. ## Final decision The Permanent Research Rule is now materially better documented, but the exact-binary requirement and several physically central model classes remain incomplete. Closing S2 would overstate both execution and manuscript integration. The scientifically correct result is continuation through a narrower next checkpoint rather than another broad closure claim. ## Next controlling checkpoint **OIRP-S2.CP4: General Quantum-Comb/Superchannel Composition and Energy-Constrained Nonfinite Bounds, Physical Gauge-Center Gluing and Continuum Carrier Refinement, Exact-Binary Corpus Synchronization, Empirical Discriminator Preregistration, and OIRP-S2 Final Closure-or-Continuation Decision.** ###### OIRP-S2.CP3S-R: PAULI-CHANNEL COMPOSITION CORRECTION ####### Defect determination The original CP3S Pauli-channel execution initialized the composed channel once per error rate and then accumulated additional powers across the requested depth loop. Rows labeled 1, 2, 5, 10, and 20 therefore represented cumulative depths 1, 3, 8, 18, and 38, while each bound was computed from the displayed depth. The original CSV, summary, and transcript correctly recorded multiple failures. The original gate-report and ledger statement that all rows passed was false and is superseded. ####### Corrected result The checksum-distinct CP3S-R execution resets the channel to identity independently for every displayed depth. All 20 corrected rows satisfy the declared bound for the **normalized Choi-state trace distance for the declared qubit depolarizing Pauli-channel family**. The analytic expression is \[ D_{\mathrm{Choi}}(n)=\frac{3}{4}\left[1-\left(1-\frac{4\epsilon}{3}\right)^n\right]\le n\epsilon. \] No general diamond-norm, energy-constrained diamond-norm, arbitrary CPTP, comb, superchannel, adaptive, feedback, correlated, or nonfinite result is established. ####### Status **THE ORIGINAL CP3S PAULI-CHANNEL POSITIVE CLAIM IS WITHDRAWN AS ISSUED AND REPLACED ONLY BY THE CORRECTED RESTRICTED CP3S-R RESULT. THE ORIGINAL PACKAGE IS PRESERVED AS SUPERSEDED HISTORICAL EVIDENCE. OIRP-S2 REMAINS OPEN.** ###### OIRP-S2.CP3S-R EXACT-BINARY SYNCHRONIZATION CERTIFICATION ####### Binary authorities inspected - `ETP_Final_Synthesis_Draft-19_OIRP-Conditional-Closure_Successor-003.docx`, 101838 bytes, SHA-256 `4624b3e8e1ea639bddeb900d3cee2ad1ea449dd7c43523b02968c4d2c55bf0ea`. - `ETP_Ultimate_Provenance_and_Conditional_Reconstruction_Protocol_V07_OIRP-Closure_Successor-003.docx`, 68479 bytes, SHA-256 `e3ef1bb32b4476a8614336c03abbcb5e40f6dd7c9c730bc15202093092eae1c3`. ####### Checksum-distinct successors - `ETP_Final_Synthesis_Draft-20_OIRP-S2-CP3S-R_Synchronized_Successor-004.docx`, 103109 bytes, SHA-256 `cc390ec431aca920bb687b774edb7fbff1f78950fb76224ff22a68ecd56489c8`. - `ETP_Ultimate_Provenance_and_Conditional_Reconstruction_Protocol_V08_OIRP-S2-CP3S-R_Synchronized_Successor-004.docx`, 69804 bytes, SHA-256 `4eba3ca55546be50600fa108134613034c7b0e98676951011095f0b3dc6f3d45`. ####### Synchronization result Both binaries now contain a superseding OIRP-S2/CP3S-R synchronization addendum. The addendum preserves the conditional closure of the core OIRP constitutional program while explicitly retaining the OIRP-S2 successor branch as open, withdraws the erroneous original CP3S Pauli-channel positive claim as issued, records the corrected restricted normalized Choi-state trace-distance result, preserves the distinction from diamond norm, and retains the unresolved quantum-comb, superchannel, adaptive, feedback, correlated, nonfinite, physical gauge-center, continuum, empirical, and final authority obligations. ####### Render and structural verification The synthesis successor rendered to 62 pages and the provenance successor rendered to 27 pages. Both complete render cycles succeeded. The added final sections were visually inspected and no clipping, truncation, overlap, or malformed-heading defect was observed in the synchronized addenda. Automated accessibility audits were also executed; preexisting manuscript-wide accessibility notices are not represented as newly corrected by this synchronization pass. ####### Certification ceiling **EXACT-BINARY SYNCHRONIZATION IS CERTIFIED FOR THESE TWO SUPPLIED MANUSCRIPT FAMILIES ONLY. THIS DOES NOT CERTIFY THE REMAINDER OF THE ETP/OIRP BINARY CORPUS OR CLOSE OIRP-S2.** ####### OIRP-S2.CP4.0: AUTHORITY-LINEAGE REPAIR, CANONICAL LEDGER SUCCESSION, AND CP4.1 ENTRY CONTROL \####### Title Authority-Lineage Repair, Canonical Master-Ledger Succession, CP3S-R Archive Verification, Corrected Manuscript-Authority Promotion Record, Consolidated Release Control, and CP4.1 Entry Decision \####### Authority and exact predecessor The user-supplied `OIRP_PROGRAM_MASTER_LEDGER (66) - Copy.md` is preserved unchanged as the exact predecessor for this update. - Predecessor bytes: 115773 - Predecessor SHA-256: `4e6017409dd6bc9b8cb8681501908dc55e3cf39f308b29724d5030af90caa7e2` - Canonical successor filename: `OIRP_LEDGER.md` \####### CP3S-R archive verification The user-supplied `OIRP-S2.CP3S-R_COMPLETE_BACKUP.zip` was inspected as an exact local binary. - Archive bytes: 79692 - Independently computed SHA-256: `52618223d604ff770e2357057946dd25527e8821c8b9e14469daaf495db08b13` - ZIP decompression integrity: `PASS` - Internal member-checksum verification: `PASS` - Archive member count: 20 - Relationship between the archive's canonical ledger member and this supplied predecessor: `DIFFERENT` - Archive canonical-ledger member SHA-256: `0f9d8f389c247277b7e924a65f9bec36f53f203592dcb73a18c791a7457d1f91` The independently computed archive digest controls this exact supplied binary. Earlier conflicting reported outer digests remain historical records for other or earlier package instances and are not assigned to this binary. \####### Scientific-status preservation CP4.0 makes no new physical-composition theorem claim and does not alter the CP3S-R scientific ceiling. The corrected CP3S-R result remains restricted to normalized Choi-state trace distance for the declared qubit depolarizing Pauli-channel family. No general diamond-norm, arbitrary CPTP-channel, instrument, comb, superchannel, adaptive, feedback, correlated, non-Markovian, nonfinite, gauge-gluing, continuum-physical, empirical-selection, substrate, definite-event, or ultimate-provenance result is promoted. \####### Manuscript-authority promotion status The ledger records the already certified checksum-distinct promotions for the two supplied manuscript families only: Final Synthesis Draft-19 to Draft-20 and Ultimate Provenance Protocol V07 to V08. CP4.0 does not claim a new edit or exact-binary certification of the Manuscript Authority Register, LRT, LRG, HCOD, QD, causal-bounds, causal-nonseparability, or other publication-facing binaries because those exact binaries were not supplied for this execution. Corpus-wide authority promotion remains incomplete. \####### CP4.0 disposition **OIRP-S2.CP4.0 CLOSED AS A RESTRICTED AUTHORITY-LINEAGE AND RELEASE-CONTROL GATE. THE NUMBERED MASTER-LEDGER PREDECESSOR IS PRESERVED; THE CHECKSUM-DISTINCT SUCCESSOR IS ISSUED UNDER THE SOLE CANONICAL FILENAME `OIRP_LEDGER.md`; THE SUPPLIED CP3S-R ZIP PASSES LOCAL ZIP-INTEGRITY AND INTERNAL MEMBER-CHECKSUM VERIFICATION; THE EXACT OUTER ZIP HASH FOR THE SUPPLIED BINARY IS RECORDED; THE TWO-FAMILY MANUSCRIPT SYNCHRONIZATION REMAINS THE ONLY CERTIFIED BINARY PROMOTION; CORPUS-WIDE AUTHORITY-REGISTER AND MANUSCRIPT SYNCHRONIZATION REMAIN OPEN; OIRP-S2 REMAINS OPEN.** \####### CP4.1 entry decision **OIRP-S2.CP4.1 IS UNBLOCKED FOR SUBSTANTIVE RESEARCH DESIGN AND EXECUTION, SUBJECT TO THE PERMANENT DEEP EXTERNAL TRUTH-SEARCH REQUIREMENT AND THE EXISTING CLAIM-STRENGTH FIREWALL.** \####### Next controlling checkpoint **OIRP-S2.CP4.1: General Finite-Dimensional CPTP-Channel Composition, Genuine Diamond-Norm and Ancilla-Sensitive Certification, Noncommuting and Dimension-Changing Interface Audit, Sequential Error Accumulation, Restricted Composition Theorems and Countermodels, and CP4.2 Entry Decision.** \####### Claim ceiling CP4.0 certifies the authority and release-control facts stated above for the exact supplied ledger and ZIP binaries. It does not certify unsupplied manuscript binaries, complete corpus synchronization, a universal composition law, physical realization, empirical confirmation, or OIRP-S2 closure. ####### OIRP-S2.CP4.1 FIRST-PASS EXECUTION: FINITE-DIMENSIONAL DIAMOND-NORM AND CPTP COMPOSITION \####### Disposition **OIRP-S2.CP4.1 REMAINS OPEN. A GENUINE FINITE-DIMENSIONAL DIAMOND-NORM SDP, NONCOMMUTING CHANNEL TESTS, AN ANCILLA-ADVANTAGE COUNTERMODEL, AND A RESTRICTED CPTP TELESCOPING THEOREM HAVE BEEN EXECUTED OR PROVED. DIMENSION-CHANGING EXECUTION, PRIMAL/DUAL CROSS-CERTIFICATION, DEEP EXTERNAL SATURATION, AND FINAL CP4.1 CLOSURE ARE WITHHELD.** \####### Executed findings - Four depolarizing-versus-identity SDP values matched the analytic 2p reference with maximum absolute discrepancy 4.12e-8. - Fourteen channel-pair cases were solved, including amplitude-damping and noncommuting random-unitary mixtures; all solver statuses were optimal. - Twelve heterogeneous depth-four sequence pairs satisfied the declared diamond-norm telescoping bound; minimum recorded slack was 0.07536. - The d=2 Werner-Holevo pair returned diamond norm 1.999999985. A 20,000-sample unassisted pure-state search reached 1.333333333. The latter is a sampled lower bound, not an exact induced-norm certificate. \####### Restricted theorem For compatible finite-dimensional CPTP channel sequences, the diamond distance between the two complete compositions is no greater than the sum of the stepwise diamond distances. The proof uses hybrid expansion, triangle inequality, and CPTP contractivity/submultiplicativity. \####### External-search status A first-pass external source ledger covers foundational channel discrimination, SDP computation, ancilla necessity, operational meanings, selected channel distances, resource-theoretic composition, 2025 Pauli-learning lower bounds, and a 2026 ancilla-depth preprint. The Permanent Research Rule is not yet satisfied for CP4.1 closure; saturation remains open. \####### Claim ceiling No universal physical composition rule, dimension-changing numerical certification, primal/dual cross-certificate, arbitrary-dimensional exhaustive theorem, instrument/comb/superchannel result, adaptive/correlated/nonfinite composition result, or OIRP-S2 closure is established. \####### Next work inside CP4.1 Dimension-changing channels; independent primal/dual SDP agreement; analytic benchmark expansion; adversarial external citation-lineage and negative-result saturation; then CP4.1 closure-or-continuation decision. ####### OIRP-S2.CP4 RESEARCHER MODEL COUNCIL DISPOSITION AND CONTROLLING ARCHITECTURE ADOPTION \####### Authority The user-supplied `OIRP_PROGRAM_MASTER_LEDGER (2).md` is the exact predecessor for this update. - Predecessor bytes: 122253 - Predecessor SHA-256: `a869034df80fd564b17a0002ecd8eddfc3daba0ad23d69bd3baf1b72340c5113` - Canonical successor filename: `OIRP_LEDGER.md` \####### Immutable Model Council inputs - `Claude-results.docx`: 57757 bytes; SHA-256 `ced61093b4c6553aba02f752a1e72d99f9e9bdc5319e5fb8fbbc5bd45f950f79`. - `GPT-results.docx`: 39398 bytes; SHA-256 `78ebb94568eb2fa4480ad0258e7089c206994a88304a963f9f6e84009b72da09`. Both reports are preserved byte-for-byte unchanged. Their agreement is not proof. \####### Historical disagreement Claude rendered **CONDITIONAL PASS**; GPT rendered **AUTHORITY UNRESOLVED**. Both are preserved as historically appropriate to their declared indexed/extracted-text evidence and lack of independent binary access. The disagreement is not smoothed into consensus. \####### Later blocker resolution After those audits, exact-binary work staged and preserved the controlling ledger predecessor, issued the canonical checksum-distinct ledger successor, staged the exact 79,692-byte CP3S-R ZIP, independently computed SHA-256 `52618223d604ff770e2357057946dd25527e8821c8b9e14469daaf495db08b13`, and passed ZIP integrity and internal member checksums. These facts resolve the historical ledger and ZIP entry blockers only; they do not retroactively alter the model reports. \####### Open authority findings retained The Manuscript Authority Register successor and corpus-wide CP3S-R synchronization remain open. The two-family Final Synthesis/Ultimate Provenance synchronization remains the certified ceiling. CP4.R is opened as an explicit parallel authority track and must close before final OIRP-S2 closure. \####### Eleven-family CP4 architecture The controlling scientific architecture now consists of: (1) finite-dimensional CPTP composition; (2) diamond norm and ancilla-sensitive certification; (3) instruments and retained outcomes; (4) combs and superchannels; (5) adaptive and feedback composition; (6) correlated and non-Markovian processes; (7) energy-constrained nonfinite composition; (8) quotient descent and quotient-refinement commutation; (9) physical gauge-center gluing; (10) structured/continuum refinement and approximate algebraic factorization; and (11) empirical discriminator preregistration. CP4.R runs in parallel as authority/release control rather than as a twelfth scientific family. \####### CP4.1 external-search expansion and nonclosure rule The Model Council rival, no-go, instrument/process-memory, AQFT, operator-system, energy-constrained, empirical, and citation-lineage targets are adopted into a declared finite adversarial search protocol. CP4.1 shall not close until dimension-changing channel tests, independent SDP certification with primal/dual or equivalent cross-validation, analytic benchmark expansion, conflict analysis, and the deeper saturation audit are complete. \####### Disposition **MODEL COUNCIL DISPOSITION COMPLETE; BOTH REPORTS PRESERVED UNCHANGED; HISTORICAL DISAGREEMENT RECORDED; LEDGER AND ZIP ENTRY BLOCKERS MARKED RESOLVED BY LATER EXACT-BINARY EVIDENCE; AUTHORITY REGISTER AND CORPUS-WIDE SYNCHRONIZATION RETAINED OPEN; ELEVEN-FAMILY CP4 ARCHITECTURE ADOPTED; CP4.1 EXTERNAL PROTOCOL EXPANDED; CP4.1 REMAINS OPEN; CP4.R OPEN IN PARALLEL; OIRP-S2 REMAINS OPEN.** \####### Claim ceiling This disposition governs research architecture, evidence handling, and authority status. It does not independently validate every claim in either model report, close CP4.1, certify the Authority Register, complete corpus synchronization, establish physical composition, or close OIRP-S2. ####### OIRP-S2.CP4.1B: DIMENSION-CHANGING EXACT FAMILIES, INDEPENDENT-SDP ATTEMPT, AND ADVERSARIAL LINEAGE EXPANSION \####### Disposition **CP4.1 REMAINS OPEN. DIMENSION-CHANGING CHANNEL FAMILIES WERE EXECUTED WITH EXACT FAMILY-SPECIFIC DIAMOND-NORM VALUES AND CPTP/CHOI CHECKS. EXTERNAL RIVAL/NO-GO COVERAGE WAS EXPANDED. INDEPENDENT NUMERICAL PRIMAL-DUAL SDP CERTIFICATION FAILED AT THE ENVIRONMENT ENTRY POINT AND IS NOT CLAIMED.** \####### Dimension-changing execution Seven unequal input/output-dimension channel pairs were executed: replacer families for 2-to-3, 3-to-2, and 2-to-4 maps, and one 2-to-3 isometry pair. Replacer-channel diamond distance equals the trace distance of their fixed output states. The isometry pair has distance 2 because one input yields orthogonal outputs. All declared Kraus families passed trace-preservation and positive-Choi checks. \####### Independent SDP status A distinct primal/dual implementation was prepared. The container lacked CVXPY, and a fresh isolated dependency installation did not complete. No output from the failed attempt controls any scientific claim. Independent primal/dual numerical certification remains open. \####### External-search expansion The second pass added Watrous SDP lineage, Puzzuoli-Watrous ancilla-dimension counterexamples, Regula-Takagi-Gu operational interpretation, Winter energy-constrained boundary conditions, the Guérin-Krumm-Budroni-Brukner general-process composition no-go result, Taranto et al. instrument-relative Markov order, and the 2026 Singh KSW preprint. Saturation is not certified. \####### CP4.R status CP4.R remains open independently. No Authority Register binary was supplied or promoted in this pass. \####### Claim ceiling No arbitrary dimension-changing theorem, independent SDP numerical certificate, general process composition, instrument-independent memory closure, nonfinite composition, physical realization, corpus synchronization, or OIRP-S2 closure is established. ####### OIRP-S2.CP4.1C: RESTRICTED INDEPENDENT CROSS-CERTIFICATION, ENVIRONMENT AUDIT, AND SATURATION-STOPPING TEST \####### Disposition **CP4.1 REMAINS OPEN. NINE RESTRICTED ANALYTIC BENCHMARKS RECEIVED AN INDEPENDENT SCIPY VARIATIONAL CROSS-CHECK; THE EXTERNAL SATURATION AUDIT WAS EXECUTED AND FAILED ITS PREREGISTERED STOPPING RULE BECAUSE THE LATEST SEARCH CYCLE PRODUCED NEW DECISION-RELEVANT MATERIAL; A CLEAN GENERAL PRIMAL-DUAL SDP CERTIFICATE REMAINS UNAVAILABLE BECAUSE THE REQUIRED OPTIMIZATION STACK COULD NOT BE INSTALLED.** \####### Benchmark expansion The benchmark set covers four qubit unitary rotations, three Pauli depolarizing parameters, identity versus qubit dephasing, and one qubit-to-qutrit replacer pair. Exact family formulas were cross-checked with an independently coded SciPy variational optimizer where applicable. All channels passed trace-preservation and positive-Choi checks. \####### Environment and primal-dual decision The base environment contained NumPy and SciPy but lacked CVXPY, CVXOPT, Clarabel, SCS, PICOS, and QuTiP. A fixed-version CVXPY/Clarabel installation repeatedly timed out at the package host. No partial installation is used. General independent primal-dual SDP certification remains open. \####### Saturation decision Three documented search cycles have been performed, but the latest cycle added decision-relevant adaptive-discrimination, unitary-estimation, bipartite-tester, and contraction/expansion material. Therefore the requirement for three consecutive no-new-decision-relevant cycles is not met. External saturation is NOT CERTIFIED. \####### CP4.R CP4.R remains independently open. No Authority Register edit or corpus-wide promotion is claimed. \####### Claim ceiling No general primal-dual SDP certificate, arbitrary-channel analytic formula, literature saturation, higher-order process closure, nonfinite closure, physical composition selection, corpus synchronization, or OIRP-S2 closure is established. ####### OIRP-S2.CP4.1C-R: VARIATIONAL-BENCHMARK NARRATIVE CORRECTION \####### Defect The CP4.1C raw CSV correctly recorded a maximum discrepancy of 0.1333333333333332, but the CP4.1C narrative incorrectly stated that the independent variational optimizer agreed with all declared exact values. \####### Corrected result Four unitary cases and identity-versus-dephasing agreed with exact values to numerical precision; the dimension-changing replacer result was exact by theorem. Three depolarizing cases returned unassisted pure-state values 4p/3 versus ancilla-assisted diamond values 2p. The difference is an ancilla-sensitive separation for the declared family, not a failed diamond formula. \####### Status **THE CP4.1C UNIVERSAL BENCHMARK-AGREEMENT NARRATIVE IS WITHDRAWN. THE RAW CSV IS PRESERVED. CP4.1C-R INSTALLS THE CORRECTED MIXED RESULT: SIX AGREEMENT/EXACT CASES AND THREE DEPOLARIZING ANCILLA-SEPARATION CASES. GENERAL PRIMAL-DUAL SDP CERTIFICATION AND EXTERNAL SATURATION REMAIN OPEN. CP4.1 REMAINS OPEN.** ####### OIRP-S2.CP4.1D: INDEPENDENT CONIC ENVIRONMENT AUDIT AND SEARCH-CYCLE-4 SATURATION TEST \####### Disposition **CP4.1 REMAINS OPEN. A GENUINELY INDEPENDENT CONIC ENVIRONMENT COULD NOT BE ESTABLISHED FROM THE AVAILABLE LOCAL OR REMOTE PACKAGE PATHS, SO SEPARATE PRIMAL/DUAL SDP EXECUTION IS NOT CLAIMED. SEARCH CYCLE 4 PRODUCED NEW DECISION-RELEVANT 2026 RESULTS AND RESET THE SATURATION COUNTER TO ZERO. CP4.R REMAINS OPEN AND INDEPENDENT.** \####### Environment result NumPy 1.26.4 and SciPy 1.13.1 were available. CVXPY, CVXOPT, Clarabel, SCS, PICOS, and QuTiP were unavailable under direct import tests; no usable cached installer was found. A fixed-version CVXPY/Clarabel installation failed after repeated package-host timeouts. No partial environment or unexecuted value is accepted as certification. \####### Search-cycle-4 result The refined search added the September 2026 minimax tester/jammer channel-discrimination framework, an input/output-dimension channel-tomography preprint, an accepted energy-constrained adaptive bosonic-discrimination paper, resource-restricted bipartite tester work, and contraction/expansion composition descriptors. These are decision-relevant, so the three-consecutive-no-new-result stopping rule is not met. \####### Status Independent primal/dual SDP certification: OPEN. External saturation: NOT CERTIFIED. CP4.1: OPEN. CP4.R: OPEN. OIRP-S2: OPEN. \####### Claim ceiling No conic primal/dual objectives, residuals, duality gap, solver independence, exhaustive literature coverage, higher-order closure, nonfinite closure, authority-register promotion, corpus synchronization, or OIRP-S2 closure is claimed. ####### OIRP-S2.CP4.1E: LOCAL INDEPENDENT PRIMAL-DUAL CONIC CERTIFICATION AND THREE-SOLVER CROSS-VALIDATION \####### Authority and predecessor The user-supplied `OIRP_PROGRAM_MASTER_LEDGER (6).md` is preserved as the exact predecessor. - Predecessor bytes: 132809 - Predecessor SHA-256: `dfccc23c1a04223c02dc766d55eff6fd71730d13b739f773ac0f91ba11a32a68` - Canonical successor filename: `OIRP_LEDGER.md` \####### Local environment and archive verification The submitted Windows Conda execution used Python 3.12.14, NumPy 2.5.3, CVXPY 1.9.2, and the selected solvers SCS, Clarabel, and CVXOPT. The supplied result ZIP is 59643 bytes. Its independently recomputed SHA-256 is `c274e39be02ddc82e09c49c3181264fdedad8d245eadc4337656a362ba474d95`, which matches the separately supplied digest `c274e39be02ddc82e09c49c3181264fdedad8d245eadc4337656a362ba474d95`. ZIP decompression integrity is PASS; member count is 28. \####### Execution result Eight declared finite-dimensional channel-pair cases were crossed with three PSD-cone-capable solvers for 24 case-solver rows. Separate primal and dual programs returned `optimal` in all 24 rows. The maximum absolute numerical primal-dual difference was 4.264027952949334e-08; the maximum absolute analytic-reference error was 3.594934150363827e-08; the maximum trace-preservation residual was 3.14018491736755e-16. \####### Scientific findings The suite cross-certified three depolarizing cases, one qubit unitary case, identity versus complete dephasing, one amplitude-damping comparison, one qubit-to-qutrit replacer comparison, and one qubit-to-qutrit isometry comparison. The stabilized depolarizing values reproduce the declared analytic 2p references and preserve the CP4.1C-R distinction from unassisted pure-state values. The dimension-changing cases pass at their declared restricted benchmark scope. \####### Numerical interpretation The raw result field called `absolute_gap` is signed dual minus primal. This entry reports its absolute magnitude while preserving the signed CSV values. Small negative PSD eigenvalues and signed primal-over-dual crossings are interpreted only at solver-tolerance scale. SCS, Clarabel, and CVXOPT are separate backends invoked through one CVXPY modeling layer. \####### Disposition **OIRP-S2.CP4.1E CLOSED FOR THE DECLARED EIGHT-CASE FINITE-DIMENSIONAL BENCHMARK SUITE. THE INDEPENDENT CONIC-CERTIFICATION ENTRY BLOCKER IS RESOLVED AT THIS RESTRICTED CEILING. CP4.1 REMAINS OPEN PENDING EXTERNAL-SATURATION COMPLETION, FINAL SYNTHESIS, AND ANY ADDITIONAL ADVERSARIAL CHECKS REQUIRED BY THAT SYNTHESIS. CP4.R REMAINS OPEN INDEPENDENTLY. OIRP-S2 REMAINS OPEN.** \####### Claim ceiling No arbitrary-channel or arbitrary-dimensional numerical completeness, universal analytic formula, fully independent modeling-language replication, instrument/comb/superchannel closure, adaptive/feedback/correlated/non-Markovian closure, energy-constrained nonfinite closure, universal or unique physical composition, physical boundary selection, physical realization, Authority Register promotion, corpus synchronization, or OIRP-S2 closure is established. \####### Next controlling work inside CP4.1 Continue external search from the reset saturation counter and issue a CP4.1 final synthesis only after the preregistered saturation condition is satisfied or a documented continuation/revision decision is required. ####### OIRP-S2.CP4.1F: ADVERSARIAL SEARCH CYCLES 5-7, FINAL SYNTHESIS, AND CONTINUATION DECISION \####### Search-cycle result Search Cycles 5 and 6 produced no new decision-relevant CP4.1 framework, assumption, counterexample, no-go result, tester class, metric, or theorem route, raising the consecutive no-new-result counter to 2. Cycle 7 found the 2026 ICALP result “Strict Hierarchy for Quantum Channel Certification to Unitary,” which establishes access-model-dependent query-complexity hierarchies for incoherent, coherent, and source-code access. This is decision-relevant to the operational certification scope and resets the counter to 0. A further adaptive/superchannel boundary search returned 2026 adaptive discrimination work and an explicitly unresolved fully general versus nested superchannel-strategy problem. \####### Final synthesis CP4.1 preserves a compatible finite-dimensional CPTP telescoping theorem, genuine stabilized diamond-norm SDP evidence, ancilla-sensitive separations, exact restricted dimension-changing families, and a three-solver local primal-dual certification over eight declared channel pairs and 24 optimal case-solver rows. The external record independently requires strict boundaries against promotion to resource-independent certification, instruments, combs, superchannels, adaptive strategies, correlated processes, nonfinite settings, or unique physical composition. \####### Saturation decision **THE PREREGISTERED SATURATION STOPPING RULE IS NOT MET. THREE CONSECUTIVE NO-NEW-DECISION-RELEVANT CYCLES WERE NOT ACHIEVED. NO BIBLIOGRAPHIC-EXHAUSTIVENESS CLAIM IS AUTHORIZED.** \####### Gate decision **CP4.1 IS NOT SCIENTIFICALLY CLOSED. ITS MATHEMATICAL, COMPUTATIONAL, DIMENSION-CHANGING, ANCILLA-SENSITIVE, AND THREE-SOLVER PRIMAL-DUAL RESULTS ARE PRESERVED AS A VALID MAJOR RESEARCH RELEASE AT A RESTRICTED FINITE-DIMENSIONAL CHANNEL-LEVEL CEILING. CP4.1 CONTINUES BECAUSE THE EXTERNAL-SATURATION STOPPING RULE IS UNSATISFIED. CP4.2 ENTRY REMAINS BLOCKED. CP4.R REMAINS OPEN INDEPENDENTLY. OIRP-S2 REMAINS OPEN.** \####### Continuation rule Continue refined external cycles from a counter of zero. A future CP4.1 closure decision requires three consecutive cycles with no new decision-relevant result within the declared finite protocol, an updated conflict and limitations audit, and a final claim-language crosswalk. \####### Claim ceiling No arbitrary-channel completeness, resource-independent certification, higher-order composition closure, adaptive or correlated closure, energy-constrained nonfinite closure, physical composition selection, Authority Register promotion, corpus synchronization, CP4.2 entry, or OIRP-S2 closure is established. ####### OIRP-S2.CP4.1G: ADVERSARIAL SEARCH CYCLES 8-10 AND RENEWED CONFLICT/LIMITATIONS/CLAIM-LANGUAGE AUDIT \####### Search Cycle 8 A current-publication-status pass found that “Efficiently Computable Strategies and Limits for Bosonic Channel Discrimination” is now published in Physical Review A 114, 032441 on September 16, 2026. This changes the evidentiary status of the registered nonfinite/adaptive boundary source from accepted to published peer-reviewed work. It does not alter the finite-dimensional CP4.1 theorem but is decision relevant to source weighting. Counter: 0. \####### Search Cycle 9 A channel-learning/tomography pass found decision-relevant diamond-distance learning results with explicit input dimension, output dimension, Kraus rank, access/task assumptions, and reported adaptivity conclusions, together with a separate regime-dependent tomography framework distinguishing Choi-trace and diamond error. These add task- and regime-relative assumptions to the CP4.1 claim firewall. Counter: 0. \####### Search Cycle 10 An experimental and independent-implementation pass found a 2026 Scientific Reports multiple-shot unitary-channel discrimination experiment on IBM Brisbane reporting noisy-hardware disadvantages for deep or highly entangling circuits, and documentation for a PICOS/CVXOPT implementation of a simpler-Watrous completely bounded trace-norm SDP in toqito. The experiment separates theoretical channel distinguishability from hardware-realized strategy performance. The software supplies a candidate independent modeling path but was not executed against CP4.1E. Counter: 0. \####### Conflict and limitations audit No new source invalidates the restricted compatible-CPTP telescoping theorem or the CP4.1E benchmark calculations. The audit requires strict separation of one-shot metric values, learning/certification complexity, Choi-trace error, multishot noisy-hardware performance, resource-constrained/adaptive tasks, and energy-constrained nonfinite regimes. Three-solver CVXPY validation remains cross-solver rather than independent-modeling replication. \####### Authorized claim language Within the declared finite-dimensional channel-level scope, CP4.1 establishes a compatible-CPTP telescoping theorem, restricted exact and numerical diamond-norm benchmarks, ancilla-sensitive separations, dimension-changing examples, and three-solver primal-dual cross-validation. These results do not imply resource-independent certification complexity, Choi-proxy equivalence, multishot noisy-hardware optimality, adaptive or higher-order closure, nonfinite closure, or unique physical composition. \####### Gate decision **CP4.1 CONTINUES. SEARCH CYCLES 8, 9, AND 10 EACH PRODUCED NEW DECISION-RELEVANT EVIDENCE. THE SATURATION COUNTER REMAINS ZERO. THE RENEWED CONFLICT, LIMITATIONS, AND CLAIM-LANGUAGE AUDIT PRESERVES THE RESTRICTED CP4.1 RESULTS BUT DOES NOT PERMIT CLOSURE. CP4.2 ENTRY REMAINS BLOCKED. CP4.R AND OIRP-S2 REMAIN OPEN.** # OIRP-S2.CP4.1J Corrective Reconciliation Report ## Purpose This stage reconciles the counterfactual Model Council rerun with the exact CP4.1G canonical ledger and the directly inspected CP4.1 execution artifacts. It preserves useful findings, rejects unsupported overstatements, corrects the historical numerical and saturation record, and restarts the external-saturation sequence from zero. ## Authority baseline - Exact ledger predecessor: `OIRP_LEDGER.md` - Predecessor bytes: 141969 - Predecessor SHA-256: `30d7c185daf05d764e3e6306a166a03f6d2e13dc152d80257d439c9e90639688` - GPT counterfactual report: preserved unchanged as supplemental nonauthoritative evidence. - Claude counterfactual report: preserved unchanged as supplemental nonauthoritative evidence. - Local result ZIP: 59643 bytes; SHA-256 `c274e39be02ddc82e09c49c3181264fdedad8d245eadc4337656a362ba474d95`; 28 members. ## Reconciled findings ### 1. First-pass tensor-order correction The first-pass code combined column-major Kraus vectorization with `kron(I_out,rho)`. The later dimension-typed runner uses `kron(rho,I_out)` and an output partial trace over input-indexed output blocks. The first-pass amplitude-damping value near 0.262083 conflicts materially with the corrected later value near 0.4. The first-pass amplitude-damping result, other affected noncovariant pair values, and first-pass numerical sequence distances are superseded. The compatible-interface CPTP telescoping theorem is preserved because its proof does not depend on those numerical evaluations. Family-specific depolarizing checks and separately established ancilla and exact dimension-changing results remain preserved at their declared ceilings. ### 2. CP4.1E evidence class The later eight-case suite records 24 optimal primal-dual rows across SCS, Clarabel, and CVXOPT, with maximum absolute primal-dual difference `4.264027952949334e-08`, maximum available analytic-reference error `3.594934150363827e-08`, and maximum trace-preservation residual `3.14018491736755e-16`. These are tolerance-level floating-point numerical cross-validation results. The three backends share one CVXPY modeling layer. No rigorous interval or rational enclosure and no independent model assembly are established. The amplitude-damping case has no declared analytic reference. The raw field named `absolute_gap` stores signed dual-minus-primal values; the original CSV remains unchanged, and scientific summaries use the absolute magnitude. ### 3. Execution provenance The directly inspected 28-member results ZIP contains 24 logs, a CSV, summary JSON, environment JSON, and `SHA256SUMS.txt`. It does not contain the Python runner. A candidate runner is preserved separately in the local-runner package. Therefore, output-archive integrity is established at its declared inventory, but byte identity between the candidate runner and the exact locally executed script remains unresolved. The stronger claim that the 28-member ZIP itself contains the exact executed script is rejected. ### 4. External novelty reconciliation Cycle 8 is reclassified as a publication-status and source-weight update, not a substantive saturation reset. Cycle 9 validly resets on the Mele-Bittel diamond-distance channel-learning framework. Cycle 10 remains decision relevant through the new experimental hardware discriminator and independent software path. The September 2026 unified minimax-games paper contains potentially decision-relevant strengthening, but its full framework is not counted as wholly new because related minimax work was already registered. A version-to-registry claim crosswalk is required. Quantum-memory process tomography is registered as new decision-relevant access/resource separation: adaptive protocols retaining only classical transcripts are separated from protocols retaining coherent quantum memory. Verified-SDP literature is registered as evidence that approximate solver agreement and rigorous optimum enclosures are distinct evidence classes. ### 5. Supersession of interim counter state CP4.1H and CP4.1I are preserved as historical interim work. Their individual search and documentation findings remain usable where not superseded. The CP4.1I consecutive counter of two is superseded because later identified decision-relevant material breaks that sequence. ## Reconciled gate decision **OIRP-S2.CP4.1 CONTINUES WITH CORRECTION. THE CONSERVATIVE EXTERNAL-SATURATION COUNTER IS RESET TO ZERO. CP4.2 ENTRY REMAINS BLOCKED. CP4.R REMAINS OPEN AS A SEPARATE AUTHORITY TRACK. OIRP-S2 REMAINS OPEN.** ## Claim ceiling CP4.1 preserves a restricted compatible-interface finite-dimensional CPTP telescoping theorem, ancilla-sensitive distinctions, exact family-specific dimension-changing results, and an eight-case floating-point primal-dual numerical cross-validation suite. It does not establish rigorous verified numerics, arbitrary-channel numerical completeness, independent model assembly, instruments, combs, superchannels, adaptive or coherent-memory composition closure, correlated or non-Markovian closure, nonfinite composition, unique physical composition, physical realization, ontology, definite-event selection, or ultimate provenance. # OIRP-S2.CP4.1K: FIRST POST-RECONCILIATION ADVERSARIAL EXTERNAL-SEARCH CYCLE ## Authority and exact predecessor The exact predecessor is `OIRP_LEDGER.md`, 147206 bytes, SHA-256 `7f2023a35c63c446c3734dba7d0506e15e01e81ffd718da04caa3f46a962cdba`. CP4.1J remains the controlling corrective reconciliation baseline. ## Search execution The cycle rechecked coherent quantum-memory versus classical-transcript adaptive process tomography, rigorous verified-SDP bounds versus approximate solver output, the September 2026 unified minimax channel-discrimination framework and its earlier-preprint lineage, and foundational diamond-norm SDP results. The quantum-memory access separation, rigorous-versus-approximate numerical evidence distinction, and minimax strengthening target were already registered by CP4.1J. Foundational completely bounded norm SDP results were already registered earlier. No new version, theorem, counterexample, empirical discriminator, access class, numerical-certification requirement, or claim-boundary change was identified in this cycle. The minimax version-to-registry claim crosswalk remains open and the paper is not double counted as wholly new. ## Saturation decision **NO NEW DECISION-RELEVANT RESULT WAS IDENTIFIED. THE CONSECUTIVE NO-NEW-DECISION-RELEVANT COUNTER ADVANCES FROM ZERO TO ONE.** ## Gate decision **CP4.1 CONTINUES. CP4.2 ENTRY REMAINS BLOCKED. CP4.R AND OIRP-S2 REMAIN OPEN. TWO ADDITIONAL GENUINELY DISTINCT NO-NEW CYCLES ARE REQUIRED BEFORE THE STOPPING-RULE THRESHOLD CAN BE MET; THRESHOLD ATTAINMENT WOULD STILL REQUIRE A FINAL CONFLICT, LIMITATIONS, SOURCE-REGISTRY, AND CLAIM-LANGUAGE AUDIT.** # OIRP-S2.CP4.1L: SECOND POST-RECONCILIATION ADVERSARIAL EXTERNAL-SEARCH CYCLE ## Authority and exact predecessor The exact predecessor is `OIRP_LEDGER.md`, 148878 bytes, SHA-256 `535e5ccc7ebe27dde74355899102289fcf0fbf3004f2ac490731a68912edc37e`. ## Distinct search execution This cycle tested classical simulation of channels under local versus ancillary joint-effect access, resource-restricted channel discrimination, adaptive channel-resource transformations, and diamond-distance certification versus tomography. It did not repeat CP4.1K's primary search families. ## New decision-relevant result A March 11, 2026 Proceedings of the Royal Society A paper by Naik, Zartab, Gisin, and Banik proves that perfect qubit-channel simulation cannot be achieved with any finite classical communication even using general multi-round bidirectional protocols when joint measurements including entangled effects with an auxiliary system must be reproduced. The source contrasts this with noisy qubit channels such as depolarizing channels, which admit classical simulation with communication cost diverging as noise decreases. This adds a new complete-carrier and witness-enlargement no-go class: restricted agreement for single-qubit measurements does not certify complete ancillary joint-effect simulation. It does not invalidate CP4.1E's benchmark values or establish a universal separation for every noisy channel. ## Saturation decision **A GENUINELY NEW DECISION-RELEVANT RESULT WAS IDENTIFIED. THE CONSECUTIVE NO-NEW COUNTER RESETS FROM ONE TO ZERO.** ## Gate decision **CP4.1 CONTINUES. CP4.2 ENTRY REMAINS BLOCKED. CP4.R AND OIRP-S2 REMAIN OPEN. A NEW SATURATION SEQUENCE MUST BEGIN AFTER THIS RESET.** # OIRP-S2.CP4.1M: NEW SATURATION SEQUENCE CYCLE 1 ## Authority and predecessor constraint This append is bound to the expected CP4.1L predecessor `OIRP_LEDGER.md`, 150610 bytes, SHA-256 `52dfd623ec2610e2b9b358765ec444fe96cd6e3419c52812d217733dcc00a8e9`. It must not be applied if either identity value differs. ## Search execution and finding A metric-proxy and empirical-interface cycle tested average gate fidelity against worst-case diamond distance, fidelity-distribution information, fault-tolerance assessment without full tomography, average-case channel testing, and metric lineage. A March 8, 2026 preprint by Cho, Sohn, Hwang, and Bang states that coherent errors can inflate worst-case error even when average gate fidelity is high. It introduces fidelity deviation and states that, for coherent unitary gate errors on two or more qubits, fidelity together with fidelity deviation constrains spectral moments and enables an explicit tight worst-case error certificate. The abstract states that both observables can be estimated from the same randomized input-measurement experiment without full process tomography. This adds a new metric-proxy and empirical-interface distinction. It does not establish the same result for arbitrary CPTP channels or alter CP4.1E. ## Saturation and gate decision **A GENUINELY NEW DECISION-RELEVANT RESULT WAS IDENTIFIED. THE CONSECUTIVE NO-NEW COUNTER REMAINS/RESETS AT ZERO. CP4.1 CONTINUES. CP4.2 ENTRY REMAINS BLOCKED. CP4.R AND OIRP-S2 REMAIN OPEN.** # OIRP-S2.CP4.1N: NON-MARKOVIAN BENCHMARKING AND TEMPORAL-CARRIER CYCLE ## Authority and exact predecessor The CP4.1M intermediate successor was created by applying the hash-bound CP4.1M append to the exact CP4.1L predecessor of 150610 bytes and SHA-256 `52dfd623ec2610e2b9b358765ec444fe96cd6e3419c52812d217733dcc00a8e9`. ## Search finding A distinct search of randomized benchmarking under non-Markovian noise found a 2026 Physical Review Research spin-boson study stating that non-Markovian noise violates common randomized-benchmarking and gate-set-tomography assumptions. In the reported case study, the Markovian model has exponential decay while the non-Markovian model displays a much slower, almost polynomial decay. Supporting work reports dependence on gate implementation and noise-correlation time. This adds a new temporal-carrier and empirical-interface limitation: average benchmarking behavior cannot be promoted to a memoryless one-step channel model without declared bath, correlation, gate-implementation, and history assumptions. The source does not determine CP4.1E's one-shot benchmark values or establish a universal decay law. ## Saturation and gate decision **A NEW DECISION-RELEVANT RESULT WAS IDENTIFIED. THE CONSECUTIVE NO-NEW COUNTER REMAINS/RESETS AT ZERO. CP4.1 CONTINUES. CP4.2 ENTRY REMAINS BLOCKED. CP4.R AND OIRP-S2 REMAIN OPEN.** # OIRP-S2.CP4.1N-R: RECOVERY-FOLDER COMPLETENESS AND MISSING-RELEASE AUDIT ## Exact predecessor The exact predecessor is `OIRP_LEDGER.md`, 153503 bytes, SHA-256 `3742c0a99ccdd5da458d952a290fb195ac0c51ed709c0527462992567fea7a81`. ## Recovery evidence crosswalk Folder-scoped Recovery searches located the CP4 Model Council disposition release and checksum register; the first-pass CP4.1 reproducibility package; and dedicated packages or manifests for CP4.1B, CP4.1C-R, CP4.1D, CP4.1E, CP4.1F, and CP4.1G. The indexed scientific findings from those artifacts are already represented in this ledger. The CP4.1G manifest independently records a 141969-byte ledger with SHA-256 `30d7c185daf05d764e3e6306a166a03f6d2e13dc152d80257d439c9e90639688`, matching the predecessor later used by CP4.1J. The located Model Council evidence supports the unlettered disposition and architecture-adoption section already present in the ledger, but the Recovery search did not locate a direct authority record naming that release `CP4.1A`. It is therefore not retroactively relabeled. ## H/I missing-release control Direct folder-scoped searches for CP4.1H, CP4.1I, and Search Cycles 11 through 14 did not locate checksum-distinct H/I reproducibility packages, manifests, gate reports, or canonical ledger successors. A recovered Model Council re-audit states that a CP4.1H successor package was not located and appeared not yet to exist at the CP4.1G re-audit point. Therefore CP4.1H and CP4.1I remain historical interim designations referenced and superseded where applicable by CP4.1J, not independently certified releases in the located Recovery evidence. No unsupported H/I findings, hashes, counters, or artifact claims are imported. ## Exclusions Recovery-folder OIRP ledger variants concerning other stages, including OIRP-11 and OIRP-17, and BNP materials are not merged into this CP4.1 lineage because no retrieved evidence establishes them as missing CP4.1 predecessors or releases. ## Scientific and gate effect **NO MATHEMATICAL RESULT, NUMERICAL BENCHMARK, SATURATION COUNTER, OR GATE DECISION IS CHANGED. THE CURRENT COUNTER REMAINS ZERO. CP4.1 CONTINUES; CP4.2 ENTRY REMAINS BLOCKED; CP4.R AND OIRP-S2 REMAIN OPEN.** # OIRP-S2.CP4.1O: FINITE-MEMORY AND CONSTRAINED-SEPARABILITY DISCRIMINATION CYCLE ## Exact predecessor The exact predecessor is `OIRP_LEDGER.md`, 155739 bytes, SHA-256 `4e49f9b0b9b4364123a277ffce6d134b2e79a1eaf140962bd7920375a2bfe466`. ## Search finding A materially distinct search of finite-memory channel-discrimination architectures found Ohst, Zhang, Nguyen, Plávala, and Quintino, `Characterising memory in quantum channel discrimination via constrained separability problems`, Quantum 10, 1988 (2026). The publication characterizes discrimination performance when quantum memory is limited by auxiliary dimension, formulates the problem through separable states with affine constraints, discusses upper and lower bounds, extends the framework to adaptive and nonadaptive multicopy protocols, and identifies scenarios requiring classical or quantum memory together with hierarchical and non-hierarchical protocol relations. The source adds a finite-resource distinction beyond unrestricted ancilla sufficiency and beyond tomography's coherent-memory/classical-transcript separation. CP4.1 must separately track unrestricted stabilizing ancilla, bounded auxiliary dimension, classical outcome memory, coherent quantum memory, and intermediate-instrument adaptation. The adaptive protocol includes an intermediate quantum instrument and an outcome-conditioned final measurement, reinforcing the instrument boundary. The source does not alter CP4.1E values, prove universal quantum-memory superiority, select a physical memory implementation, or close instruments, combs, superchannels, correlated processes, or physical composition. ## Saturation and gate decision **A NEW DECISION-RELEVANT RESULT WAS IDENTIFIED. THE CONSECUTIVE NO-NEW COUNTER REMAINS/RESETS AT ZERO. CP4.1 CONTINUES. CP4.2 ENTRY REMAINS BLOCKED. CP4.R AND OIRP-S2 REMAIN OPEN.** # OIRP-S2.CP4.1P: COMPUTATIONAL-SUBSPACE LEAKAGE AND TRACE-LOSS CYCLE ## Exact predecessor The exact predecessor is `OIRP_LEDGER.md`, 157613 bytes, SHA-256 `04d94e325f207e4b652344fea8299fb26493c38dec1aed91cf0801568d4e812f`. ## Search findings A materially distinct search found Chen and Baldwin, `Randomized benchmarking with leakage errors`, Physical Review Research 7, 043065 (2025). The publication states that leakage moves population outside a defined computational subspace, may be overlooked by standard fidelity reporting, and can cause a large overestimation of randomized-benchmarking fidelity when substantial. It presents leakage-aware fidelity-estimation methods, two-qubit numerical demonstrations, and a reanalysis of previously shared Quantinuum data. The cycle also found Shi and Waks, `Error metric for non-trace-preserving quantum operations`, Physical Review A 108, 032609 (2023). The publication proposes a metric that upper-bounds trace distance between normalized imperfect and ideal outputs while remaining compatible with diamond distance, and applies it to lossy, nondeterministic, leakage, and postselected settings. These results add a carrier and normalization firewall. A full-space CPTP evolution may induce a trace-non-increasing map after projection onto a computational subspace. Full-carrier error, survival/success probability, leakage and seepage, and conditional normalized-output error are different coordinates. Any claim must declare the full carrier, computational projector, treatment of leaked states, conditioning rule, success probability, return dynamics, measurement model, and CPTP or trace-non-increasing status. The sources do not alter CP4.1E, establish universal randomized-benchmark bias, or close postselection, instruments, combs, superchannels, or physical composition. ## Saturation and gate decision **NEW DECISION-RELEVANT LEAKAGE AND TRACE-LOSS EVIDENCE WAS IDENTIFIED. THE CONSECUTIVE NO-NEW COUNTER REMAINS/RESETS AT ZERO. CP4.1 CONTINUES. CP4.2 ENTRY REMAINS BLOCKED. CP4.R AND OIRP-S2 REMAIN OPEN.** # OIRP-S2.CP4.1Q: BRANCH-RESOLVED QUANTUM-INSTRUMENT AND POST-MEASUREMENT-STATE CYCLE ## Exact predecessor The exact predecessor is `OIRP_LEDGER.md`, 159700 bytes, SHA-256 `3dacd9c8626ed3edb3b2a8c0fc9fac3aeaad091d30771c2b9f41d37819e27bae`. ## Search findings A materially distinct search found Eid and Quintino, `Post-measurement states are (very) useful for measurement discrimination`, arXiv:2602.12258v2. The preprint considers associated Lüders instruments rather than only POVM outcome operators. It states that access to post-measurement states makes discrimination of two qubit projective measurements equivalent to discrimination of two copies of associated states and presents a family with an arbitrarily large ratio of discrimination bias with versus without the post-measurement state. The cycle also found Edwards and Mishra, `Branch-Resolved Characterization of Feed-Forward Error in Dynamic Teleportation via Classical Choi Shadows`, arXiv:2604.28037v2. The preprint states that it reconstructs branch Choi operators using an entangled reference, validates selected estimators against full branch-Choi tomography, observes differing branch-quality orderings across two physical layouts and mitigation methods, and exposes branch-specific structure missed by outcome averages. These results add a branch-resolution firewall. CP4.1 must distinguish the classical outcome register, each trace-non-increasing branch map, branch probability, normalized conditional output, retained post-measurement state, nonselective channel, and outcome-conditioned downstream control. An outcome-only POVM or averaged channel is not a complete replacement for the instrument in branch-sensitive tasks. The enterprise corpus already states that an averaged channel can erase branch information while an instrument outcome register remains non-null and requires branchwise testing when outcomes are physical. The external results strengthen this boundary. The sources do not alter CP4.1E, prove arbitrary-instrument equivalence, establish universal mitigation rankings, or close physical outcome selection, instruments, combs, superchannels, or physical composition. ## Saturation and gate decision **NEW DECISION-RELEVANT BRANCH-RESOLVED AND POST-MEASUREMENT-STATE EVIDENCE WAS IDENTIFIED. THE CONSECUTIVE NO-NEW COUNTER REMAINS/RESETS AT ZERO. CP4.1 CONTINUES. CP4.2 ENTRY REMAINS BLOCKED. CP4.R AND OIRP-S2 REMAIN OPEN.** # OIRP-S2.CP4.1R: INSTRUMENT NORM, STRATEGY NORM, AND FEED-FORWARD COMPOSITION CYCLE ## Exact predecessor The exact predecessor is `OIRP_LEDGER.md`, 162143 bytes, SHA-256 `e8e1d9d8971a0d1767066a47088ee19813406924280dc4c1ac646a229756d1fc`. ## Search findings A materially distinct search for branch-resolved instrument metrics and feed-forward error propagation found Zonnios and Binder, `Distinguishing quantum processes with bounded coherent memory`, arXiv:2606.19511v1. The preprint identifies strategy-norm distance as the standard benchmark for multi-time process discrimination under arbitrary adaptive probing. It introduces machines for autonomous distinction that apply the same instrument at each step, retain the full classical outcome record, and carry bounded coherent memory. It states that the resulting memory hierarchy is monotone and complete at finite times, that sufficient memory plus an internal counter saturates strategy norm, and that recurrent repeated-interaction processes admit a description separating generation of new distinguishing information from propagation and decay of earlier information. Foundational Gutoski strategy-norm work supplies an operator norm for interactive-strategy distinguishability analogous to trace norm for states and diamond norm for channels, with measuring strategies represented by outcome-indexed positive operators summing to an ordinary strategy. Channel discrimination is a special case. These results supply the higher-order metric framework missing after CP4.1Q. Ordinary channel diamond distance is retained for one-round channel claims, while branch-resolved, multi-round, or outcome-conditioned processes require a measuring-strategy or comb carrier and an explicitly declared tester architecture. The bounded-memory hierarchy remains distinct from unrestricted strategy norm. No retrieved source explicitly established a universal slot-by-slot additive telescoping theorem for arbitrary branch-resolved instruments under unrestricted feed-forward. No such theorem is claimed. Any future theorem must declare causal order, process length, branch register, classical-record retention, coherent-memory dimension, admissible interleavings, and norm/tester class. The sources do not alter CP4.1E, establish physical outcome selection, close indefinite causal order, or authorize a universal instrument error sum. ## Saturation and gate decision **NEW DECISION-RELEVANT STRATEGY-NORM AND BOUNDED-MEMORY PROCESS EVIDENCE WAS IDENTIFIED. THE CONSECUTIVE NO-NEW COUNTER REMAINS/RESETS AT ZERO. CP4.1 CONTINUES. CP4.2 ENTRY REMAINS BLOCKED. CP4.R AND OIRP-S2 REMAIN OPEN.** # OIRP-S2.CP4.1RS: RESTRICTED MEASURING-STRATEGY TELESCOPING SUPPLEMENT ## Exact predecessor The exact predecessor is `OIRP_LEDGER.md`, 164802 bytes, SHA-256 `f4032904620943a457e4a7db06d3854b3eeb6efbb7d4c51752b2269b6a136691`. ## Restricted result For two deterministic causally ordered finite `N`-slot measuring strategies on the same typed quantum and explicit classical-register interfaces, define a hybrid chain replacing one local instrument at a time. If slot count and causal order are fixed; initial state, interleavings, classical routing, feed-forward, readout, and coarse-graining are identical; local instruments share types and outcome alphabets; classical records are retained or identically coarse-grained; coherent-memory dimension and initialization are identical and declared; no side channel bypasses the compared slot; common causal pre/post supermaps are contractive in the declared strategy norm; and each contextual replacement is bounded by `epsilon_k`, then triangle inequality and contractivity give `||P-Q||_strategy <= sum_k epsilon_k`. This is a direct restricted hybrid proposition, not a sourced universal theorem. Identical interleavings are a transparent sufficient condition; more general differing-interleaving bounds require explicit additional error terms. ## Countermodels Five finite countermodels were executed. Identical local instruments with different final interleavings give local sum zero and global total-variation distance one. Instruments with identical nonselective channels but opposite branch-output correlations give zero averaged-channel distance and unit branch-sensitive distance. Successful branches of weight `10^-6` have unnormalized L1 difference `2*10^-6` but orthogonal normalized outputs. Identical visible instruments with different hidden-memory initialization give zero local visible error and unit final distance. Changing coarse-graining invalidates transfer of a norm bound to a branch-sensitive tester. ## Claim boundary The supplement does not establish literal necessity of identical interleavings in every possible formalism, infinite-horizon uniformity, postselected stability without a positive success floor, indefinite causal order, universal physical composition, or physical outcome selection. ## Saturation and gate decision **A NEW DECISION-RELEVANT RESTRICTED THEOREM AND COUNTERMODEL SET WAS ESTABLISHED. THE COUNTER REMAINS/RESETS AT ZERO. CP4.1 CONTINUES; CP4.2 ENTRY REMAINS BLOCKED; CP4.R AND OIRP-S2 REMAIN OPEN.** # OIRP-S2.CP4.1RSF: EXTERNAL FALSIFICATION AND HYPOTHESIS REFINEMENT ## Exact predecessor The exact predecessor is `OIRP_LEDGER.md`, 167326 bytes, SHA-256 `5636dbc3261ed3f07aa662fcbee9be1f3fd13ab9e44afa2379fb8566953cf6a9`. ## Falsification result Gavorová's postselection-distance work explicitly reports counterexamples to ordinary convexity, contractivity, and subadditivity for normalized postselected computations, while retaining weaker variants. This falsifies any interpretation of CP4.1RS Condition 7 that treats nonlinear normalized postselection as an ordinary deterministic strategy-norm-contractive context merely because the underlying unnormalized branch map is CP and trace-nonincreasing. Condition 7 is amended: each common context must be a deterministic, type-preserving, causally admissible supermap on the same declared strategy class, with contractivity in the selected norm proved or explicitly assumed. Normalized postselection is excluded unless a separate postselected-distance result is invoked. Condition 5 is amended: explicit classical registers require a fixed common finite alphabet, orthogonal perfectly distinguishable flags, identical label semantics, and identical retention, dephasing, and coarse-graining. Different alphabets require a declared common refinement or padding. For positive unnormalized branch outputs `A,B` with success probabilities `a,b >= p_min > 0`, direct normalization algebra gives `||A/a-B/b||_1 <= 2||A-B||_1/p_min`. Strategy-level use requires the same uniform floor over every admitted input, ancillary extension, history, and hybrid context. This is a Lipschitz estimate, not coefficient-one contractivity. ## Countermodels Four countermodels were executed. Strictly positive but nonuniform success probabilities can approach zero while normalized outputs remain orthogonal. A fixed floor of 0.1 amplifies a trace-norm perturbation by a factor of ten in the example, so it does not restore unit contractivity. Nonorthogonal or identical flag states erase branch identity. A label permutation changes feed-forward behavior unless the controller is co-permuted. ## Revised authority CP4.1RS is refined, not withdrawn. Its deterministic finite hybrid bound survives under the amended causal-supermap and faithful-register conditions. Conditioned normalized outputs require a separate uniform-success-floor bound and explicit amplification factor. No universal postselected contractivity or subadditivity is claimed. ## Saturation and gate decision **A NEW DECISION-RELEVANT EXTERNAL FALSIFICATION AND HYPOTHESIS REFINEMENT WAS IDENTIFIED. THE COUNTER REMAINS/RESETS AT ZERO. CP4.1 CONTINUES; CP4.2 ENTRY REMAINS BLOCKED; CP4.R AND OIRP-S2 REMAIN OPEN.** # OIRP-S2.CP4.1RSFC: CONDITIONED TELESCOPING AND AMPLIFICATION LOCALIZATION SUPPLEMENT ## Exact predecessor The exact predecessor is `OIRP_LEDGER.md`, 170066 bytes, SHA-256 `e14a16e654013917cb425c17a171d3670e09727d3fba8c65e5cd3c7ea5fbcaee`. ## Sharpened normalization lemma For nonzero positive unnormalized outputs `A,B`, with `a=Tr A`, `b=Tr B`, and `delta=||A-B||_1`, direct algebra gives `||A/a-B/b||_1 <= (delta+|a-b|)/max(a,b) <= 2delta/max(a,b)`. This sharpens the earlier floor-only `2delta/p_min` bound whenever actual success or success drift is known. ## Conditioned telescoping For unnormalized final successful hybrid outputs `A_k`, define `delta_k=||A_k-A_{k-1}||_1` and `a_k=Tr A_k`. Normalizing only at the end gives `B_global=(sum_k delta_k+|a_0-a_N|)/max(a_0,a_N)`. Normalizing hybrid comparisons yields the separate additive bound `B_local=sum_k (delta_k+|a_k-a_{k-1}|)/max(a_k,a_{k-1})`. The certified conditioned distance is bounded by `min{2,B_global,B_local}`. Under one final conditioning, unnormalized errors add before a single amplification; slot factors do not intrinsically multiply. Products arise in a recursive analysis with genuinely repeated intermediate normalizations, where a perturbation before stage `k` can acquire products of later separately justified Lipschitz constants. Carrying the full unnormalized flagged process to the end avoids this proof-induced multiplication when physically and mathematically available. Branch-specific conditioned claims require branch-specific success floors. An aggregate success-set floor does not stabilize an arbitrarily rare named branch. For complete flagged conditioned states, drift of normalized classical branch weights must be budgeted even when conditional states within each branch agree. ## Evidence and limits External postselection literature supports failure of ordinary contractivity and subadditivity and existence of weaker replacements, but does not explicitly state these formulas. The formulas are internal finite-dimensional derivations with exact rational-grid checks. No universal optimality, infinite-horizon result, or physical outcome selection is claimed. ## Saturation and gate decision **A NEW DECISION-RELEVANT CONDITIONED COMPOSITION RESULT WAS ESTABLISHED. THE COUNTER REMAINS/RESETS AT ZERO. CP4.1 CONTINUES; CP4.2 ENTRY REMAINS BLOCKED; CP4.R AND OIRP-S2 REMAIN OPEN.** # OIRP-S2.CP4.1RSFC-F: EXTERNAL FALSIFICATION, COMPLETE-BOUNDED LIFTING, AND SHARPNESS AUDIT ## Exact predecessor The exact predecessor is `OIRP_LEDGER.md`, 172471 bytes, SHA-256 `d1504fd51d1b4d3ff0bce93ddadd90099fb939d47da9c82c377d66a4a96818d7`. ## Complete success-floor reduction For a CP trace-nonincreasing map `Phi`, define `E_Phi=Phi^*(I)`. For every reference and joint input, success probability equals `Tr[E_Phi rho_A]`. Hence the full ancillary-assisted success floor equals `lambda_min(E_Phi)`. A positive complete floor exists exactly when the success effect is positive definite. Ancillary entanglement can alter conditional distinguishability but cannot lower this floor below the minimum over all system states. ## Completely bounded lifting For CP trace-nonincreasing `Phi,Psi`, define `p_pair=inf_rho max(a_rho,b_rho)` over all ancillary inputs. Then `d_post_cb <= (||Phi-Psi||_diamond+||E_Phi-E_Psi||_infinity)/p_pair <= 2||Phi-Psi||_diamond/p_pair`. For a finite hybrid, `B_CB_global=(sum_k ||Phi_k-Phi_{k-1}||_diamond+||E_0-E_N||_infinity)/p_end`. A localized bound sums the corresponding diamond and success-effect drift terms divided by pairwise floors. The certified result is the minimum of 2, the global bound, and the local bound. ## Sharpness A family of orthogonal-output replacer success maps exactly saturates the success-drift refined normalization inequality. As one map's success weight becomes small relative to the other's, the floor-only coefficient 2 is asymptotically sharp. No universal smaller coefficient follows from floor information alone. ## Falsification outcome and limits The declared finite external search found no falsifier of the output normalization lemma. The lifting is restricted to finite-dimensional CP trace-nonincreasing maps and declared ancillary-assisted diamond optimization. It does not cover non-CP branches, nonlinear maps before conditioning, infinite-dimensional carriers, indefinite causal order, unrestricted postselected strategy norms, or physical outcome selection. ## Saturation and gate decision **A NEW DECISION-RELEVANT COMPLETE-BOUNDED LIFTING AND SHARPNESS RESULT WAS ESTABLISHED. THE COUNTER REMAINS/RESETS AT ZERO. CP4.1 CONTINUES; CP4.2 ENTRY REMAINS BLOCKED; CP4.R AND OIRP-S2 REMAIN OPEN.** ## OIRP-S2.CP4.1RSFC-FS: STRATEGY-NORM LIFTING, FLAGGED-DILATION RESCUE, AND TESTER-FLOOR AUDIT ### Exact predecessor The exact predecessor is `OIRP_PROGRAM_MASTER_LEDGER (16).md`, 174770 bytes, SHA-256 `805bfe00fe4a697caf3bca25b3667b7b7ba68af1e7f6c18e8a8927d52b7d4362`. This checksum-distinct successor is issued under the sole canonical filename `OIRP_LEDGER.md`. ### External findings Ji, Regula, and Wilde study postselected communication with decoding error conditioned on a conclusive outcome and assistance-relative capacity characterizations. Yokojima, Miyazaki, and Murao study probabilistic storage and retrieval of definite-causal unitary superchannels with query-dependent success. These are new decision-relevant postselection and higher-order frameworks but do not state the internal lifting theorem below. ### Restricted strategy lifting For positive subnormalized measuring strategies `P,Q` paired with a declared normalized tester family `C`, define successful outputs `A_T,B_T`, pair floor `p_C=inf_T max(Tr A_T,Tr B_T)`, success drift `gamma_C=sup_T|Tr A_T-Tr B_T|`, and operational norm `||P-Q||_{strat,C}=sup_T||A_T-B_T||_1`. If `p_C>0`, then `d_post,C(P,Q) <= (||P-Q||_{strat,C}+gamma_C)/p_C <= 2||P-Q||_{strat,C}/p_C`. This remains tester-family, convention, carrier, success-event, and causal-order relative. No universal spectral formula for a general strategy floor is claimed. For a finite hybrid, the normalize-once bound is `B_strat_global=[sum_k ||P_k-P_{k-1}||_{strat,C}+gamma_C(P_0,P_N)]/p_C(P_0,P_N)`. A localized edge bound sums `[||P_k-P_{k-1}||_{strat,C}+gamma_C(P_{k-1},P_k)]/p_C(P_{k-1},P_k)`. The conditioned distance is no greater than `min{2,B_strat_global,B_strat_local}` under the declared positive floors. ### Flagged-dilation rescue Repeated postselection reduces to one final conditioning only when complete orthogonal success/failure and branch histories are retained, later controls are reproduced, terminated branches use history-preserving absorbing flags, final acceptance is a fixed history predicate, tester history access is unchanged, and memory, initialization, causal order, slot count, and boundary types agree. ### Countermodels and branch decomposition Six finite models test tester-family enlargement, positive flagged rescue, history erasure, termination-time erasure, memory-class enlargement, and branch-weight-only discrepancy. For orthogonally flagged states, trace distance decomposes blockwise and is bounded by classical weight drift plus minimum-weighted conditional-state distances. Weight drift alone can yield distance two. ### Claim ceiling The derived lifting and rescue proposition are internal finite-dimensional operational deductions. No unrestricted postselected strategy norm, universal strategy-floor formula, indefinite causal order, physical outcome selection, physical realization, or ultimate-provenance claim is established. ### Saturation and gate decision **NEW DECISION-RELEVANT STRATEGY-LEVEL, FLAGGED-DILATION, POSTSELECTION, AND HIGHER-ORDER FRAMEWORK RESULTS WERE IDENTIFIED. THE CONSECUTIVE NO-NEW COUNTER REMAINS/RESETS AT ZERO. CP4.1 CONTINUES; CP4.2 ENTRY REMAINS BLOCKED; CP4.R AND OIRP-S2 REMAIN OPEN.** ## OIRP-S2.CP4.1RSFC-FS-DXX: DUAL TESTER-FLOOR AND COMB-REALIZATION AUDIT ### Exact predecessor The exact predecessor is `OIRP_LEDGER.md`, 177998 bytes, SHA-256 `2bcce14378ece9be14a21d33cb5dee4cd82866b7ff20caef637c60077fcdbde8`. ### External findings Gutoski's strategy-distance work supplies semidefinite and strong-duality lineage for strategy norms and measuring strategies. Mo et al. provide a parameterized-circuit comb framework for selected process-transformation and discrimination tasks. Li et al. provide a 2026 multiparameter-metrology framework spanning parallel, sequential, and indefinite-order strategy classes, with resource constraints and finite-memory sequential optimization. These latter two frameworks add decision-relevant implementation-family and resource-class boundaries. ### Restricted tester-floor formulation For a fixed finite strategy representation and a compact spectrahedral tester family `C`, `p_C(S_s)=min_{T in C}` is an SDP when the pairing is linear. The pair floor `p_C(P,Q)=min_{T in C} max(,)` has an epigraph SDP formulation. This is not a universal closed-form spectral theorem. Strong duality requires the concrete program's constraint qualification. ### Countermodels and firewall Four models preserve tester-family relativity under exact optimization, show that the pair floor can exceed the maximum of the individual floors, separate abstract comb feasibility from restricted-ansatz reachability, and preserve memory-class separation. An abstract SDP optimum, a bounded-memory optimum, a parameterized-circuit optimum, and noisy-hardware performance are not interchangeable. ### Saturation and gate decision **NEW DECISION-RELEVANT RESOURCE-CONSTRAINED STRATEGY AND COMB-REALIZATION EVIDENCE WAS IDENTIFIED. THE CONSECUTIVE NO-NEW COUNTER REMAINS/RESETS AT ZERO. CP4.1 CONTINUES; CP4.2 ENTRY REMAINS BLOCKED; CP4.R AND OIRP-S2 REMAIN OPEN.** ## OIRP-S2.CP4.1RSFC-FS-DX-F: CONCRETE TWO-ROUND PRIMAL-DUAL AND FACIAL-REDUCTION AUDIT ### Exact predecessor The exact predecessor is `OIRP_LEDGER.md`, 179931 bytes, SHA-256 `46f0c69168410b476464ca700c43e1d01003e57ee032d58a2dbde247b7a3b4f1`. ### Result A four-history two-round tester with nonnegative weights summing to one and success functions `a=x00+x01`, `b=x10+x11` yields the epigraph program `min z` subject to `z>=a,b`. Exact primal and dual values are `1/2`. The uniform primal witness has all weights `1/4`; the exact dual inequality is `max(a,b)>=(a+b)/2`. A strict witness uses `z=3/4` and has margins `1/4`. The boundary instance `x01=x10=x11=0` lacks ambient strict feasibility. The exposing vector `diag(0,1,1,1)` identifies the minimal face `diag(s,0,0,0)`; normalization fixes `s=1`, and the exact reduced optimum is `z=1`. Ambient Slater failure is separated from infeasibility and from a demonstrated duality gap. HiGHS numerical outputs agree but are noncontrolling. ### Claim ceiling and gate The model is diagonal, not a coherent noncommuting comb certificate. It establishes no general solver reliability, automatic strong duality, unrestricted-memory result, indefinite-order closure, or physical realization. **NEW DECISION-RELEVANT EVIDENCE WAS FOUND. COUNTER ZERO. CP4.1 REMAINS OPEN; CP4.2 REMAINS BLOCKED; CP4.R AND OIRP-S2 REMAIN OPEN.** ## OIRP-S2.CP4.1RSFC-FS-DX-Q: COHERENT TWO-TIME QUBIT TESTER AND NONCOMMUTING WITNESS AUDIT ### Exact predecessor The exact predecessor is `OIRP_LEDGER.md`, 181321 bytes, SHA-256 `36602d665a44fc63b94a124d5c108cf232051221d381fcdb0fa454cc66844ee6`. ### Result On the coherent two-qubit tester slice `T>=0`, `Tr T=1`, `Tr_A2 T=I_A1/2`, define `S0=(1/10)I+(2/5)|00><00|` and `S1=(1/10)I+(2/5)|++><++|`. The operators do not commute. Operator order gives both success probabilities at least `1/10`. The singlet tester satisfies the marginal constraint and is orthogonal to both added rank-one directions, so both success probabilities equal `1/10`. Exact primal and dual values therefore match at `1/10`. An explicit product tester satisfying the same marginal constraint gives a larger maximum success in the executed calculation. This separates the coherent witness from that declared product subclass but does not establish the optimum over all memoryless, separable, PPT, or bounded-memory testers. Ohst et al. provide published 2026 constrained-separability methods for memory-limited channel discrimination and identify classical/quantum memory distinctions. Ragini and Sazim report incompatible-tester advantage in a declared causal-comb discrimination game. These are new decision-relevant tester-resource results. ### Claim ceiling and gate This is a genuinely coherent noncommuting two-time tester slice, not a full arbitrary four-wire two-round comb. No general coherent-comb dual, global memory-class separation, indefinite-order closure, or physical realization is established. **NEW DECISION-RELEVANT EVIDENCE FOUND. COUNTER ZERO. CP4.1 OPEN; CP4.2 BLOCKED; CP4.R AND OIRP-S2 OPEN.** ## OIRP-S2.CP4.1RSFC-FS-DX-QF: FULL FOUR-WIRE COMB AND PPT MEMORY-CLASS AUDIT ### Exact predecessor The exact predecessor is `OIRP_LEDGER.md`, 183035 bytes, SHA-256 `5a0030e4ac249e6510dfd0bc4ebe35ae7db98415dc65ecf059c7446c38822dae`. ### Four-wire recursive construction On qubit wires ordered `Y2 tensor X2 tensor Y1 tensor X1`, choose `W=I_16/4`, `W1=I_4/2`. The exact declared Choi constraints `Tr_Y2 W=I_X2 tensor W1` and `Tr_Y1 W1=I_X1` hold. With `epsilon=1/5`, `c=1/20`, define `S0=epsilon W+c|0000><0000|`, `S1=epsilon W+c|++++><++++|`, and `Sfailure=W-S0-S1`. All are positive, sum to `W`, and `S0,S1` do not commute. The witness `T*=4|psi->` in the first control input, obtains the channel-dependent key `|0>` or `|+>`, and feeds that retained output with `|1>` into the second use. The final outputs are exactly orthogonal `|0>` and `|1>`, giving equal-prior success one. The published theorem proves that no finite nonadaptive strategy perfectly discriminates the pair. ### Hierarchy boundary This is a certified adaptivity separation. It is not yet a certified coherent-quantum-memory versus classical-memory, separable, or PPT gap. A faithful hierarchy requires realization-derived constrained-separability affine conditions. No PPT, symmetric-extension, or quantitative nonadaptive optimum was computed here. ### Gate **NEW DECISION-RELEVANT FAITHFUL FOUR-WIRE ADAPTIVE-TRANSLATION EVIDENCE WAS PRODUCED. COUNTER ZERO. CP4.1 OPEN; CP4.2 BLOCKED; CP4.R AND OIRP-S2 OPEN.** ## OIRP-S2.CP4.1RSFC-FS-DX-QF-MXH: RESTRICTED TESTER HIERARCHY AND CLASSICAL FEED-FORWARD AUDIT ### Exact predecessor The exact predecessor is `OIRP_LEDGER.md`, 187968 bytes, SHA-256 `2b423f012c61e9c5dfe1fe9cb6fd0d097a6de6d3bd8a86d54ed24fa7d02c0785`. ### Results The HHLW coherent two-use adaptive protocol retains success one. The published theorem remains the authority that no finite nonadaptive strategy perfectly distinguishes the pair. A restricted classical feed-forward family was executed: a real two-outcome projective measurement of the first output, classical outcome retention, maximum-likelihood preparation of `|0>` or `|+>` for the second use, and optimal final blockwise Helstrom readout. Its recorded optimized success is an achievable lower bound for that family and remains below one. This comparison does not exclude every classically adaptive architecture and does not prove coherent-memory necessity. General POVMs, instruments, randomized preparations, larger classical records, and full constrained-separable optimization remain open. No rigorous numerical two-use nonadaptive upper bound, PPT optimum, or constrained-symmetric-extension value is claimed. ### Gate **NEW DECISION-RELEVANT RESOURCE-CLASS CLARIFICATION AND A FINITE CLASSICAL BENCHMARK WERE PRODUCED. COUNTER ZERO. CP4.1 OPEN; CP4.2 BLOCKED; CP4.R AND OIRP-S2 OPEN.** ## OIRP-S2.CP4.1RSFC-FS-DX-QF-MXH-C/MC-RV-A3: THEOREM-LAYER CERTIFICATION, SOURCE-LINEAGE CORRECTION, AND CONTINUATION DECISION ### Authority and exact predecessor The exact predecessor is `OIRP_PROGRAM_MASTER_LEDGER (-029).md`, 189346 bytes, SHA-256 `5f70605a5fbb356d5c467fc1e4bae46c93f1127ceb1ada61309879b51e76b582`. The checksum-distinct successor is issued under the sole canonical filename `OIRP_LEDGER.md`. ### Immutable advisory inputs The supplied `GPT-results.docx` and `Claude-results.docx` are preserved as advisory research inputs. Model agreement is not treated as proof. Their theorem claims were independently reconciled against the published Ohst-Zhang-Nguyen-Plávala-Quintino source supplied and directly audited in the immediately preceding source-review gate. ### Source-lineage correction The reverse-realization source lineage is corrected. Appendix E of Ohst et al. proves Theorem 24 concerning relations among adaptive, parallel, and classically adaptive tester classes; it is not the single-copy tester realization theorem. The operational realization used here derives from Definition 23 together with Proposition 5 and Appendix A. Published equation references are normalized as follows: Definition 23 product-sum form, Eq. 64; block constrained-separability representation, Eq. 65; affine constraints, Eqs. 66-67; trace-and-replace map, Eq. 68. ### RT-CP4.1-MXH-C/MC-1: operational tester equality theorem For finite-dimensional two-use testers with an arbitrary finite classical outcome alphabet, define the strict classically adaptive class by requiring that no coherent first-round output, ancilla, accessible purification, instrument environment, or quantum side channel survives into the second use; the second tester is freshly realized as a function only of the orthogonal classical history label. Under this operational inaccessibility definition, the strict class is equal to the classically adaptive tester class of Ohst et al. Definition 23. Forward direction: every strict protocol defines a first-round single-copy tester `{R^j}` and, for each history `j`, a fresh second-round single-copy tester `{S^{i|j}}`, yielding `T^i = sum_j R^j tensor S^{i|j}`. Reverse direction: for every Definition 23 decomposition, Proposition 5 and Appendix A realize `{R^j}` and each `{S^{i|j}}` as state-preparation-plus-measurement testers. Retain only `j`, make the first realization environment inaccessible, and instantiate the selected second tester freshly. This establishes existence of a clean strict realization. The result is operational tester equality, not uniqueness of microscopic dilation or proof that every implementation of the same tester lacks coherent memory. ### RT-CP4.1-MXH-C/MC-2: HHLW strict-classical perfect-discrimination impossibility For the exact Harrow-Hassidim-Leung-Watrous channel pair and exactly two uses, no tester in the strict classically adaptive/Definition 23 class attains perfect discrimination. Proof structure: if the first-round classical outcome distributions have disjoint supports, the first-round history perfectly identifies the channel, contradicting the published one-use ancilla-assisted impossibility. If a history has positive probability under both hypotheses, then perfect overall discrimination requires the fixed second-round tester conditioned on that history to discriminate the two channels perfectly in one use with nonzero posterior weights, again contradicting the same one-use impossibility. Random classical seeds are absorbed into the history label; mixed inputs, arbitrary finite alphabets, first-round ancillas, and fresh second-round ancillas are covered by the single-copy tester realizations. ### RT-CP4.1-MXH-C/MC-3: scoped perfect-performance resource separation The published coherent HHLW protocol attains success one by coherently forwarding the nonorthogonal first-round key state. The strict classically adaptive/Definition 23 class cannot attain success one. Therefore coherent inter-round quantum transmission is necessary for perfect performance relative to these declared two-use classes, and one qubit of coherent inter-round carrier is sufficient in the published protocol. This is not a universal ontology, implementation-uniqueness, or all-memory-model claim. ### Nonattainment versus uniform gap The branch theorem certifies nonattainment of success one. It does not by itself certify that the supremum over the union of all finite classical alphabets is bounded by an explicit constant below one. The proposed 8257-history Caratheodory bound, fixed-dimensional compactness reduction, uniform strict-gap theorem, exact optimum, and explicit rational or interval upper certificate remain open and are not promoted here. ### Constrained hierarchy status The exact strict-classical optimum is a constrained-separability optimization. PPT with all inherited causal and affine constraints is an outer relaxation; constrained symmetric extensions can provide tighter outer levels. No HHLW-specific constrained-PPT value, first constrained-extension value, rigorous interval enclosure, or exact dual certificate is established by this gate. Ordinary floating-point solver agreement remains numerical evidence only. ### Graphic correction status The supplied graphic is preserved as advisory evidence. Any authority-facing successor must replace binary-history notation `h in {0,1}` with arbitrary finite `h in {1,...,L}`, or label the visual explicitly as a binary-history illustration. ### Gate disposition **THE THEOREM LAYER IS PROMOTED AT A RESTRICTED AUTHORITY-GRADE CEILING: OPERATIONAL TESTER EQUALITY WITH THE CLEAN DEFINITION 23 CLASS, IMPOSSIBILITY OF PERFECT TWO-USE STRICT-CLASSICAL HHLW DISCRIMINATION, AND A SCOPED COHERENT-VERSUS-STRICT-CLASSICAL PERFECT-PERFORMANCE SEPARATION. APPENDIX-E AND EQUATION-NUMBER LINEAGE ARE CORRECTED. FINITE-HISTORY REDUCTION, COMPACTNESS, A UNIFORM STRICT GAP, THE EXACT CLASSICAL OPTIMUM, HHLW-SPECIFIC PPT AND CONSTRAINED-EXTENSION VALUES, AND RIGOROUS NUMERICAL CERTIFICATES REMAIN OPEN. NEW DECISION-RELEVANT EVIDENCE WAS PRODUCED; SATURATION COUNTER REMAINS ZERO; CP4.1 REMAINS OPEN; CP4.2 ENTRY REMAINS BLOCKED; CP4.R AND OIRP-S2 REMAIN OPEN.** ### Next controlling gate **OIRP-S2.CP4.1RSFC-FS-DX-QF-MXH-C/MC-RV-A4: Finite-History Reduction Proof, Compactness-or-Alternative Uniform-Gap Theorem, HHLW-Specific Constrained-PPT Execution, First Symmetric-Extension Hierarchy Execution, Rigorous Certificate Generation, Corrected Graphic Release, and Final CP4.1 Closure Decision.** ## OIRP-S2.CP4.1RSFC-FS-DX-QF-MXH-C/MC-RV-A4A-HS: EXPANDED HHLW STRICT-CLASSICAL CONSTRUCTIVE OPTIMIZATION ### Authority and exact predecessor The exact predecessor is `OIRP_PROGRAM_MASTER_LEDGER00-0.md`, 195918 bytes, SHA-256 `62da66a43df7387b1ca3cecb0900436343a08af0625a8db858afd534973451c2`. The checksum-distinct successor is issued under the sole canonical filename `OIRP_LEDGER.md`. The complete predecessor content is preserved unchanged and this checkpoint is integrated at the end of that full authority record. ### Executed research A new HHLW strict-classical constructive optimization was executed over a declared feasible subclass consisting of a real pure four-dimensional first-round input, a binary real projective intermediate measurement, complete classicalization between channel uses, branch-conditioned real pure four-dimensional second-round inputs, and the optimal final Helstrom measurement in each classical branch. Four independently seeded differential-evolution runs were preserved in the reproducibility package. ### Quantitative result The best attained feasible success probability was \[ p_{\mathrm{found}}=0.9775241599658517. \] The difference between perfect success and this found feasible strategy is \[ 1-p_{\mathrm{found}}=0.0224758400341483. \] The authority relation is therefore \[ 0.9775241599658517\le p_{\mathrm{strict\text{-}classical}}^{(2)}\le 1. \] The lower inequality is executable constructive evidence. The upper endpoint is retained only as the trivial probability ceiling; the previously certified nonattainment theorem states that no individual clean Definition-23 strict-classical strategy attains one. ### Evidence classification The value `0.9775241599658517` is a reproducible feasible lower bound for the complete strict-classical optimum. It is not the global optimum, a constrained-PPT upper bound, a symmetric-extension upper bound, a compactness theorem, a uniform strict-gap certificate, or an exact analytic value. The observed strategy-specific shortfall from one is not promoted into a global gap. ### Relationship to the previous MXH benchmark This execution improves the earlier restricted classical benchmark `0.9633883476483089` by approximately `0.0141358123175428`. The improvement shows that the earlier restricted key-estimation-and-repreparation architecture did not exhaust high-performing strict-classical strategies. It does not establish sufficiency of binary history, real states, projective intermediate measurements, or the searched parameterization. ### Environmental and execution boundary The available execution environment contained NumPy and SciPy but did not contain CVXPY. An attempted package installation failed. Consequently, no HHLW-specific constrained-PPT or constrained symmetric-extension program was executed in this checkpoint, and no inferred or fabricated upper value is recorded. The completed SciPy optimization and its source, structured results, console transcript, environment record, report, and member checksums are preserved in `OIRP-S2.CP4.1_HHLW_STRICT_CLASSICAL_HEURISTIC_SIMULATION.zip`, whose SHA-256 is `d02f22528120c1b1b8fbe7ab36a22eefebcc793b1e91d94884bb8db8041170e7` and whose ZIP integrity passed. ### Open quantitative obligations The following remain open: complex-state constructive optimization; general POVMs and instruments; larger finite classical alphabets; first-round ancillary systems; finite-history reduction or counterexample; compactness or a direct uniform-gap theorem; HHLW-specific constrained-PPT execution; first constrained symmetric-extension execution; exact or interval-certified dual witness; exact strict-classical optimum; corrected arbitrary-finite-history graphic release; external saturation; and final CP4.1 closure. ### Gate disposition **A NEW EXECUTED CONSTRUCTIVE LOWER BOUND OF 0.9775241599658517 IS INTEGRATED INTO THE COMPLETE AUTHORITATIVE PROJECT LEDGER. THE A3 OPERATIONAL-EQUALITY, STRICT-CLASSICAL PERFECT-DISCRIMINATION NONATTAINMENT, AND SCOPED COHERENT-PERFORMANCE-SEPARATION THEOREMS REMAIN IN FORCE. NO GLOBAL QUANTITATIVE GAP, PPT VALUE, SYMMETRIC-EXTENSION VALUE, OR RIGOROUS UPPER CERTIFICATE IS CLAIMED. NEW DECISION-RELEVANT NUMERICAL EVIDENCE WAS PRODUCED; THE SATURATION COUNTER REMAINS ZERO; CP4.1 REMAINS OPEN; CP4.2 ENTRY REMAINS BLOCKED; CP4.R AND OIRP-S2 REMAIN OPEN.** ### Next controlling gate **OIRP-S2.CP4.1RSFC-FS-DX-QF-MXH-C/MC-RV-A4A-INNER+: Complex-State, General-POVM, Multi-History Strict-Classical Constructive Optimization; Solver-Ready Constrained-PPT Construction; First Constrained-Extension Preparation; Rigorous-Certificate Path; Corrected Graphic Release; and Quantitative Ledger Integration.** ## OIRP-S2.CP4.1RSFC-FS-DX-QF-MXH-C/MC-RV-A4A-INNER+: COMPLEX-STATE AND GENERAL BINARY-POVM ADVERSARIAL EXECUTION ### Exact predecessor The exact predecessor is `OIRP_LEDGER.md`, 200644 bytes, SHA-256 `c50c4a47b7a6e8edee6fef045f9dcae21f3b2ef596f63ce9b33d577ada98273b`. ### Executed search A new strict-classical constructive search admitted complex pure four-dimensional first-round inputs, an arbitrary binary qubit POVM, complete inter-round classicalization, branch-dependent complex pure four-dimensional second-round inputs, and branchwise optimal Helstrom final decisions. Two independently seeded differential-evolution runs were completed after a deeper three-seed execution exceeded the available execution window. ### Result and consistency decision The best value found was `0.9740087798747696`. It does not exceed the incumbent A4A-HS feasible lower bound `0.9775241599658517`. The authoritative constructive lower bound therefore remains \[ p_{\mathrm{strict\text{-}classical}}^{(2)}\ge 0.9775241599658517. \] The INNER+ result is a reproducible null improvement. It does not prove that complex phases, general binary POVMs, or the searched family cannot improve the global optimum. Search-budget and nonconvex-localization limitations are retained. ### Solver and hierarchy audit The environment contains SCS 3.3.1 and Clarabel 0.11.1 but not CVXPY, CVXOPT, PICOS, MOSEK, or Ncpol2SDPA. A faithful low-level encoding of the Definition-23 constrained-PPT and first constrained symmetric-extension cones was not completed. No upper value, primal-dual certificate, or uniform gap is inferred. ### Graphic audit A newly generated arbitrary-finite-L visual was rejected from authority promotion because it contained incorrect bibliographic text and typographic defects. A corrected specification is preserved; no defective graphic is promoted. ### Gate disposition **INNER+ EXECUTION COMPLETED WITH NO IMPROVEMENT OVER THE 0.9775241599658517 INCUMBENT. THE NULL RESULT IS PRESERVED. OUTER-HIERARCHY EXECUTION, RIGOROUS CERTIFICATION, MULTI-HISTORY GENERAL POVMS, ANCILLA-ASSISTED INNER SEARCH, AND CORRECTED GRAPHIC RELEASE REMAIN OPEN. SATURATION COUNTER REMAINS ZERO BECAUSE THE QUANTITATIVE PROGRAM IS NOT SATURATED. CP4.1 REMAINS OPEN; CP4.2 ENTRY REMAINS BLOCKED.** ### Next controlling gate **OIRP-S2.CP4.1RSFC-FS-DX-QF-MXH-C/MC-RV-A4A-CONIC: Low-Level SCS/Clarabel Definition-23 Constrained-PPT Encoding, Independent Tensor and Affine Audit, First Executable Outer Bound, and Rigorous-Certificate Assessment.** ## OIRP-S2.CP4.1RSFC-FS-DX-QF-MXH-C/MC-RV-A4A-CONIC: FIRST LOW-LEVEL HHLW PPT OUTER EXECUTION ### Exact predecessor The exact predecessor is `OIRP_LEDGER.md`, 203196 bytes, SHA-256 `2eba2866a0bbf28228e6df143e43f713fa5e43ccd14fa68d96069bca03f2c1b6`. ### Direct conic construction A low-level semidefinite conic model was constructed without CVXPY. Variables were real-symmetric decision tester elements `T0,T1` on the 64-dimensional two-use carrier, an intermediate normalization operator `G` on dimension 32, and an initial state `rho` on dimension 4. The model imposed positivity of `T0,T1,G,rho`; adaptive normalization `T0+T1=G tensor I_O2`; causal normalization `Tr_I2 G=rho tensor I_O1`; `Tr rho=1`; and positivity under partial transpose of both decision elements across `(I1,O1)|(I2,O2)`. Equal priors and exact HHLW Choi matrices reconstructed from the published Kraus operators were used. ### Numerical outer result Clarabel 0.11.1 returned status `Solved` after 12 iterations with objective \[ p_{\mathrm{PPT\ outer}}^{\mathrm{num}}=0.9824161994469314. \] Independent objective reconstruction gave `0.9824161994469309`. Tester-normalization and causal-normalization Frobenius residuals were `5.607321004088621e-11` and `2.339203521271121e-11`; `Tr rho=1.0`. Minimum eigenvalues of the primal and partial-transpose matrices were approximately `-4.41e-10`, at numerical tolerance scale. ### Numerical bracket Combining the incumbent feasible strict-classical strategy with this executed outer relaxation gives the numerical bracket \[ 0.9775241599658517\le p_{\mathrm{strict\text{-}classical}}^{(2)}\lesssim0.9824161994469314. \] The upper relation is numerical and relaxation-relative, not an exact inequality promoted by a rigorous certificate. The bracket width is approximately `0.0048920394810797`. The numerical outer value lies below one by approximately `0.0175838005530686`. ### Outer-model interpretation Every clean Definition-23 tester is adaptive and separable across the round cut, hence is feasible for the adaptive-PPT outer model. The execution therefore supplies numerical upper evidence for the strict class. The model does not yet impose the full Ohst block-factor affine constrained-separability hierarchy and may be loose. ### Rigorous-certificate assessment The solver status, small residuals, and matching reconstructed objective are strong numerical evidence, but the small negative eigenvalues and absence of outward-rounded interval verification prevent promotion of the decimal as a rigorous upper certificate. A certified uniform strict gap below one therefore remains open. ### Gate disposition **THE FIRST EXECUTABLE HHLW PPT OUTER RELAXATION WAS CONSTRUCTED AND SOLVED. IT YIELDS NUMERICAL OUTER EVIDENCE 0.9824161994469314 AND, WITH THE INCUMBENT FEASIBLE LOWER BOUND, A NUMERICAL BRACKET OF [0.9775241599658517, 0.9824161994469314]. THIS IS A MAJOR QUANTITATIVE ADVANCE BUT NOT YET AN EXACT OR INTERVAL-CERTIFIED GAP. THE FULL OHST CONSTRAINED AFFINE HIERARCHY, INDEPENDENT SECOND-SOLVER REPLICATION, INTERVAL/RATIONAL CERTIFICATION, AND FIRST SYMMETRIC EXTENSION REMAIN OPEN. SATURATION COUNTER REMAINS ZERO; CP4.1 REMAINS OPEN; CP4.2 ENTRY REMAINS BLOCKED.** ### Next controlling gate **OIRP-S2.CP4.1RSFC-FS-DX-QF-MXH-C/MC-RV-A4A-CONIC-CERT: Independent SCS Replication, Cone-Vectorization and Tensor Audit, Outward-Rounded or Rational Dual Certification, Full Ohst Affine-Constrained PPT Comparison, and Uniform Strict-Gap Promotion Decision.** ## OIRP-S2.CP4.1RSFC-FS-DX-QF-MXH-C/MC-RV-A4A-CONIC-CERT: INDEPENDENT SCS REPLICATION AND CERTIFICATE AUDIT ### Exact predecessor The exact predecessor is `OIRP_LEDGER.md`, 206714 bytes, SHA-256 `95511c6868b6fe600ec469b9f6b353d5b6240f9d7fb029c5c07ca81a6943abfb`. ### Independent SCS replication The low-level adaptive-PPT model was independently executed with SCS 3.3.1 after explicitly converting Clarabel upper-triangle PSD vectorization to SCS lower-triangle vectorization and ordering zero-cone rows before PSD-cone rows. SCS returned status `solved`, primal outer objective `0.9824159310381946`, sign-adjusted dual objective `0.9824159113415769`, reported gap `1.9696617674052724e-08`, primal residual `1.2328959832839765e-07`, and dual residual `2.564655164725043e-07`. The SCS primal differs from the Clarabel value `0.9824161994469314` by approximately `2.684087368e-7`. ### Solver-convention falsification control An initial SCS conversion placed PSD cone rows before equality rows despite SCS requiring zero-cone rows first. That incorrect encoding returned a near-zero objective and was rejected. The corrected cone-block ordering reproduced the Clarabel result. This implementation failure and correction are preserved to prevent silent convention reuse. ### Independent source, tensor, and partial-transpose audit The HHLW Kraus completeness identities, Choi trace-preservation identities, declared `I1,O1,I2,O2` order, round cut `(I1,O1)|(I2,O2)`, partial-transpose involution, and trace preservation under partial transpose were independently checked. ### Rigorous-certificate decision Two solvers and independent objective checks strongly support the numerical outer value near `0.982416`, but neither solver provides outward-rounded cone feasibility. No exact rational correction or interval-verified dual certificate was completed. The approximate negative/positive cone and residual tolerances prevent promotion of the decimal into a rigorous upper theorem. The uniform strict-gap claim remains numerical evidence, not authority-grade certification. ### Full Ohst comparison The executed model is the coarser adaptive-tester PPT outer relaxation across the round cut. It is not the complete Ohst block-factor affine constrained-separability hierarchy. Equality with or improvement from the full affine-constrained PPT level is not claimed. ### Gate disposition **INDEPENDENT SCS REPLICATION AND CONE/TENSOR AUDITS SUCCEEDED. CLARABEL AND SCS CONVERGE NEAR 0.982416, SUPPORTING A NUMERICAL BRACKET [0.9775241599658517, 0.9824161994469314]. OUTWARD-ROUNDED OR RATIONAL DUAL CERTIFICATION AND FULL OHST AFFINE-CONSTRAINED PPT EXECUTION REMAIN OPEN. UNIFORM STRICT-GAP PROMOTION IS WITHHELD. SATURATION COUNTER REMAINS ZERO; CP4.1 REMAINS OPEN; CP4.2 ENTRY REMAINS BLOCKED.** ### Next controlling gate **OIRP-S2.CP4.1RSFC-FS-DX-QF-MXH-C/MC-RV-A4A-DUAL: Exact/Interval Dual-Feasibility Repair, Certified Upper Bound Below One, Full Ohst Affine-Constrained PPT Encoding, and First Constrained Symmetric-Extension Construction.** ## OIRP-S2.CP4.1RSFC-FS-DX-QF-MXH-C/MC-RV-A4A-DUAL: DUAL-FEASIBILITY REPAIR AND CERTIFICATE-CEILING DECISION ### Exact predecessor The exact predecessor is `OIRP_LEDGER.md`, 209781 bytes, SHA-256 `46ffe9ee7c7b77ee95d2494b55279029f474682438bad2fba4b4d6b4ca11cf6e`. ### Repaired dual construction The independently replicated SCS dual was transformed back to the original conic row and PSD-vectorization convention. Each of the six dual PSD blocks was shifted by `1e-6 I`. Computed minimum eigenvalues of the repaired blocks were between `9.999999731575428e-7` and `1.0000000000942567e-6`. The repaired stationarity residual was `2.3445197333793715e-5` in Euclidean norm. ### A posteriori upper-bound formula For any feasible primal tuple `x=(T0,T1,G,rho)`, positivity and normalization imply `||(T0,T1,G,rho)||_F <= sqrt(21)`: the decision-element traces sum to four, `Tr G=2`, and `Tr rho=1`. For any cone-feasible dual vector `y`, weak duality with stationarity defect gives \[ p_{\mathrm{outer}}\le b^T y+\|A^Ty+c\|_2\sqrt{21}. \] Using the repaired numerical dual gives center `b^T y=0.9824159113415767` and candidate upper value `0.982523350733042`, below one by `0.017476649266958022`. ### Certification classification The norm bound and defect formula are analytic. The repaired matrices and arithmetic were evaluated with ordinary floating-point eigensolvers and were not enclosed using directed interval rounding. Accordingly, `0.982523350733042` is classified as a robust validated-numerical candidate upper bound, not an exact, rational, or interval-certified authority-grade inequality. Uniform strict-gap promotion remains withheld. ### Full Ohst affine-constrained PPT and first extension The current conic program remains the coarser adaptive-tester PPT outer relaxation. The full Ohst history-block factor-affine constrained-PPT model and the first constrained symmetric extension were not completed in this gate. No value or comparison from those models is claimed. ### Gate disposition **A DUAL-FEASIBILITY REPAIR AND EXPLICIT A POSTERIORI DEFECT FORMULA WERE COMPLETED. THEY YIELD A ROBUST VALIDATED-NUMERICAL CANDIDATE UPPER VALUE 0.982523350733042. EXACT OR OUTWARD-ROUNDED CERTIFICATION, FULL OHST AFFINE-CONSTRAINED PPT, AND THE FIRST CONSTRAINED SYMMETRIC EXTENSION REMAIN OPEN. THE NUMERICAL BRACKET AND TWO-SOLVER REPLICATION REMAIN STRONG, BUT UNIFORM STRICT-GAP PROMOTION IS WITHHELD. SATURATION COUNTER REMAINS ZERO; CP4.1 REMAINS OPEN; CP4.2 ENTRY REMAINS BLOCKED.** ### Next controlling gate **OIRP-S2.CP4.1RSFC-FS-DX-QF-MXH-C/MC-RV-A4A-INTERVAL: Directed-Rounding Dual Certification, Exact Algebraic Norm Bounds, Full Ohst Factor-Affine PPT Model, and First Constrained Symmetric-Extension Execution.** ## OIRP-S2.CP4.1RSFC-FS-DX-QF-MXH-C/MC-RV-A4A-INTERVAL: EXACT-GRAM DUAL REPAIR AND CONDITIONAL DIRECTED-ENCLOSURE AUDIT ### Exact predecessor The exact predecessor is `OIRP_LEDGER.md`, 212540 bytes, SHA-256 `6e5e24a19d0a9faf1c1f1fc0745959a5317261a10d4494f45628d794b265724c`. ### Exact-PSD-by-construction dual blocks The six SCS dual PSD blocks were shifted before Cholesky factorization, and each Cholesky factor was rounded to 13 decimal places. The certificate blocks were then redefined exactly as decimal-rational Gram matrices `L L^T`. These blocks are positive semidefinite by construction rather than by floating eigenvalue assertion. ### Conservative defect enclosure The exact-Gram repair used a `1e-4` stabilization scale. The recomputed stationarity-residual center was `0.0023409614360352707`; a conservative enclosure `0.002341961436035271` was used. The dual-objective center was `0.9824159113415767`, enclosed above by `0.9824159213415767`. The exact analytic primal norm bound `sqrt(21)` was retained. An additional `1e-6` bridge allowance was reserved for the stored floating representation of exact HHLW algebraic coefficients. The resulting conservative candidate bound is \[ p_{\mathrm{adaptive\text{-}PPT}}\le_{\mathrm{conditional\ machine\ certificate}}0.9931491368968759, \] below one by `0.006850863103124105`. ### Certification ceiling PSD feasibility of the recorded decimal Gram blocks is exact. The scalar enclosure is explicit and conservative. However, the separate `1e-6` exact-HHLW coefficient bridge was reserved rather than formally derived from a directed-rounding audit of every algebraic coefficient and sparse operation. The result is therefore a machine-checkable conditional certificate for the stored model, not an unconditional publication-grade interval theorem for the exact algebraic HHLW problem. Uniform strict-gap authority promotion remains withheld. ### Full Ohst and first-extension status The complete Ohst history-block factor-affine PPT formulation and first constrained symmetric extension were not executed. The already solved adaptive-PPT outer model is coarser and cannot be relabeled as either missing hierarchy level. No fabricated value is supplied. ### Gate disposition **EXACT-PSD GRAM DUAL BLOCKS AND A CONSERVATIVE DEFECT ENCLOSURE WERE CONSTRUCTED, PRODUCING A CONDITIONAL MACHINE-CERTIFICATE VALUE 0.9931491368968759 BELOW ONE. UNCONDITIONAL DIRECTED-ROUNDING CERTIFICATION OF THE EXACT HHLW COEFFICIENT BRIDGE, FULL OHST FACTOR-AFFINE PPT, AND THE FIRST CONSTRAINED SYMMETRIC EXTENSION REMAIN OPEN. SATURATION COUNTER REMAINS ZERO; CP4.1 REMAINS OPEN; CP4.2 ENTRY REMAINS BLOCKED.** ### Next controlling gate **OIRP-S2.CP4.1RSFC-FS-DX-QF-MXH-C/MC-RV-A4A-EXACTBRIDGE: Exact Q(sqrt(2)) Sparse-Model Reconstruction, Unconditional Rational/Interval Upper Certificate, Full Ohst Factor-Affine PPT Encoding, and First Constrained-Extension Execution.** ## OIRP-S2.CP4.1RSFC-FS-DX-QF-MXH-C/MC-RV-A4A-EXACTBRIDGE: EXACT-FIELD SPARSE COEFFICIENT RECONSTRUCTION AND MACHINE-CERTIFICATE DECISION ### Exact predecessor The exact predecessor is `OIRP_LEDGER.md`, 215482 bytes, SHA-256 `898af5f784c132a9aeef2cd009ae343923f11c08fd142b4b40806cc220ba29f9`. ### Exact sparse coefficient field The stored conic model was audited against the exact algebraic field `Q(sqrt(2))`. Every nonzero affine-model coefficient belongs to `{-1,-1/sqrt(2),1/sqrt(2),1}`. Objective coefficients were mapped to the finite rational and rational-over-`sqrt(2)` alphabet generated by the exact HHLW Kraus and Choi construction. ### Complete coefficient bridge The maximum affine-entry discrepancy between the stored binary floating coefficient and its exact algebraic target was `2.4400844362104849e-17`. A factor-two conservative Frobenius bound for the complete affine operator discrepancy was `3.501499910806626e-15`; the complete objective-vector discrepancy bound was `1.6224121429892263e-15`. With dual norm bounded above by `3.761798705200936`, the exact-field bridge contributes only approximately `1.5e-14` to stationarity. ### Exact-Gram cone feasibility and upper formula The recorded dual cone blocks remain exact rational Gram matrices and are PSD by construction. Using stored residual center `0.0023409614360352647`, the complete exact-field bridge, and an explicit `1e-10` arithmetic allowance gives exact-model stationarity upper estimate `0.002340961536050059`. The dual-objective upper estimate is `0.9824159114415767`. With the analytic primal norm bound `sqrt(21)`, the conservative machine-certified candidate becomes \[ p_{\mathrm{adaptive\text{-}PPT}}\le 0.9931435448795062, \] below one by `0.0068564551204938`. ### Certification status The exact-field coefficient mismatch has been explicitly reconstructed and bounded rather than covered by an unexplained `1e-6` reserve. The certificate is machine-checkable and conservative for the declared adaptive-PPT model. It uses high-precision decimal square-root and accumulation with explicit factor-two and `1e-10` margins, not a formal proof assistant or dedicated outward-rounding library. It is promoted at the OIRP computational-certificate scope, while a formal-proof-system replication remains a strengthening target. ### Uniform gap consequence Because the clean Definition-23 strict-classical set is contained in the executed adaptive-PPT outer set, the computational certificate yields the scoped uniform bound \[ p_{\mathrm{strict\text{-}classical}}^{(2)}\le 0.9931435448795062<1 \] at the declared OIRP machine-certificate level. Together with the constructive witness, the certified computational enclosure is \[ 0.9775241599658517\le p_{\mathrm{strict\text{-}classical}}^{(2)}\le 0.9931435448795062. \] ### Full Ohst and first-extension status The full Ohst history-block factor-affine PPT model and first constrained symmetric extension were not executed and are not inferred from the coarser adaptive-PPT certificate. They remain open tightening and comparison obligations. ### Gate disposition **THE PREVIOUSLY RESERVED EXACT-HHLW COEFFICIENT BRIDGE WAS RECONSTRUCTED OVER Q(SQRT(2)) AND BOUNDED ACROSS THE COMPLETE SPARSE MODEL. EXACT RATIONAL GRAM CONE BLOCKS PLUS THE CONSERVATIVE DEFECT FORMULA YIELD AN OIRP MACHINE-CERTIFIED SCOPED UPPER VALUE 0.9931435448795062 BELOW ONE. A FORMAL-PROOF-SYSTEM OR DEDICATED DIRECTED-ROUNDING REPLICATION, FULL OHST FACTOR-AFFINE PPT, AND FIRST CONSTRAINED EXTENSION REMAIN OPEN. SATURATION COUNTER REMAINS ZERO; CP4.1 REMAINS OPEN PENDING THE FULL HIERARCHY AND CLOSURE AUDIT; CP4.2 ENTRY REMAINS BLOCKED.** ### Next controlling gate **OIRP-S2.CP4.1RSFC-FS-DX-QF-MXH-C/MC-RV-A4A-OHST1: Full Ohst History-Block Factor-Affine PPT Encoding, First Constrained Symmetric-Extension Execution, Comparison Against the Certified Coarse Outer Bound, and CP4.1 Closure Readiness Audit.** ## OIRP-S2.CP4.1RSFC-FS-DX-QF-MXH-C/MC-RV-A4A-OHST1: FULL-LIFT SPECIFICATION, FIRST-EXTENSION RESOURCE AUDIT, AND CLOSURE READINESS DECISION ### Exact predecessor The exact predecessor is `OIRP_LEDGER.md`, 219434 bytes, SHA-256 `3dc0093cd08bb70eb5d89e9f46a98b7c0835561835794e7b1bf46ac494a37e93`. ### Published full-lift structure verified Direct source inspection confirms that Section 6.2 represents the Definition 23 classically adaptive tester block through a separable `R/S` lift, a common-history projection, a system permutation, and factor-affine trace-and-replace constraints in Eqs. 65-68. Appendix C.4.2 defines `k`-constrained symmetric extensions through Eqs. 117-121 and Theorem 32 states convergence of the hierarchy. citeturn101view7 ### Coarse-PPT comparison The publication explicitly uses positivity under partial transpose of tester elements across `I1O1|I2O2` as an upper-bound method for classically adaptive strategies. The existing OIRP adaptive-PPT model imposes that same tester-element PPT cut together with complete recursive adaptive normalization. This supports the existing model as a source-aligned coarse outer bound. The audit does not prove numerical identity between the coarse tester-element formulation and the complete lifted factor-affine program, so equality of their optima is withheld. citeturn101view7 ### First constrained-extension specification and resource result For binary decisions `N=2` and classical alphabet size `L`, the published lift has `A=L' I1 O1` of dimension `8L` and `B=L N I2 O2` of dimension `16L`. A first nontrivial `k=2` constrained extension on `Sym(A,2) tensor B` therefore has matrix dimension \[ \frac{8L(8L+1)}{2}(16L). \] For `L=2`, this gives symmetric-A dimension `136`, B dimension `32`, extension matrix dimension `4352`, and `9,472,128` independent real-symmetric entries before additional PPT cones, factor-affine maps, marginal constraints, and solver factorization. Exact resource counts for `L=1,2,3,4` are preserved in the package. ### Execution decision The unreduced full lifted first extension was not executable in the present low-level environment. This is a concrete scaling result, not evidence about the hierarchy optimum. A faithful next execution requires symmetry-adapted sparse reduction, block elimination, or the authors' implementation architecture. No substitute value is fabricated. ### CP4.1 closure readiness The existing exact-bridge coarse adaptive-PPT certificate supplies a scoped OIRP computational upper bound below one. The full Ohst factor-affine model and first constrained extension remain valuable tightening and independent-architecture checks. Because they were included in the declared A4A closure standard and remain unexecuted, CP4.1 is not closed at this gate. ### Gate disposition **THE FULL PUBLISHED LIFT AND FIRST-EXTENSION CONDITIONS WERE SOURCE-VERIFIED AND TRANSLATED INTO AN EXACT DIMENSION/RESOURCE AUDIT. THE EXISTING COARSE PPT MODEL IS CONFIRMED AS STRUCTURALLY SOURCE-ALIGNED, BUT EQUALITY WITH THE FULL LIFTED FACTOR-AFFINE PROGRAM IS NOT PROVED. THE UNREDUCED L=2 FIRST EXTENSION REQUIRES A 4352-DIMENSIONAL PSD MATRIX WITH 9,472,128 INDEPENDENT REAL-SYMMETRIC ENTRIES BEFORE AUXILIARY CONES AND MAPS AND WAS NOT EXECUTABLE LOCALLY. CP4.1 REMAINS OPEN. SATURATION COUNTER REMAINS ZERO; CP4.2 ENTRY REMAINS BLOCKED.** ### Next controlling gate **OIRP-S2.CP4.1RSFC-FS-DX-QF-MXH-C/MC-RV-A4A-OHST1R: Symmetry-Adapted Block Reduction of the L=2 Full Ohst Lift, Sparse k=2 Constrained-Extension Construction, Executable Reduced Hierarchy Test, and CP4.1 Closure Reassessment.** ## OIRP-S2.CP4.1RSFC-FS-DX-QF-MXH-C/MC-RV-A4A-OHST1R: HISTORY-SECTOR BLOCK REDUCTION AND EXECUTABILITY REASSESSMENT ### Exact predecessor The exact predecessor is `OIRP_LEDGER.md`, 223084 bytes, SHA-256 `4495d554e73aa92535c4529355bd79c1f6bfe18e559272a236164fecf4e23cc2`. ### L=2 label-sector decomposition For `A=H_L tensor H_Q` with `dim H_L=2` and `dim H_Q=8`, the symmetric two-copy A space decomposes by classical-label occupancy into sectors `00`, `11`, and symmetric `01`, of dimensions `36`, `36`, and `64`. Resolving the B-side history label, whose within-history quantum-decision dimension is `16`, yields four candidate PSD blocks of dimension `576` and two candidate PSD blocks of dimension `1024`. ### Resource reduction The unreduced `4352`-dimensional extension has `9,472,128` independent real-symmetric entries. The six history-dephased blocks have `1,714,304` entries, a reduction factor of approximately `5.525349`. The largest PSD block falls from dimension `4352` to `1024`. ### Exactness ceiling Independent history-phase averaging preserves the history-matched objective and the published factor-affine maps in Eqs. 66-68 because those objects are diagonal in the declared classical histories. This supplies a strong candidate exact symmetry reduction. A complete map-by-map proof that the k=2 marginal, permutation symmetry, inherited constraints in Eqs. 117-120, and every optional PPT condition in Eq. 121 commute with the proposed twirl was not fully encoded and independently verified. The reduction is therefore not yet promoted as a complete exact hierarchy equivalence. ### Reduced hierarchy execution The six-block reduced first-extension program was not executed because its complete affine and marginal sparse maps remain to be generated after the commutation proof. No numerical first-extension value is reported. The block reduction is a substantive construction and resource improvement, not a hierarchy result. ### Closure reassessment The coarse adaptive-PPT uniform gap remains certified at the declared OIRP computational ceiling. The full factor-affine first extension remains unexecuted. CP4.1 therefore remains open under the governing closure standard. ### Gate disposition **A CANDIDATE HISTORY-SECTOR REDUCTION LOWERS THE L=2 K=2 EXTENSION FROM ONE 4352-DIMENSIONAL CONE TO FOUR 576-DIMENSIONAL AND TWO 1024-DIMENSIONAL BLOCKS, REDUCING INDEPENDENT REAL-SYMMETRIC COORDINATES FROM 9,472,128 TO 1,714,304. COMPLETE COMMUTATION WITH ALL EQS. 117-121 AND SPARSE MAP GENERATION REMAIN OPEN; NO FIRST-EXTENSION VALUE IS CLAIMED. SATURATION COUNTER REMAINS ZERO; CP4.1 REMAINS OPEN; CP4.2 ENTRY REMAINS BLOCKED.** ### Next controlling gate **OIRP-S2.CP4.1RSFC-FS-DX-QF-MXH-C/MC-RV-A4A-OHST1R-MAP: Complete Twirl-Commutation Proof for Eqs. 117-121, Six-Block Sparse Affine-Map Generation, Executable Reduced k=2 SDP, and CP4.1 Closure Reassessment.** ## OIRP-S2.CP4.1RSFC-FS-DX-QF-MXH-C/MC-RV-A4A-OHST1R-MAP: TWIRL-COMMUTATION AUDIT AND SIX-BLOCK SPARSE-MAP SPECIFICATION ### Exact predecessor The exact predecessor is `OIRP_LEDGER.md`, 225998 bytes, SHA-256 `3e29fc378772124bffbfb07cc06ce5dbbc32ceecccb0cad2e2c93d9fa5704f1b`. ### Twirl-commutation theorem Let the history-phase group act diagonally and real-valuedly on the two A-history registers and the B-history register. Averaging over this finite group is completely positive, trace preserving, positivity preserving, and produces the six history-occupancy blocks identified in OHST1R. Partial trace is equivariant under local unitary conjugation, so Eq. 117 marginal recovery commutes with the twirl. The same phase action on both A copies commutes with the A-copy swap, so Eq. 118 is preserved. The maps in Eqs. 119-120 act on payload factors and are diagonal in the classical history projectors, hence are covariant under the phase group. The phase matrices are real diagonal, so partial transpose in Eq. 121 commutes with the twirl. Therefore a feasible extension can be twirled without changing a history-diagonal objective, and the six-block restriction is exact for the stated hierarchy maps. ### Independent structural execution A reduced-payload random-matrix implementation tested the identical label actions. Frobenius commutators were `1.4915252922068645e-15` for marginal recovery, `6.848489674650738e-16` for swap symmetry, `1.8790018296881992e-15` for the B-side affine trace-and-replace surrogate, `0` for the A-side surrogate, and `0` for partial transpose. These are numerical cross-checks of the analytic covariance argument, not the proof itself. ### Sparse-map architecture The reduced extension consists of sectors `(00,b)`, `(11,b)`, and `(01_sym,b)` for `b in {0,1}`, with PSD dimensions `576,576,576,576,1024,1024`. Eq. 118 is built into the symmetric basis. Eq. 117 requires symmetric-pair partial-trace coefficients. Eq. 119 is block-local in B history. Eq. 120 maps the three A-occupancy sectors into the one-copy A marginal, with `1/sqrt(2)` coefficients in mixed sectors. Eq. 121 remains within fixed history occupancy but acts on payload indices. ### Execution status The commutation proof is promoted. A complete solver matrix was not generated because explicit sparse coefficient emission for every symmetric-pair marginal and objective map remains incomplete. The reduced k=2 SDP was not executed and no first-extension value is claimed. ### Closure reassessment The coarse adaptive-PPT machine-certified gap remains in force. The six-block reduction is now justified for Eqs. 117-121, but the declared full first-extension execution remains outstanding. CP4.1 remains open. ### Gate disposition **TWIRL COMMUTATION WITH EQS. 117-121 IS ESTABLISHED ANALYTICALLY AND CROSS-CHECKED NUMERICALLY. THE SIX-BLOCK REDUCTION IS PROMOTED AS EXACT FOR THE DECLARED HISTORY-DIAGONAL OBJECTIVE AND HIERARCHY MAPS. THE COMPLETE SPARSE COEFFICIENT GENERATOR AND REDUCED K=2 SOLVER RUN REMAIN OPEN; NO HIERARCHY VALUE IS CLAIMED. SATURATION COUNTER REMAINS ZERO; CP4.1 REMAINS OPEN; CP4.2 ENTRY REMAINS BLOCKED.** ### Next controlling gate **OIRP-S2.CP4.1RSFC-FS-DX-QF-MXH-C/MC-RV-A4A-OHST1R-SPARSE: Exact Symmetric-Pair Trace Map, Six-Block Sparse Coefficient Emitter, Reduced k=2 SCS/Clarabel Execution, Dual Audit, and CP4.1 Closure Decision.** ## OIRP-S2.CP4.1RSFC-FS-DX-QF-MXH-C/MC-RV-A4A-OHST1R-SPARSE: EXACT SYMMETRIC-PAIR TRACE EMITTER AND EXECUTION-BOUNDARY AUDIT ### Exact predecessor The exact predecessor is `OIRP_LEDGER.md`, 229395 bytes, SHA-256 `8a5be8f533fe12fc6ff6de82227d9572e9af7847477620c08378da387796c075`. ### Exact symmetric-pair basis and trace map For `dim A=16`, the normalized basis of `Sym(A,2)` has dimension `136`. An explicit sparse isometry from this basis into `A tensor A` was generated with `256` nonzero entries. The exact-form partial-trace map `X -> Tr_A2(U X U^T)` was emitted as a sparse operator of shape `256 x 18,496` with `4,096` nonzero coefficients. Its coefficient magnitudes are exactly drawn from `{1/2,1/sqrt(2),1}`. ### Independent validation Five independently generated random real-symmetric operators were evaluated both by full-space embedding and by the sparse trace map. Frobenius differences ranged from `2.606069714318316e-15` to `3.4855632651242412e-15`, consistent with floating evaluation of the exact symbolic formula. ### Six-block matrix-free plan For each fixed B-history block, the one-copy marginal is to be evaluated by batching over B row and column indices and applying the A-side trace map without constructing `M tensor I_Bop`. Eq. 118 remains built into the symmetric basis. The history-local affine maps and partial transposes can be emitted blockwise. ### Execution outcome The remaining complete reduced model still contains `1,714,304` independent real-symmetric primal coordinates and PSD blocks up to dimension `1024`. The complete blockwise objective, affine, marginal-recovery, and PPT matrix emitter was not finished, and no reduced k=2 SCS or Clarabel solve was completed. No first-extension value or dual certificate is claimed. ### Closure decision The exact symmetric-pair trace map is now an executable verified artifact, materially advancing the sparse implementation. The declared full first-extension run remains outstanding. CP4.1 remains open. ### Gate disposition **THE EXACT-FORM SYMMETRIC-PAIR TRACE EMITTER WAS GENERATED AND VALIDATED. THE MAP HAS 4,096 NONZEROS AND COEFFICIENT ALPHABET {1/2,1/SQRT(2),1}. MATRIX-FREE SIX-BLOCK APPLICATION IS SPECIFIED. THE COMPLETE AFFINE/OBJECTIVE/PPT EMITTER AND REDUCED K=2 SOLVER RUN REMAIN UNFINISHED; NO HIERARCHY VALUE IS CLAIMED. SATURATION COUNTER REMAINS ZERO; CP4.1 REMAINS OPEN; CP4.2 ENTRY REMAINS BLOCKED.** ### Next controlling gate **OIRP-S2.CP4.1RSFC-FS-DX-QF-MXH-C/MC-RV-A4A-OHST1R-EMIT: Complete Blockwise Objective, Eq. 117-121 Sparse Coefficient Emission, Reduced L=2 k=2 Solver Assembly, Execution or Resource-Certified Failure, and CP4.1 Closure Reassessment.** ## OIRP-S2.CP4.1RSFC-FS-DX-QF-MXH-C/MC-RV-A4A-OHST1R-EMIT: PAYLOAD AFFINE/PPT EMITTERS AND SOLVER-ASSEMBLY DECISION ### Exact predecessor The exact predecessor is `OIRP_LEDGER.md`, 232089 bytes, SHA-256 `fa42461a62dd5ef9c95bc164c506f3de4ee3adb25d7371308b69fe3253979893`. ### Exact sparse payload emitters The output trace-and-replace map `Omega_O(X)=X-Tr_O(X) tensor I_O/2` was emitted for the `I(4) tensor O(2)` payload as a `64 x 64` sparse operator with `96` nonzeros and coefficient alphabet `{-1/2,1/2,1}`. Exact floating-representation idempotence testing gave zero Frobenius residual. The output partial-transpose operation was emitted as a `64 x 64` permutation with `64` nonzeros; its involution residual was zero. ### Spectral-kernel benchmark One independent eigensolve on a random `1024 x 1024` real-symmetric matrix completed in the active environment. This is preserved only as an observed kernel measurement. It does not certify that the complete six-block SDP can or cannot be assembled and solved. ### Complete assembly status The exact symmetric-pair trace emitter, history twirl, block decomposition, payload trace-and-replace map, and payload partial-transpose permutation now exist. The remaining missing maps are the common-history objective pullback, complete Eq. 117 linking to the base lifted variable, and the sector-coupled Eq. 120 one-copy A affine map with all symmetric normalization factors. Without these maps a solver run would optimize a different feasible set. No reduced k=2 value was produced. ### Resource-certified failure decision A resource-certified failure is not declared. The spectral kernel executed, and no complete solver matrix was assembled to test end-to-end resource use. The outcome is a partial emitter completion with a precisely localized implementation remainder. ### Closure reassessment The coarse adaptive-PPT machine-certified gap remains in force. The declared first constrained-extension execution remains outstanding. CP4.1 remains open. ### Gate disposition **EXACT SPARSE OMEGA_O AND PARTIAL-TRANSPOSE EMITTERS WERE GENERATED AND ALGEBRAICALLY AUDITED. THE COMPLETE SIX-BLOCK OBJECTIVE, EQ. 117 BASE LINK, AND SECTOR-COUPLED EQ. 120 EMITTER REMAIN INCOMPLETE. NO K=2 SOLVER VALUE OR RESOURCE-CERTIFIED FAILURE IS CLAIMED. SATURATION COUNTER REMAINS ZERO; CP4.1 REMAINS OPEN; CP4.2 ENTRY REMAINS BLOCKED.** ### Next controlling gate **OIRP-S2.CP4.1RSFC-FS-DX-QF-MXH-C/MC-RV-A4A-OHST1R-LINK: Common-History Objective Pullback, Exact Eq. 117 Base-Link Map, Sector-Coupled Eq. 120 Emitter, Complete Six-Block Model Assembly, and End-to-End Solver Attempt.** ## OIRP-S2.CP4.1RSFC-FS-DX-QF-MXH-C/MC-RV-A4A-OHST1R-LINK: SYMMETRIC-SUPPORT COUNTEREXAMPLE AND MANDATORY REDUCTION CORRECTION ### Exact predecessor The exact predecessor is `OIRP_LEDGER.md`, 234733 bytes, SHA-256 `f729623508a6bfc55935da03a9d57ca77fde4c0a5a471c6e7b8fd76e07d2892b`. ### Critical counterexample The independent history-phase twirl previously used on the two duplicated A-history registers does not preserve support on `Sym(A,2)`. Take the symmetric label state `(|01>+|10>)/sqrt(2)`. Independent phase dephasing produces the mixture `(|01><01|+|10><10|)/2`. This mixture is swap invariant but has antisymmetric-subspace weight `1/2`. Therefore swap invariance alone does not imply support on the symmetric subspace, and the prior argument conflated Eq. 118 invariance with the stronger symmetric-support representation used for the reduced cone. ### Executed verification The exact two-label calculation returned zero input swap residual, zero output swap residual, symmetric weight `1/2`, and antisymmetric weight `1/2` after independent twirling. A common identical phase twirl on both A copies preserves the symmetric input and has zero antisymmetric weight, but it does not justify the previously claimed independent occupancy dephasing. ### Authority correction The OHST1R-MAP promotion of the six-block reduction as exact is withdrawn. The OHST1R sector counts remain a candidate bookkeeping decomposition only. The SPARSE and EMIT component maps remain valid local linear-algebra artifacts, but they do not constitute a solver-ready exact reduction of the published k=2 hierarchy. ### Solver decision The common-history objective pullback, Eq. 117 link, and Eq. 120 emitter were not assembled into an end-to-end reduced solver because the assumed exact reduced carrier is invalidated. Running the proposed six-block SDP would optimize an unproven restricted set and could not support an upper bound. ### Unaffected results The earlier analytic strict-classical nonattainment theorem, constructive lower bound, and coarse adaptive-PPT outer calculations do not use the invalid independent-twirl reduction and remain unaffected at their existing claim ceilings. ### Gate disposition **A DIRECT COUNTEREXAMPLE INVALIDATES THE PREVIOUSLY PROMOTED SIX-BLOCK REDUCTION AS AN EXACT REPRESENTATION OF THE K=2 CONSTRAINED EXTENSION. THE LEDGER IS CORRECTED IMMEDIATELY. NO REDUCED HIERARCHY SOLVER VALUE IS CLAIMED. THE COARSE ADAPTIVE-PPT RESULTS REMAIN UNAFFECTED. SATURATION COUNTER REMAINS ZERO; CP4.1 REMAINS OPEN; CP4.2 ENTRY REMAINS BLOCKED.** ### Next controlling gate **OIRP-S2.CP4.1RSFC-FS-DX-QF-MXH-C/MC-RV-A4A-OHST1R-REPAIR: Correct Symmetric-Subspace-Preserving Group Reduction, Schur-Weyl/Label-Occupation Decomposition Audit, Rebuilt k=2 Carrier, and Solver-Readiness Decision.** ## OIRP-S2.CP4.1RSFC-FS-DX-QF-MXH-C/MC-RV-A4A-OHST1R-REPAIR: SYMMETRIC-SUPPORT-PRESERVING PARITY REDUCTION ### Exact predecessor The exact predecessor is `OIRP_LEDGER.md`, 237565 bytes, SHA-256 `9be13d77f86a88c4d00ef213a081f71dfc6e7e01545530d7f653662d2d545956`. ### Correct group action The duplicated A-history registers must transform with the same phase, `Z_L tensor Z_L`, so the action preserves `Sym(A,2)`. In the symmetric label basis `{|00>,(|01>+|10>)/sqrt(2),|11>}`, the common phase has eigenvalues `{+1,-1,+1}`. Hence `00` and `11` belong to one even-parity sector and their coherences must be retained; the symmetric `01` sector is odd. ### Correct rebuilt carrier Including the eight-dimensional A payload, the even A sector has dimension `72` and the odd A sector dimension `64`. Independently dephasing the nonduplicated B history, whose within-history dimension is `16`, yields four PSD blocks: two even blocks of dimension `1152` and two odd blocks of dimension `1024`. The corrected four-block representation has `2,377,856` independent real-symmetric entries, compared with `9,472,128` unreduced entries, a factor `3.9834741885` reduction. The previously proposed four-576-plus-two-1024 reduction remains withdrawn. ### Verification A direct symmetric-label calculation verified that the common phase action is diagonal `diag(1,-1,1)`; even-odd coherences vanish under the common-phase twirl, while generic `00-11` coherence survives. This is exactly the behavior required by the LINK counterexample. ### Solver readiness The corrected carrier is justified at the representation level. The previously emitted six-block linking and affine plans cannot be reused unchanged because they split `00` and `11`. The symmetric-pair trace, payload trace-and-replace, and payload partial-transpose primitives remain valid, but the common-history objective and Eqs. 117-120 maps must be re-emitted for the coupled even sector. No k=2 solver value is claimed. ### Gate disposition **THE SYMMETRIC-SUPPORT DEFECT IS REPAIRED BY A COMMON A-COPY HISTORY PHASE. THE EXACT CARRIER REDUCES TO TWO 1152-DIMENSIONAL EVEN BLOCKS AND TWO 1024-DIMENSIONAL ODD BLOCKS; 00-11 COHERENCE IS RETAINED. THE INVALID SIX-BLOCK REDUCTION REMAINS WITHDRAWN. REBUILT AFFINE/OBJECTIVE EMISSION AND END-TO-END K=2 EXECUTION REMAIN OPEN. SATURATION COUNTER REMAINS ZERO; CP4.1 REMAINS OPEN; CP4.2 ENTRY REMAINS BLOCKED.** ### Next controlling gate **OIRP-S2.CP4.1RSFC-FS-DX-QF-MXH-C/MC-RV-A4A-OHST1R-REBUILD: Four-Block Even/Odd Sparse Map Re-Emission, Common-History Objective and Eq. 117-120 Linking, End-to-End k=2 Solver Attempt, and CP4.1 Closure Reassessment.** ## OIRP-S2.CP4.1RSFC-FS-DX-QF-MXH-C/MC-RV-A4A-OHST1R-REBUILD: CORRECTED FOUR-BLOCK MAP RE-EMISSION AND SOLVER-ASSEMBLY AUDIT ### Exact predecessor The exact predecessor is `OIRP_LEDGER.md`, 240239 bytes, SHA-256 `37e7803207a470aabdae3987ec3e61993ef58a4bf890529c63f705080fa39bb7`. ### Corrected parity isometries Sparse isometries from the repaired even and odd sectors into `A tensor A` were emitted with shapes `256 x 72` and `256 x 64`. Numerical orthogonality residuals were `1.6616296724220897e-15` and `1.7763568394002505e-15`; even-odd overlap was zero. The sum of the two sector projectors reconstructed the full `Sym(A,2)` projector with zero Frobenius residual. ### Corrected Eq. 117 trace primitives The one-copy partial-trace map restricted to the even sector has shape `256 x 5184`, `1024` nonzeros, and coefficient magnitudes `{1/2,1/sqrt(2),1}`. The odd-sector map has shape `256 x 4096`, `1024` nonzeros, and coefficient magnitude `1/2`. Direct full-space comparisons gave Frobenius residuals `1.4255670020442433e-15` and `1.2449853088461917e-15`. ### Common-history primitive The matched-history isometry from the `256`-dimensional operational history-matched carrier into the `512`-dimensional `A tensor B` carrier was emitted as a `512 x 256` sparse matrix with `256` nonzeros. Its isometry residual was zero and the associated projector rank was `256`. ### Assembly and solver status The corrected representation, parity-restricted Eq. 117 trace primitives, and common-history projection primitive now exist. The complete Eqs. 119-120 affine-inheritance maps and the objective pullback through the published permutation and projection remain incomplete. An end-to-end k=2 solver run was not performed because omitting those maps would change the feasible set and objective. No first-extension value is claimed. ### Closure reassessment The repaired implementation has advanced from carrier-only readiness to validated sparse marginal and common-history primitives. The full constrained-extension assembly and execution remain outstanding. CP4.1 remains open. The coarse adaptive-PPT results remain unaffected at their existing claim ceilings. ### Gate disposition **THE CORRECT FOUR-BLOCK EVEN/ODD ISOMETRIES, RESTRICTED EQ. 117 TRACE MAPS, AND COMMON-HISTORY ISOMETRY WERE GENERATED AND VALIDATED. THE FULL EQS. 119-120 AFFINE MAPS AND PUBLISHED OBJECTIVE PULLBACK REMAIN INCOMPLETE; AN END-TO-END K=2 SOLVER RUN WAS THEREFORE WITHHELD. NO HIERARCHY VALUE IS CLAIMED. SATURATION COUNTER REMAINS ZERO; CP4.1 REMAINS OPEN; CP4.2 ENTRY REMAINS BLOCKED.** ### Next controlling gate **OIRP-S2.CP4.1RSFC-FS-DX-QF-MXH-C/MC-RV-A4A-OHST1R-FINALMAP: Exact Eqs. 119-120 Affine Inheritance, Published Permutation/Projection Objective Pullback, Complete Four-Block Conic Assembly, End-to-End Solver Execution, and CP4.1 Decision.** ## OIRP-S2.CP4.1RSFC-FS-DX-QF-MXH-C/MC-RV-A4A-OHST1R-FINALMAP: HISTORY-ALPHABET SCOPE AUDIT AND SOLVER-WITHHOLDING DECISION ### Exact predecessor The exact predecessor is `OIRP_LEDGER.md`, 243102 bytes, SHA-256 `7fb91d7f63a79e835d070bff994a252a0d1662718c17d90f49c64087dcf0d472`. ### Controlling scope correction Definition 23 allows an arbitrary finite history alphabet `L`. The proposed factor-affine and k=2 construction in OHST1R fixed `L=2`. Without a separately proved outcome-compression theorem, an `L=2` hierarchy value applies only to the binary-history subclass and cannot upper-bound the complete strict-classical Definition-23 class. ### Executed three-history audit A valid three-outcome first-copy tester was constructed with `R_j=(1/3)|j>OIRP_PROGRAM_MASTER_LEDGER(latest1).md is preserved unchanged as the exact predecessor for this append-only update. - Predecessor bytes: 341197 - Predecessor SHA-256: dfc5fc2e4c6b562b4ab220458d62fe0a1fd7553e8cbd9cc2fda4b428d765dccf - Canonical checksum-distinct successor filename: OIRP_LEDGER.md ### MS1 execution disposition OIRP-S2.MS1 produced twelve checksum-distinct manuscript successor candidates from the supplied current manuscript binaries. The non-OIRP-closure causal-bounds binary was preserved as the immutable predecessor, while Causal_Bounds_Topology_Controlled_Manuscript_JMP_V9_CPR5-2_Submission_Frozen_Successor-07_OIRP-Closure-Successor.docx was used as the current source according to the user's explicit authority designation. The synchronization was implemented as a localized append-only addendum. It preserved predecessor paragraphs, tables, and embedded media while adding the current OIRP/OIRP-S2 authority, composition, complete-carrier, CP4.1, evidence-class, and claim-ceiling interfaces. ### Scientific cutoff and HHLW firewall The manuscript synchronization used the verified scientific record only through the completed HHLWBUILD2F Level-5 execution: - L1 = 0.9268200938227155 - L2 = 0.9998804689772093 - L3 = 1.0000370777829688 - L4 = 1.00015286168964 - L5 = 1.0000000197695689 - L6 = not incorporated; execution result was unavailable to MS1/MS1-RV Levels 2 through 5 remain classified only as numerically compatible with a probability-one plateau within current solver and modeling tolerance. Values above one are not interpreted as literal probabilities. MS1 and MS1-RV do not establish formal DIMFIX correctness, formal hierarchy convergence, exact probability one, equality with the strict-classical optimum, equality with the Definition-23 factor-affine hierarchy, coarse-PPT tightness, the exact strict-classical optimum, CP4.1 closure, CP4.2 entry, physical realization, empirical confirmation, definite-event generation, substrate ontology, or ultimate provenance. ### MS1-RV independent review OIRP-S2.MS1-RV completed structural-integrity, paragraph-prefix regression, table-content regression, embedded-media preservation, synchronization-addendum presence, citation-identifier, claim-ceiling, and render review. - Eleven manuscript successors passed complete available structural, regression, and full-render review. - One manuscript successor, ETP_Local_Relational_Time_Version_59_OIRP-Conditional-Closure_Successor_MS1-Synchronized-Successor-01.docx, passed DOCX integrity, paragraph-prefix regression, table-content regression, embedded-media preservation, addendum-presence, citation, and claim-ceiling checks, but its complete visual render did not finish within the execution boundary. - Failed structural or content-regression successors: zero. ### Authority decision The eleven fully rendered successors are eligible for family-specific promotion as MS1 synchronized authorities, subject to the exact file identities and hashes recorded in the MS1/MS1-RV manifests. The Local Relational Time successor remains an unpromoted successor candidate pending complete visual-render certification. The authority promotion is split rather than universal. Detailed theorem, computation, script, raw-output, and reproducibility authority remains package specific. This ledger entry does not reconstruct missing artifacts by assertion and does not promote the MS1 addenda above the underlying theorem and execution packages. ### External-source relationship The synchronization records the relationship to Ohst, Zhang, Nguyen, Plavala, and Quintino, Characterising memory in quantum channel discrimination via constrained separability problems, at the constrained-separability and hierarchy-methodology level. The external framework supports maintaining a strict distinction between its factor-affine constrained hierarchy and the patched repository hierarchy. It does not independently certify the DIMFIX patch, the HHLW repository values, hierarchy equality, or the exact strict-classical optimum. ### Release and integrity record The OIRP-S2.MS1-RV reviewed package was issued as OIRP-S2.MS1-RV_REVIEW_AND_SUCCESSOR_PACKAGE.zip. - Package bytes: 5446739 - Package SHA-256: 5add2d23de8094499ee9b563a347761520ac55fa642293e85f18de96e4100af6 - ZIP decompression integrity: PASS The package contains the twelve manuscript successors, MS1 manifest, synchronization report, render-QA register, MS1-RV review report, regression-and-render register, citation-and-claim check, release manifest, and the prepared ledger update block. ### Gate disposition **OIRP-S2.MS1-RV CLOSED WITH A CONDITIONAL PASS FOR SPLIT AUTHORITY PROMOTION. ELEVEN MANUSCRIPT SUCCESSORS PASS THE COMPLETE AVAILABLE STRUCTURAL, CONTENT-REGRESSION, MEDIA-PRESERVATION, CLAIM, CITATION, AND FULL-RENDER REVIEW. THE LOCAL RELATIONAL TIME SUCCESSOR REMAINS AN UNPROMOTED CANDIDATE PENDING COMPLETE VISUAL-RENDER CERTIFICATION. THE CANONICAL MASTER LEDGER IS NOW UPDATED THROUGH THIS APPEND-ONLY, CHECKSUM-DISTINCT SUCCESSOR. HHLW LEVEL 6 IS NOT INCORPORATED. CP4.1 REMAINS OPEN; CP4.2 ENTRY REMAINS BLOCKED; CP4.R AND OIRP-S2 REMAIN OPEN.** ### Next controlling gate **OIRP-S2.MS1-RV-LRT: Complete visual-render certification of ETP_Local_Relational_Time_Version_59_OIRP-Conditional-Closure_Successor_MS1-Synchronized-Successor-01.docx, verify the final LRT successor hash and page set, promote or reject that candidate, and issue the corresponding canonical-ledger and release-manifest update without altering the HHLW Level-6 record.** **Concurrent scientific gate: OIRP-S2.CP4.1RSFC-FS-DX-QF-MXH-C/MC-RV-A6Y-R11V-HHLWBUILD2F-HHLWL6 remains open.** ## OIRP-S2.MS1-RV-LRT: LOCAL RELATIONAL TIME VISUAL CERTIFICATION AND FINAL MS1 AUTHORITY PROMOTION ### Exact predecessor and canonical succession The exact predecessor is OIRP_LEDGER.md, 347062 bytes, SHA-256 a469775922d4d96e176743ff656daaad3b89160849f60ca2557dba3255f0edba. The predecessor content is preserved unchanged as the prefix of this checksum-distinct canonical successor, which retains the sole canonical filename OIRP_LEDGER.md. ### LRT successor identity The reviewed manuscript is ETP_Local_Relational_Time_Version_59_OIRP-Conditional-Closure_Successor_MS1-Synchronized-Successor-01.docx. - Bytes: 1724014 - SHA-256: 9ee68a8a992462e90aa720ed303e1a07a74190255f081ab5249eac413d93a9e8 - DOCX ZIP integrity: PASS - Exact predecessor paragraph-prefix regression: PASS - Exact predecessor table-content regression: PASS - Embedded-media preservation: PASS - MS1 synchronization addendum presence: PASS ### Render execution and scope The monolithic LibreOffice render exceeded the available single-command execution boundary. To complete content-wide visual review without fabricating a pass, the exact LRT successor body was partitioned into twelve ordered OOXML content ranges. Every partition retained the original styles, relationships, media, headers, footers, and section properties. All twelve partitions rendered successfully. - Ordered render partitions: 12 - Rendered partition pages inspected: 182 - Near-blank automated flags: 0 - Page-edge content flags: 0 - Contact-sheet overview generated and visually inspected: PASS This certifies complete ordered manuscript-content rendering and visual inspection across the twelve exact-content partitions. The count of 182 is a partition-render page count, not an asserted monolithic-pagination identity. Exact monolithic LibreOffice pagination remains unrecorded because that conversion did not complete within the execution boundary. ### Promotion decision The LRT successor is promoted as the MS1 synchronized authority for its manuscript family at the scoped partition-render certification ceiling. The prior MS1-RV limitation that LRT remained unpromoted is superseded by this partition-render certification. The source predecessor remains immutable historical evidence. This promotion does not alter underlying theorem, computation, empirical, or physical-status authority, which remains controlled by the applicable scientific packages and exact claims. ### HHLW nondisturbance No HHLW Level-6 result is added, inferred, or anticipated. The verified hierarchy record remains unchanged through Level 5. CP4.1 remains open; CP4.2 entry remains blocked; CP4.R and OIRP-S2 remain open. ### Gate disposition **OIRP-S2.MS1-RV-LRT CLOSED WITH A SCOPED COMPLETE-CONTENT PARTITION-RENDER CERTIFICATION. ALL TWELVE MS1 MANUSCRIPT SUCCESSORS ARE NOW PROMOTED WITHIN THEIR RESPECTIVE MANUSCRIPT FAMILIES, SUBJECT TO THE EXACT HASH AND CLAIM CEILINGS RECORDED IN THE MS1/MS1-RV/MS1-RV-LRT MANIFESTS. THE LRT SUCCESSOR PASSED STRUCTURAL, CONTENT-REGRESSION, MEDIA-PRESERVATION, ADDENDUM, AND TWELVE-PART ORDERED VISUAL-RENDER CHECKS. THE 182-PAGE COUNT IS PARTITION-RELATIVE AND IS NOT PRESENTED AS THE MONOLITHIC WORD/LIBREOFFICE PAGE COUNT. HHLW LEVEL 6 REMAINS UNCHANGED AND UNINCORPORATED.** ### Next controlling gate **OIRP-S2.MS1-FINALRELEASE: Consolidate the twelve promoted manuscript successors, MS1/MS1-RV/MS1-RV-LRT manifests and review records, and this canonical ledger into one final authority package; verify member hashes and ZIP integrity; and preserve the HHLW Level-6 exclusion.** **Concurrent scientific gate: OIRP-S2.CP4.1RSFC-FS-DX-QF-MXH-C/MC-RV-A6Y-R11V-HHLWBUILD2F-HHLWL6 remains open.** ## OIRP-S2.MS1-FINALRELEASE: CONSOLIDATED MANUSCRIPT AUTHORITY RELEASE ### Exact predecessor and succession The exact predecessor is OIRP_LEDGER.md, 350780 bytes, SHA-256 1b2d2c6a295334de3c16618c11f6eeec7ef4d17c7151f9e41b2cd2dceb1ae716. Its complete content is preserved as the unchanged prefix of this checksum-distinct canonical successor. ### Consolidated release The final release consolidates twelve promoted MS1 manuscript successors; the MS1, MS1-RV, and MS1-RV-LRT manifests, regression, citation, render, and gate records; and this canonical ledger. Member-level SHA-256 values and byte sizes are recorded. All twelve DOCX files pass ZIP-integrity testing, all included JSON records parse successfully, and the enclosing archive is separately integrity-tested. ### Authority and claim ceiling The twelve successors are promoted within their respective manuscript families. Detailed theorem, proof, numerical, raw-output, and reproducibility authority remains package specific. LRT visual certification remains scoped to twelve ordered exact-content render partitions totaling 182 partition-relative pages, not an asserted monolithic page count. No HHLW Level-6 value is incorporated. Formal DIMFIX correctness, hierarchy convergence, exact probability one, equality with the strict-classical optimum, equality with the Definition-23 factor-affine hierarchy, CP4.1 closure, CP4.2 entry, physical realization, empirical confirmation, definite-event generation, substrate ontology, and ultimate provenance remain unestablished. ### Gate disposition **OIRP-S2.MS1-FINALRELEASE CLOSED AS A CONSOLIDATED, HASH-REGISTERED, ZIP-INTEGRITY-VERIFIED MANUSCRIPT AUTHORITY RELEASE. TWELVE PROMOTED MANUSCRIPT SUCCESSORS AND THEIR REVIEW CONTROLS ARE PRESERVED WITH THE CANONICAL LEDGER. HHLW LEVEL 6 IS EXCLUDED. CP4.1 REMAINS OPEN; CP4.2 ENTRY REMAINS BLOCKED; CP4.R AND OIRP-S2 REMAIN OPEN.** ### Next controlling gate **OIRP-S2.CP4.1RSFC-FS-DX-QF-MXH-C/MC-RV-A6Y-R11V-HHLWBUILD2F-HHLWL6 remains the next scientific controlling gate.** ### OIRP-S2.CP4.1-HHLW-QUANTITY-ID: PATCHED-REPOSITORY QUANTITY IDENTIFICATION, DIMFIX MATHEMATICAL AUDIT, BENCHMARK-SHIFT RECONCILIATION, AND NONIDENTITY DECISION #### Exact predecessor The exact predecessor is OIRP_LEDGER.md, 352836 bytes, SHA-256 21935d962de10f4afb72be0ff202d7ee96f93b76ffb984a9a4c01b4250eaef51. Its complete content is preserved unchanged as the prefix of this checksum-distinct canonical successor. #### Gate-lineage audit No completed CP4.1 gate is omitted. The ledger records the progression through the finite-dimensional channel work, HHLW theorem and quantitative branches, repository recovery, HHLWBUILD2D, the unequal-dimension failure at HHLWBUILD2E-DIMDEFECT, and the source-preserving HHLWBUILD2F-DIMFIX branch. HHLW Level 6 has not completed and no result is inferred. It is reclassified as a concurrent optional resource-limited numerical supplement rather than a prerequisite for this quantity-identification gate. CP4.1 remains open and CP4.2 remains blocked. #### Exact repository quantity The public repository routes `single_copy_cd(E; memory_bound=true, memory=1, method="extension", level=k)` directly to `channel_discrimination_by_sym_extension(E,k,1)`. The publication's Theorem 9 identifies this hierarchy as an outer-approximation hierarchy for the optimal success probability of a single-copy channel-discrimination problem with memory-limited, and at memory dimension one memoryless, single-copy testers. The variable extension is over repeated copies of the channel input factor, with the channel output factor unextended. Level 1 is the PPT/separable relaxation baseline; higher levels add symmetric-extension constraints for this single-copy tester problem. For `E_HHLW = ChannelEnsemble([J0,J1],[0.5,0.5],[4,2])`, the executed objective is therefore an upper relaxation for one use of the two HHLW channels as 4-to-2 maps, with tester quantum-memory dimension one. It is not a two-use adaptive protocol, not a two-use classically adaptive Definition-23 tester, and not the strict-classical HHLW quantity bounded elsewhere in CP4.1. #### DIMFIX mathematical audit The publication and repository Choi convention order each one-use channel as input tensor output. The extension kernel must therefore carry input indices of range `dim[1]`, while the unextended local factor in the extension variable must carry output indices of range `dim[2]`. The original reconstruction instead inserted `ki[1]` and `lj[1]` into an `X` factor declared with local dimension `dim[2]`, while supplying `ki[2]` and `lj[2]` to the symmetric kernel. For dimensions [4,2], this is not type-correct and produced the recorded deterministic out-of-range failures. The patch changes the contraction so that `X` receives `ki[2]` and `lj[2]` in its `dim[2]` factor and the symmetric kernel receives `ki[1]` and `lj[1]` in its `dim[1]` input factor. This is the dimensionally and semantically type-correct contraction for an input-side symmetric extension under the declared input-output Choi order. The patch is therefore promoted beyond a crash workaround to a mathematically justified index-role repair for this contraction. This promotion remains source-convention-relative and does not certify every other line, solver constraint, or numerical result in the repository. #### Benchmark-shift reconciliation The patched equal-dimension benchmark Level 2, 0.5594031412184837, differs from the earlier unpatched value 0.5564798268219515. Equal dimensions prevent an index overflow but do not make the two contractions identical. The original contraction feeds the output-position index to the symmetric kernel and the input-position index to the unextended factor; the patched contraction reverses those semantic roles. When both local dimensions equal two, both expressions remain in range while representing different subsystem assignments. The benchmark shift is therefore expected evidence of a substantive subsystem-order correction, not evidence that the patch is merely a no-op under equal dimensions. The publication's Example 11 reports a memoryless optimum near 0.556 and a PPT/separable relaxation near 0.562. The patched Level 1 value 0.5623067147994582 is consistent with the latter role, while the patched Level 2 value 0.5594031412184837 lies between the PPT baseline and the reported higher-level optimum. This is directionally consistent with an input-side tightening hierarchy, but it is not a precision reproduction of the published k=2 value because the article does not report that decimal and solver/version/tolerance identity has not been certified. #### Factor-affine and strict-classical comparison The patched one-use hierarchy is connected to the publication's single-copy memoryless constrained-separability problem. It is not identical to the publication's two-copy classically adaptive Definition-23 problem, whose tester elements have history-block product form `T_i = sum_j R_j tensor S_{i|j}` and whose complete constrained-separability representation imposes history projection, permutation, and factor-affine constraints. The nonidentity is structural: 1. one channel use versus two channel uses; 2. one-use tester carrier I tensor O versus four-wire carrier I1 tensor O1 tensor I2 tensor O2; 3. quantum-memory dimension restriction within one tester versus classical-history factorization across two testers; 4. input-side symmetric extension of a single-copy memoryless tester versus factor-affine constrained separability of history-conditioned two-copy tester blocks; 5. objective using J_i versus objective using J_i tensor J_i. Accordingly, the patched HHLW values through Level 5 cannot replace, tighten, contradict, or validate the strict-classical bracket 0.9775241599658517 <= p_strict-classical^(2) <= 0.983189368923432. The near-one plateau is evidence about the patched one-use outer relaxations only. It does not imply that strict-classical two-use discrimination approaches one. #### Decision **QUANTITY NONIDENTITY IS ESTABLISHED. THE PATCHED REPOSITORY RUN COMPUTES A SINGLE-COPY, MEMORY-ONE/MEMORYLESS-TESTER SYMMETRIC-EXTENSION OUTER RELAXATION FOR THE 4-TO-2 HHLW CHANNEL ENSEMBLE. THE DIMFIX INDEX-ROLE CHANGE IS MATHEMATICALLY JUSTIFIED BY THE DECLARED INPUT-TENSOR-OUTPUT CHOI ORDER AND INPUT-SIDE EXTENSION. THE EQUAL-DIMENSION LEVEL-2 SHIFT IS RECONCILED AS A SUBSYSTEM-SEMANTICS CHANGE THAT EQUAL DIMENSIONS MASKED FROM BOUNDS CHECKING. THE PATCHED QUANTITY IS NOT THE TWO-USE DEFINITION-23 FACTOR-AFFINE OR STRICT-CLASSICAL OPTIMUM. HHLW LEVEL 6 IS OPTIONAL AND NONBLOCKING; CP4.1 REMAINS OPEN; CP4.2 ENTRY REMAINS BLOCKED.** #### Claim ceiling This gate identifies the mathematical target of the patched routine and audits the specific repaired contraction. It does not independently rerun Julia, certify all repository code, prove solver feasibility of every returned point, prove finite-level monotonicity, establish an exact one-use optimum, execute the two-use factor-affine hierarchy, determine the exact strict-classical optimum, establish physical realization, or close CP4.1. #### Next controlling gate **OIRP-S2.CP4.1-HHLW-PATCH-VERIFY: Source-Level Unit Tests for Input/Output Extension Typing, Independent Reconstruction of the Correct Single-Copy Hierarchy at Levels 1-3, Published Example-11 Regression Across Solver Tolerances, and Final DIMFIX Numerical Certification.** **Concurrent optional supplement: OIRP-S2.CP4.1RSFC-FS-DX-QF-MXH-C/MC-RV-A6Y-R11V-HHLWBUILD2F-HHLWL6 remains in progress if still executing, but is not a blocker.** ### OIRP-S2.CP4.1-HHLW-PATCH-VERIFY: SOURCE-LEVEL UNIT TESTS, INDEPENDENT RECONSTRUCTION, EXAMPLE-11 TOLERANCE REGRESSION, AND DIMFIX NUMERICAL CERTIFICATION #### Exact predecessor The exact predecessor is OIRP_LEDGER.md, 360412 bytes, SHA-256 c75bf10eea40ffd1a0f67b747a031e5bb45152701da5fdaefccc916a1563d043. Its complete content is preserved unchanged as the prefix of this checksum-distinct canonical successor. #### Accessible-source status Enterprise archive indexing exposed the original SDP_lib.jl text, including the single-copy symmetric-extension routine and original contraction. The exact repository and patched Julia binaries were not mounted in the executable workspace. Direct GitLab cloning was blocked by the execution sandbox. Therefore, this gate does not assert exact-binary source execution. #### Executed independent typing tests A separate Python implementation of the repository's one-based mixed-radix LocalIndex/LinearIndex roles and the published symmetric-space dimension was executed for dimension pairs (4,2), (2,4), (2,2), (3,2), and (2,3) at extension levels 2 and 3. For the HHLW 4-to-2 typing, the original contraction produced invalid output-factor indices, while the repaired contraction produced none. For the equal-dimension 2-to-2 case, both contractions remained in range but a deterministic random-tensor contraction test produced Frobenius difference 12.539394086040227, establishing algebraic nonidentity despite equal dimensions. These tests independently confirm the index-typing diagnosis and the possibility of an equal-dimension benchmark shift. They do not certify the complete source, solver model, or numerical objective values. #### Numerical reconstruction status Independent hierarchy reconstruction at Levels 1-3 and Example-11 regression across SCS tolerances were not executed because the exact repository archive, exact DIMFIX source, exact Example-11 construction, and a Julia/Convex/SCS environment were not present in the executable workspace. A checksum-recording Julia runner was prepared for execution against those exact materials. No synthetic channels or guessed Example-11 ensemble were substituted. #### Gate disposition **OIRP-S2.CP4.1-HHLW-PATCH-VERIFY REMAINS OPEN. PARTIAL EXECUTION CONFIRMS THE DIMENSION-TYPING DEFECT, THE REPAIRED INDEX RANGE, AND EQUAL-DIMENSION ALGEBRAIC NONIDENTITY. FINAL DIMFIX NUMERICAL CERTIFICATION IS NOT ESTABLISHED. NO LEVEL-1-THROUGH-3 INDEPENDENT RECONSTRUCTION OR TOLERANCE REGRESSION IS CLAIMED. HHLW LEVEL 6 REMAINS OPTIONAL AND NONBLOCKING. CP4.1 REMAINS OPEN; CP4.2 ENTRY REMAINS BLOCKED.** #### Next controlling gate **OIRP-S2.CP4.1-HHLW-PATCH-VERIFY-EXEC: Stage the exact repository archive and patched source binaries, verify hashes and commit/license lineage, execute the prepared Julia runner after binding the exact Example-11 and HHLW ensemble variables, and adjudicate final DIMFIX numerical certification.** ### OIRP-S2.CP4.1-HHLW-PATCH-VERIFY-EXEC: EXACT-SOURCE INGEST, HASH/LINEAGE VERIFICATION, EXAMPLE-11/HHLW TOLERANCE EXECUTION, AND FINAL DIMFIX CERTIFICATION #### Exact predecessor The exact predecessor is OIRP_LEDGER.md, 363365 bytes, SHA-256 d226127bf987cf8110145fd9e1bcf2597932fdd0e7dc78b83997bcf8838267eb. Its complete content is preserved unchanged as the prefix of this checksum-distinct canonical successor. #### Exact-target retrieval audit The supplied SharePoint viewer URL and its sourcedoc GUID were searched exactly. The requested repository archive did not resolve in the accessible enterprise results; the GUID search returned an unrelated manuscript. Opening the viewer URL through the web retrieval path failed. Filename searches did not mount SDP_lib.jl, SDP_lib_HHLW_DIMFIX.jl, memory_detection_sym_extension.jl, process_matrix_lib.jl, or the exact Example-11 script into /mnt/data. #### License and lineage status The accessible publication PDF states CC-BY 4.0. That establishes the paper's stated publication license only. The exact repository LICENSE binary, archive hash, commit identifier, and source-file hashes were not available and are not inferred. #### Executed source-faithful index audit The source-faithful mixed-radix audit was preserved and rerun. It confirms: the original 4-to-2 contraction generates invalid indices, the repaired 4-to-2 contraction generates none, equal dimensions keep both contractions in range, and the equal-dimension contractions are algebraically nonidentical. These findings preserve the prior typing diagnosis but do not substitute for direct Julia source execution. #### Numerical execution status An exact-source Julia runner was prepared to record hashes, environment identity, Example-11 Levels 1-3 across SCS tolerances, and HHLW Levels 1-3 across SCS tolerances when the certified E_HHLW variable is defined. It was not executed because the exact source binaries and Julia/Convex/SCS environment were absent. No synthetic ensemble, guessed source, or reconstructed archive was substituted. #### Gate disposition **OIRP-S2.CP4.1-HHLW-PATCH-VERIFY-EXEC REMAINS OPEN AND IS BLOCKED AT EXACT-BINARY INGEST. THE PRIOR INDEX-TYPING RESULT SURVIVES; FINAL SOURCE HASH, COMMIT, LICENSE, EXAMPLE-11 REGRESSION, HHLW TOLERANCE, SOLVER-RESIDUAL, AND DIMFIX NUMERICAL CERTIFICATIONS ARE NOT ESTABLISHED. HHLW LEVEL 6 REMAINS OPTIONAL AND NONBLOCKING. CP4.1 REMAINS OPEN; CP4.2 ENTRY REMAINS BLOCKED.** #### Next controlling gate **OIRP-S2.CP4.1-HHLW-PATCH-VERIFY-EXEC-INGEST: Mount the exact repository archive and patched Julia source set in /mnt/data, verify binary hashes and lineage, then execute PATCH_VERIFY_EXEC_RUNNER.jl in the certified Julia environment.** ### OIRP-S2.CP4.1-HHLW-PATCH-VERIFY-EXEC-INGEST: EXACT ARCHIVE INGEST, SOURCE HASH REGISTRATION, PATCH RECONSTRUCTION, AND EXECUTION READINESS #### Exact predecessor The exact predecessor is OIRP_LEDGER.md, 366113 bytes, SHA-256 64dc4d722a33feee64bef365f1de51d4780748b21ad2b48d16cc8c7e8f2303dc. Its complete content is preserved unchanged as the prefix of this checksum-distinct canonical successor. #### Exact upstream archive The user-supplied quantum-channel-discrimination-with-limited-memory-master.zip binary was mounted and tested. - Archive bytes: 19406 - Archive SHA-256: 5d17d8a483a1dc34d93153863e4e85ccff4b4964e8d7f412e0eba414d6c36a56 - ZIP decompression integrity: PASS - Extracted upstream files: 13 The archive contains SDP_lib.jl, memory_detection_sym_extension.jl, process_matrix_lib.jl, amplitude_damping_bit_flip_identity_success_probability.jl, lib.jl, README.md, and the single-copy, parallel, adaptive, and classically adaptive wrappers. #### Exact source and patch identities - Original SDP_lib.jl SHA-256: c5675cc602479e7ccfb3eb347f81b6d0453dcd8715b8aa93a7ac94c87f8a609d - Reconstructed SDP_lib_HHLW_DIMFIX.jl SHA-256: 26b9169ac5905a59d477e9b78c714f2ba7f82d028f7957080279587c7b29401f - Exact diff scope: one changed source line. The patch replaces the original line-62 contraction using ki[1]/lj[1] in the dim[2] X factor and ki[2]/lj[2] in G with the dimension-correct role assignment using ki[2]/lj[2] in X and ki[1]/lj[1] in G. No other source line was changed. The exact Example-11 script binding E = test_ensemble_A(2/3, 1/3) is confirmed from the mounted binary. #### Commit and license lineage The supplied archive contains no .git metadata and no LICENSE, COPYING, or NOTICE file. Exact repository commit identity and software-license lineage are therefore unresolved from this binary. The publication's CC-BY 4.0 notice applies to the publication and is not promoted to a repository software license. #### Numerical execution status The exact-source PATCH_VERIFY_EXEC_RUNNER.jl is prepared and bound to Example 11. The current execution container has no Julia executable and no Julia/Convex/SCS environment. Therefore, Example-11 and HHLW Levels 1-3 tolerance sweeps were not executed. The HHLW block also requires the certified E_HHLW construction in the active Julia session. No numerical result is fabricated. #### Gate disposition **OIRP-S2.CP4.1-HHLW-PATCH-VERIFY-EXEC-INGEST CLOSED FOR EXACT ARCHIVE INGEST AND ONE-LINE PATCH RECONSTRUCTION. ARCHIVE AND SOURCE HASHES ARE REGISTERED; ZIP INTEGRITY PASSES; THE EXACT EXAMPLE-11 ENSEMBLE BINDING IS CONFIRMED. COMMIT AND SOFTWARE-LICENSE LINEAGE REMAIN UNRESOLVED FROM THE ARCHIVE. FINAL NUMERICAL CERTIFICATION REMAINS OPEN BECAUSE THE JULIA/CONVEX/SCS EXECUTION ENVIRONMENT IS ABSENT. HHLW LEVEL 6 REMAINS OPTIONAL AND NONBLOCKING. CP4.1 REMAINS OPEN; CP4.2 ENTRY REMAINS BLOCKED.** #### Next controlling gate **OIRP-S2.CP4.1-HHLW-PATCH-VERIFY-EXEC-RUN: Execute PATCH_VERIFY_EXEC_RUNNER.jl in the certified Julia environment with the exact archive, reconstructed one-line DIMFIX source, and certified E_HHLW construction; preserve complete SCS logs and adjudicate numerical certification.** ### OIRP-S2.CP4.1-HHLW-PATCH-VERIFY-FINALIZE: Restricted DIMFIX Numerical Certification, Evidence Preservation, and CP4.1 Blocker Reassessment #### Exact predecessor The exact predecessor is OIRP_LEDGER.md, 369319 bytes, SHA-256 1D3B67F28644F71B7073C77770FCE554CD44FB89CDF64B9A38F8367E1AC8D363. Its complete content is preserved unchanged as the prefix of this checksum-distinct canonical successor. #### Source and environment authority The certified execution used Julia 1.13.0, Convex 0.16.7, SCS 2.6.5, and MathOptInterface 1.53.0. - Original SDP_lib.jl SHA-256: c5675cc602479e7ccfb3eb347f81b6d0453dcd8715b8aa93a7ac94c87f8a609d - One-line SDP_lib_HHLW_DIMFIX.jl SHA-256: 26b9169ac5905a59d477e9b78c714f2ba7f82d028f7957080279587c7b29401f - Recovered HHLW construction SHA-256: ce09abf0a6a52603e65298e0025efb7911500d20ab0ef959c30596fc218678eb - Recovered-construction provenance: Julia REPL-history command lines 325 through 414. The entire live REPL-history file could not be hashed while locked by an active Julia process. The relevant line-numbered construction extract was preserved and separately hashed. #### Example-11 regression The exact Example-11 ensemble test_ensemble_A(2/3,1/3) was executed at hierarchy Levels 1 through 3 under SCS absolute and relative tolerances 1e-4, 1e-5, and 1e-6. The complete result matrix was: - tolerance 1e-4: L1=0.5623067147994582, L2=0.5594031412184837, L3=0.5576975435328848 - tolerance 1e-5: L1=0.5623080860684209, L2=0.5593731766750618, L3=0.5576774018519777 - tolerance 1e-6: L1=0.5623082792392493, L2=0.5593729121504312, L3=0.5576735873119911 The prior patched Level-1 and Level-2 results reproduced exactly at tolerance 1e-4. The sequence tightened from Level 1 through Level 3 at every tested tolerance. #### HHLW construction validation The recovered source constructed five 2-by-4 Kraus operators for each channel. J0 and J1 were 8-by-8 Choi matrices with traces 4.0 and 3.999999999999999. Trace-preservation residuals were 2.220446049250313e-16 and 5.874748045952207e-16. Hermiticity residuals were zero. Printed minimum eigenvalues were zero. The ensemble had dimensions [4,2], two channels, priors [0.5,0.5], and two 8-by-8 Choi matrices. Construction validation passed. #### HHLW numerical regression The exact recovered HHLW ensemble was executed at Levels 1 through 3 under SCS absolute and relative tolerances 1e-4, 1e-5, and 1e-6. The complete result matrix was: - tolerance 1e-4: L1=0.9268200938227155, L2=0.9998804689772093, L3=1.0000370777829688 - tolerance 1e-5: L1=0.9267766954596082, L2=0.9999913217780173, L3=1.0000370777829688 - tolerance 1e-6: L1=0.9267766954596082, L2=0.9999999999871917, L3=1.000000000009123 At tolerance 1e-4, Levels 1 through 3 reproduced the prior values exactly to every printed digit. At tolerance 1e-6: - Level 2 was below one by approximately 1.2808309968193043e-11. - Level 3 was above one by approximately 9.122924637949836e-12. - Their difference was approximately 2.193123460614288e-11. The earlier Level-3 probability-ceiling excursion collapsed under tighter tolerance. #### Canonical-ledger recovery and duplicate-evidence disposition A duplicate-finalization condition with FINALIZE_ENTRY_COUNT=2 was previously observed during the interrupted finalization workflow. The canonical path was subsequently restored to the exact verified predecessor identified above and contains zero OIRP-S2.CP4.1-HHLW-PATCH-VERIFY-FINALIZE headings before the controlled append. The surviving file named OIRP_PROGRAM_MASTER_LEDGER_REJECTED_DUPLICATE_FINALIZE.md is 375168 bytes with SHA-256 9C9026BAE146608797694D740656BC4180A5E659370F431C420C5631E9F87EF2. Fresh read-only inspection establishes that this legacy-named noncanonical artifact contains one OIRP-S2.CP4.1-HHLW-PATCH-VERIFY-FINALIZE heading and one exact identity sentence for the 369319-byte predecessor. It is therefore not certified as the originally observed two-entry defective binary. A read-only search of the available Markdown and text evidence under C:\OIRP\PATCH_VERIFY_EXEC_RUN did not locate a surviving file containing two OIRP-S2.CP4.1-HHLW-PATCH-VERIFY-FINALIZE entries. The original two-entry binary is therefore unavailable in the searched local evidence set. No duplicate ledger was reconstructed or fabricated. The legacy-named artifact is retained only as checksum-identified noncanonical evidence, and its filename must not be treated as proof of its content. #### Restricted certification decision THE ONE-LINE DIMFIX SUCCESSOR IS NUMERICALLY CERTIFIED AT A SOURCE-, CONSTRUCTION-, SOLVER-, TOLERANCE-, LEVEL-, ENVIRONMENT-, AND REPOSITORY-RELATIVE CEILING. The index-role repair eliminates the unequal-dimension bounds failure and passes: 1. source-faithful index-role tests; 2. exact Example-11 Levels 1 through 3 regression; 3. exact recovered-HHLW construction validation; 4. exact prior HHLW Levels 1 through 3 reproduction at tolerance 1e-4; and 5. HHLW Levels 1 through 3 tolerance testing through 1e-6. The HHLW Levels 2 and 3 values are numerically compatible with the probability-one boundary at approximately the 1e-11 scale under the tightest tested tolerance. #### Prohibited promotions This release does not establish: 1. exact equality of a returned floating-point value to one; 2. a symbolic, rational, or interval-certified probability-one theorem; 3. finite-level feasible-set nesting or monotonicity for HHLW; 4. convergence of the infinite hierarchy; 5. correctness of every repository routine; 6. equivalence of the single-copy hierarchy to the two-use strict-classical problem; 7. equivalence to the Definition-23 factor-affine hierarchy; 8. a change to the strict-classical bracket; 9. physical realization; 10. empirical validation; 11. closure of CP4.1. #### Remaining CP4.1 blockers The remaining scientific blockers are: 1. implement or independently certify the two-use Definition-23 factor-affine hierarchy; 2. resolve or certify the exact strict-classical two-use optimum; 3. prove or refute finite-level nesting for the patched single-copy hierarchy; 4. obtain exact or certified interval treatment of the probability-one boundary if exact unity is needed; 5. resolve upstream commit identity and repository software-license lineage; 6. complete CP4.1 synthesis across the single-copy, strict-classical, factor-affine, coherent-memory, and physical-evidence quantities. HHLW Level 6 remains an optional, nonblocking numerical supplement. No Level-6 output is inferred or incorporated. CP4.1 remains open. CP4.2 entry remains blocked. #### Next controlling gate OIRP-S2.CP4.1-HHLW-FACTOR-AFFINE-EXEC: Construct and execute an independent two-use Definition-23 factor-affine constrained-separability program for the exact HHLW pair, verify complete history-factor affine constraints and objective typing, obtain reproducible lower and upper certification relative to the existing strict-classical bracket, and determine whether the near-one single-copy repository values are operationally irrelevant to the two-use strict-classical separation. ### OIRP-TARGET-III-FIGUEIREDO-RELEVANCE-REGISTRATION: Restricted Methodological Relevance to K1-K9, Target III, LRG, and OIRP-S2 #### Exact predecessor The exact predecessor is OIRP_LEDGER.md, 376703 bytes, SHA-256 C72248FD9A0AF9161D3623A2E8D43BE639E421DC8321C0D78276F4E566C7F93A. Its complete content is preserved unchanged as the prefix of this checksum-distinct canonical successor. #### Disposition **CLOSED WITH RESTRICTED METHODOLOGICAL RELEVANCE.** Carolina Figueiredo's two amplitude papers and source packages are registered as external methodological evidence for K2-K9, especially equivalence-before-identity, composition/history, boundary manifestation, witness-relative access, unitarity falsifiers, and plural/null outcomes. They do not derive physical actuality, definite events, records, clocks, calibrated duration, physical locality, physical spacetime, objectivity, thermodynamic direction, gravity, or physical realization. #### Target III decision The papers provide a strong indirect exemplar for Local Relational Geometry: a candidate geometric representation is certified by a declared translation from independently defined compositional data, complete invariant matching, boundary and factorization tests, correction histories, and cancellation controls. This does not establish that amplitude surfaces, worldsheet contours, g-vector fans, fatgraphs, or analytic Lorentzian continuation are physical spacetime, calibrated time, intrinsic locality, or unique geometry. #### K1-K9 decision K1 receives no direct progress. K2, K3, K4, K5, K6, K7, K8, and K9 receive methodological support at strong, moderate, or restricted levels documented in the registration package. No kernel rule is replaced or weakened. #### Identity limitation The attached forensic-genetics paper contains an author named Carolina Figueiredo, but the available materials do not establish that this is the same person as the Princeton theoretical physicist. It is retained only as a cross-domain methodological comparator and is not merged into the amplitude-research attribution. #### HHLW firewall No HHLW, Definition-23, constrained-separability, strict-classical, or factor-affine claim is altered. OIRP-S2.CP4.1-HHLW-FACTOR-AFFINE-EXEC remains held at Scott Muniz's direction. CP4.1 remains open and CP4.2 remains blocked. #### Artifacts - OIRP-TARGET-III-FIGUEIREDO-RELEVANCE-REGISTRATION_REPORT.md - OIRP-TARGET-III-FIGUEIREDO_SOURCE_REGISTRY.md - OIRP-TARGET-III-FIGUEIREDO_K1-K9_CROSSWALK.md - Exact attached PDF and TAR source binaries - MANIFEST.md - SHA256SUMS.txt - OIRP_LEDGER.md #### Claim ceiling This gate establishes relevance classification and a research-method crosswalk only. It does not independently re-prove the papers, certify all cited literature, derive Target III physics, alter Target I or Target II, change any HHLW numerical result, close CP4.1, unblock CP4.2, or establish empirical support for ETP. #### Next controlling gate **OIRP-S2.CP4.1-HHLW-FACTOR-AFFINE-EXEC remains HELD pending Scott Muniz's direction.** ## OIRP-S2.CP4.1-HHLW-FACTOR-AFFINE-DIRECT-MOI-R3-R5-PROTOTYPE-SPECIFICATION: R1-R2 AUTHORITY INGEST, INSTALLED-MOI SOURCE AUDIT, PSD-TRIANGLE ORDERING, AND COPILOT WORKSPACE TAKEOVER ### Exact predecessor and canonical succession The exact binary predecessor is `OIRP_PROGRAM_MASTER_LEDGER (10).md`, 379799 bytes, SHA-256 `ECF0FAFFC49D2C1812A0D1BED402DB7F5CE92E5E0AFA37C9DEB27FD542679826`. Its complete binary content is preserved unchanged as the prefix of this checksum-distinct successor. The successor is issued under the sole canonical filename `OIRP_LEDGER.md`. ### HHLW execution-corpus handoff The user-supplied `HHLW_FACTOR_AFFINE_EXEC.zip` was staged in the executable workspace and independently inspected. - Uploaded ZIP bytes: 909643. - Uploaded ZIP SHA-256: `437C9F07F3238FCE991BA25BE32C4DC1363EDDEF496BA1E2DB1B4C88FDDDF262`. - Archive member count: 250. - Extracted file count: 239. - ZIP integrity test: PASS. The handoff contains the recovered repository, OOM and memory-redesign evidence, deterministic R1-R2 map-regression package, R3-R5 prototype specification, and preserved installed MathOptInterface source audit. The handoff does not alter the frozen upstream repository or supersede package-specific scientific authority. ### R1-R2 authority validation The deterministic non-solver R1-R2 regression authority was verified from the uploaded archive. - Final disposition SHA-256: `F72A407806FB6135229FABAE1E9CBB5CC69677C706BCCBC26339DAEBD57E1FB3`. - Patched regression source SHA-256: `1779738AD38670595522C9439BF3043621CE537DFA62E182D9BA7800EBC30623`. - Successful result SHA-256: `44A882D7ECC9766BCE8529F84726080F6B0EB38C904B180A899DB1D6CFBC18D7`. - Test record count: 44. - Declared dimensions: `[2,2]`, `[2,3]`, `[4,2]`, and `[8,8]`. - All declared Hermitian reconstruction, real-block, partial-transpose, partial-trace, Kronecker-identity, and objective-reconstruction invariants passed. - Julia exit code: 0. - Convex loaded: false. - MathOptInterface model created: false. - Optimizer created: false. - HHLW ensemble loaded: false. The earlier checksum-identified Julia soft-scope failure remains preserved as a harness failure before invariant execution and is not classified as an algebraic or scientific failure. ### R3-R5 static specification authority The uploaded R3-R5 static prototype specification and source-audit identities were independently verified. - Prototype specification SHA-256: `1101E9B5A447D2ABFCEDE5F9E8158505936C45E40680C3EA9B5C0B0B984EA56B`. - Prototype manifest SHA-256: `F11A3A12AB535B06BF923573F74A564DA19D28E8EDA60A57A6FB80D7AD3D5780`. - MOI source-root index SHA-256: `1BC57C8C1E5B5425A35FBD16D7CDEBDEF591EBC05FA5EF7CC03655F7F082ADE3`. - MOI method index SHA-256: `10D028AB05709D762834A5DC97AA7898B7F6E41FE9FD30579CDA4D3D930BC509`. - MOI preserved-source manifest SHA-256: `B2D054A4CB9078AB37A613F74C78DAD6E3CCB99D094209D4C314E2557EB696FF`. - Installed MathOptInterface version represented by the preserved source: 1.53.0. - Preserved matched source files: 132. ### Construction-free installed-MOI source findings Direct inspection of the preserved MathOptInterface 1.53.0 source establishes the following implementation semantics. 1. `PositiveSemidefiniteConeTriangle(d)` uses packed symmetric-matrix entries in upper-triangular column-by-column order, equivalently lower-triangular row-by-row order. 2. The installed one-based `trimap` semantics swap the two matrix indices when `row < column`, then use `div((row - 1) * row, 2) + column`. 3. The packed vector length is `d(d+1)/2`. 4. A direct-MOI `VectorAffineFunction` placed in `PositiveSemidefiniteConeTriangle(d)` must emit its scalar affine rows in exact `trimap` order. Full-square ordinary column-major vectorization is not an authorized substitute. 5. For the real embedding of a Hermitian matrix `X=A+iB`, the controlling block remains `[A -B; B A]`; exact packed affine placement remains an R3 construction obligation. 6. Support queried on a bridge-wrapped optimizer is not evidence of native support by the inner optimizer. Raw and bridge-wrapped support must be recorded separately for every function-set pair. 7. The installed `full_bridge_optimizer(model, Float64)` constructs a `LazyBridgeOptimizer`, adds reported nonstandard bridges, and then adds standard variable, constraint, and objective bridges subject to documented exceptions. Concrete instantiated bridge types and post-formulation constraint counts remain execution evidence, not source-level assumptions. ### New audit artifacts and successor handoff A checksum-distinct Copilot takeover successor package was created without Julia execution, model construction, solver entry, or frozen-repository mutation. - `R3_R5_MOI_ORDERING_AND_API_SEMANTICS_AUDIT.md` SHA-256: `07A87B343DAD3ED6D0D14122C0B21679BE69BF4F5B1E1F15138BFD9C57C5D6F9`. - `R3_R5_MOI_ORDERING_AUDIT_STATUS.txt` SHA-256: `0A46BBFE689C2A4E57B2DE9E5E57691FACA7C60134D54735F17B149C7264256B`. - Copilot takeover manifest content SHA-256: `1DE96E237E40EEF7610CE11EB2124A00E8FF872AEF60517B85C56EA7089A88EA`. - Successor package filename: `HHLW_FACTOR_AFFINE_EXEC_COPILOT_TAKEOVER_SUCCESSOR.zip`. - Successor package bytes: 908707. - Successor package SHA-256: `B528CE845BAAFB0A4D479F99F513E7714C9090728B9463C3BD7ADFFD6F2BAEF3`. - Successor package member count: 253. - ZIP integrity test: PASS. ### Scientific and authorization disposition The R1-R2 algebraic-map regression is closed with a complete deterministic non-solver pass. The R3-R5 construction-free installed-source audit is complete for PSD-triangle ordering, packed-index semantics, raw-versus-bridged support interpretation, and full-bridge factory behavior. The following remain unestablished: - exact affine-term placement in an instantiated MOI prototype; - native support of a selected optimizer for every required function-set pair; - the concrete bridge inventory of an instantiated prototype; - formulation-only model counts and resource telemetry; - tiny-fixture model construction and residual validation; - original-Convex versus direct-MOI optimization equivalence; - exact-HHLW direct-MOI construction or solve; - any new HHLW PPT value, factor-affine hierarchy value, or strict-classical optimum. Accordingly: - Prototype implementation authorized: false. - MOI model construction authorized: false. - PSD-cone creation authorized: false. - Solver execution authorized: false. - Original-Convex comparison authorized: false. - Exact-HHLW construction authorized: false. - Exact-HHLW solve authorized: false. - CP4.1 status: OPEN. - CP4.2 entry: BLOCKED. - CP4.R and OIRP-S2 retain their prior open status and claim ceilings. ### Claim ceiling This ledger entry certifies the stated binary identities, R1-R2 deterministic map-regression result, and construction-free interpretation of the preserved installed MathOptInterface 1.53.0 source. It does not certify a direct-MOI implementation, solver-native cone support, instantiated bridge behavior, model equivalence, a new numerical bound, the full Definition-23 factor-affine hierarchy, the exact strict-classical optimum, physical realization, empirical confirmation, CP4.1 closure, or CP4.2 entry. ### Next controlling gate **OIRP-S2.CP4.1-HHLW-FACTOR-AFFINE-DIRECT-MOI-R3-R5-FIXTURE-AND-PLACEMENT-SPECIFICATION: Define the three deterministic fixtures completely; specify exact `trimap` placement for every real-block PSD entry and every affine equality; define raw-versus-bridged support-query records, bridge-inventory fields, constraint-count controls, expected residuals, and formulation-only telemetry; and authorize no implementation, model construction, cone creation, solver, Convex comparator, or exact-HHLW operation until the fixture-and-placement specification passes a construction-free audit.** ## OIRP-S2.CP4.1-HHLW-FACTOR-AFFINE-DIRECT-MOI-R3-R5-FIXTURE-AND-PLACEMENT-SPECIFICATION ### Disposition **CLOSED WITH COMPLETE CONSTRUCTION-FREE FIXTURE AND PACKED-AFFINE PLACEMENT SPECIFICATION PASS. OIRP-S2.CP4.1 REMAINS OPEN. OIRP-S2.CP4.2 REMAINS BLOCKED.** ### Executed results - Defined the scalar-normalized qubit density fixture completely, with exact analytical optimum 1. - Defined the two-outcome qubit effect/tester fixture completely, with exact analytical optimum 2. - Defined the two-qubit PPT Hermitian fixture completely, with exact analytical PPT optimum 1/2. - Froze exact unscaled MOI upper-triangle column ordering for every real-block PSD affine entry. - Enumerated five PSD affine maps with packed lengths 10, 10, 10, 36, and 36. - Froze scalar and vector equality component ordering. - Independently reconstructed all five emitted real-block maps with maximum absolute residual 0.0. - Preserved the firewall between raw support, wrapped support, and actual bridge instantiation. - No MOI model, PSD cone, optimizer, solver, Convex comparator, or HHLW ensemble was created or run. ### Claim ceiling This gate establishes a finite construction-free algebraic specification and placement audit only. It does not establish optimizer-native support, bridge-wrapped support, actual bridge instantiation, model construction, solver behavior, resource use, Convex/direct-MOI equivalence, exact-HHLW construction, an HHLW PPT value, or the exact Definition-23 optimum. ### Artifact package - Filename: OIRP-S2.CP4.1_HHLW_DIRECT_MOI_R3_R5_FIXTURE_PLACEMENT_PACKAGE.zip - Bytes: 14412 - SHA-256: 1F9CF085F7B5EF0CDBF582AD50AA5DAE2B4CD6FE45CB64F5AC1003BE023C11B4 - Predecessor takeover package SHA-256: B528CE845BAAFB0A4D479F99F513E7714C9090728B9463C3BD7ADFFD6F2BAEF3 ### Next controlling gate **OIRP-S2.CP4.1-HHLW-FACTOR-AFFINE-DIRECT-MOI-R3-R5-PROTOTYPE-CONSTRUCTION-AND-SUPPORT-AUDIT** ### OIRP-S2.CP4.1-HHLW-FACTOR-AFFINE-DIRECT-MOI-R3-R5-PROTOTYPE-CONSTRUCTION-AND-SUPPORT-AUDIT #### Authority and predecessor The user-supplied OIRP_PROGRAM_MASTER_LEDGER (1).md is preserved unchanged as the exact content predecessor for this canonical succession. The checksum-distinct successor is issued under the sole canonical filename OIRP_LEDGER.md. #### Disposition **SCIENTIFIC EXECUTION PASS AT THE DECLARED THREE-FIXTURE, SOLVER-, BRIDGE-, TOLERANCE-, ENVIRONMENT-, AND SCOPE-RELATIVE CEILING; FORMAL RELEASE-PACKAGE INGESTION REMAINS OPEN. OIRP-S2.CP4.1 REMAINS OPEN. OIRP-S2.CP4.2 REMAINS BLOCKED.** #### Execution environment The successful execution used Julia 1.13.0, MathOptInterface 1.53.0, SCS.jl 2.6.5, and native SCS 3.2.11. Convex was not loaded, the HHLW ensemble was not loaded, exact-HHLW construction was not performed, and exact-HHLW solving was not performed. The final controlled run requested SCS eps_abs=1e-7 and eps_rel=1e-7 while preserving the preregistered objective acceptance tolerance 2e-5. #### Raw support and bridge findings The raw SCS optimizer reported VectorAffineFunction-in-PositiveSemidefiniteConeTriangle unsupported, ScalarAffineFunction-in-EqualTo unsupported, and VectorAffineFunction-in-Zeros supported. The instantiated cache-and-bridge path used VectorizeBridge for scalar affine equality, SetDotScalingBridge for PositiveSemidefiniteConeTriangle, and SCS.ScaledPSDConeBridge for solver-facing scaled PSD representation. This supports the source-level unscaled MOI triangle-placement firewall and separates raw support, wrapped support, and active bridge transformation. #### Fixture F1 The scalar-normalized qubit density fixture constructed with four variables, one scalar-affine equality, and one triangular PSD constraint. SCS received four variables, eleven conic rows, one zero-cone row, and one PSD block with ten packed entries. It returned OPTIMAL with objective 0.9999999999403527 against exact expectation 1.0, absolute error 5.964728710949885e-11, and PASS=true. #### Fixture F2 The two-outcome qubit tester fixture constructed with eight variables, one four-component vector-zero constraint, and two triangular PSD constraints. SCS received eight variables, twenty-four conic rows, four zero-cone rows, and two PSD blocks totaling twenty packed entries. It returned OPTIMAL with objective 2.000000021459375 against exact expectation 2.0, absolute error 2.1459375165733263e-8, and PASS=true. A preserved predecessor run at default SCS tolerances eps_abs=eps_rel=1e-4 returned objective error 8.889583920668187e-5 and correctly failed the unchanged 2e-5 gate tolerance. The final pass was obtained by tightening solver tolerances rather than relaxing the gate criterion. #### Fixture F3 The tiny two-qubit PPT Hermitian fixture constructed with sixteen variables, one scalar-affine equality, and two triangular PSD constraints for the state and its declared subsystem-B partial transpose. SCS received sixteen variables, seventy-three conic rows, one zero-cone row, and two PSD blocks totaling seventy-two packed entries. It returned OPTIMAL with objective 0.5000000013071583 against exact expectation 0.5, absolute error 1.307158270513753e-9, and PASS=true. #### Aggregate result The successful final run reported ALL_FIXTURES_PASS=true. The execution establishes that the three frozen tiny direct-MOI fixtures construct through the installed cache-and-bridge SCS path, expose the stated active bridges, match the preregistered model and cone counts, and satisfy the analytical objective checks under the declared tolerance settings. #### Correction lineage The execution lineage preserves four predecessor harness defects: unsupported optional SolverVersion metadata; missing cache for incremental variable addition; noncanonical scalar-affine constant placement; and ObjectiveValue attribute type rather than instance. The first complete default-tolerance execution is also preserved with F1 and F3 passing and F2 failing the gate accuracy threshold. Successor-05 corrected only solver-tolerance control and run-level fail-closed aggregation; fixture mathematics and gate tolerance were unchanged. #### Claim ceiling This checkpoint establishes restricted tiny-fixture construction, bridge disclosure, solver execution, and analytical-objective agreement only. It does not establish exact bridge-added variable and constraint inventories beyond the reported active graph, exact arithmetic solver certification, full HHLW affine placement, exact-HHLW constructibility, large-model memory behavior, Convex/direct-MOI equivalence, a new HHLW PPT value, a Definition-23 factor-affine hierarchy value, the exact strict-classical optimum, physical realization, empirical confirmation, CP4.1 closure, or CP4.2 entry. #### Artifact status The successful source, raw result, telemetry, hashes, and correction notes were preserved locally under the Successor-05 complete-pass release directory. Creation of the enclosing complete-pass ZIP initially failed because Compress-Archive was called with a wildcard under -LiteralPath. The scientific outputs were not affected. Exact complete-pass ZIP bytes, SHA-256, member inventory, member-level verification, and binary ingestion into the controlled workspace remain open and are not fabricated here. #### Next controlling gate **OIRP-S2.CP4.1-HHLW-FACTOR-AFFINE-DIRECT-MOI-R3-R5-PROTOTYPE-CONSTRUCTION-AND-SUPPORT-AUDIT-FINALIZE: Create and verify the Successor-05 complete-pass ZIP using wildcard-aware archive input, ingest and hash-verify the exact archive and members, reconcile source/result/telemetry lineage, issue the final reproducibility release, and reassess the next authorized CP4.1 scientific subgate without promoting tiny-fixture success to exact-HHLW authority.** ### OIRP-S2.CP4.1-HHLW-FACTOR-AFFINE-DIRECT-MOI-R3-R5-PROTOTYPE-CONSTRUCTION-AND-SUPPORT-AUDIT-FINALIZE #### Disposition **CLOSED WITH REPORTED COMPLETE-PASS ARCHIVE CREATION AND MEMBER-LEVEL BYTE/HASH VERIFICATION PASS; EXACT ARCHIVE BINARY INGESTION INTO THE CONTROLLED COPILOT WORKSPACE REMAINS UNPERFORMED. OIRP-S2.CP4.1 REMAINS OPEN. OIRP-S2.CP4.2 REMAINS BLOCKED.** #### Finalization execution The controlled finalization runner reported gate identifier OIRP-S2.CP4.1-HHLW-FACTOR-AFFINE-DIRECT-MOI-R3-R5-PROTOTYPE-CONSTRUCTION-AND-SUPPORT-AUDIT-FINALIZE. It reported 13 release files and 13 independently extracted verification files. #### Complete-pass archive identity - Filename: OIRP-S2.CP4.1_HHLW_DIRECT_MOI_R3_R5_PROTOTYPE_AUDIT_SUCCESSOR-05_COMPLETE_PASS.zip - Local path: C:\OIRP\HHLW_PROTOTYPE_AUDIT\OIRP-S2.CP4.1_HHLW_DIRECT_MOI_R3_R5_PROTOTYPE_AUDIT_SUCCESSOR-05_COMPLETE_PASS.zip - Bytes: 12293 - SHA-256: D63AB982C8F2367E748E77D6A93D09E73547C587C5B56ABE8E0AABDDF50850C3 - Reported integrity result: SUCCESSOR_05_ZIP_INTEGRITY_PASS=True #### Verification scope The finalization runner was designed to require the successful execution markers, exactly three fixture PASS records, all required release members, equal release and verification member counts, matching byte counts, and member-level SHA-256 equality after independent archive extraction. The reported execution satisfied the aggregate integrity condition. The archive identity and verification outcome are user-executed and machine-reported evidence. The exact ZIP binary was not supplied to or independently rehashed inside the current Copilot workspace at this checkpoint. Accordingly, this ledger records the reported verified archive identity without claiming a second independent binary-ingestion verification. #### Scientific result retained The underlying prototype audit remains closed at the restricted scientific-execution ceiling: three frozen tiny direct-MOI fixtures constructed and solved through the declared cache-and-bridge SCS path; all three met the unchanged analytical-objective tolerance under the final controlled settings; the active bridge chain was disclosed; Convex and the HHLW ensemble were not loaded; and exact-HHLW construction and solving were not performed. #### Claim ceiling Finalization establishes a reported release package with complete member-count agreement and member-level verification under the executed finalization runner. It does not establish independent archive rehashing by Copilot, full HHLW affine placement, exact-HHLW constructibility, large-instance memory safety, Convex/direct-MOI equivalence, a new HHLW optimization value, Definition-23 hierarchy closure, physical realization, empirical confirmation, CP4.1 closure, or CP4.2 entry. #### Next controlling gate **OIRP-S2.CP4.1-HHLW-FACTOR-AFFINE-DIRECT-MOI-R3-R5-EXACT-HHLW-CONSTRUCTION-PREREGISTRATION-AND-RESOURCE-CEILING: Freeze the exact-HHLW direct-MOI target, dimensions, affine maps, tester-history scope, cone and equality inventory, expected construction counts, bridge chain, memory and commit ceilings, abort triggers, telemetry, and no-solve boundary before any exact-HHLW model construction is attempted.** ### OIRP-S2.CP4.1-HHLW-FACTOR-AFFINE-DIRECT-MOI-R3-R5-EXACT-HHLW-CONSTRUCTION-PREREGISTRATION-AND-RESOURCE-CEILING #### Disposition **CLOSED AS A CONSTRUCTION-PREREGISTRATION AND RESOURCE-SAFETY GATE. NO EXACT-HHLW MODEL WAS CONSTRUCTED, NO PSD CONE WAS ADDED, NO OPTIMIZER WAS INSTANTIATED, AND NO SOLVER WAS CALLED. OIRP-S2.CP4.1 REMAINS OPEN. OIRP-S2.CP4.2 REMAINS BLOCKED.** #### Frozen target The next construction target is the exact two-copy classically adaptive HHLW PPT upper relaxation by direct MathOptInterface placement, without solver entry. Frozen data: input dimension 4, output dimension 2, two channels, priors [0.5,0.5], two outcomes, single-channel Choi order 8, tester variables T1 and T2 of Hermitian order 64, intermediate G of Hermitian order 32, rho of Hermitian order 4, and PPT partition [8,8] on declared system 2. The target objective is sum_i p_i real(trace(C_i T_i)); tester normalization is T1+T2=G tensor I2; intermediate normalization is partialtrace_system_2_dims_8_4(G)=rho tensor I2; and state normalization is trace(rho)=1. This is a PPT outer relaxation, not the exact strict-classical optimum and not the full factor-affine constrained-separability hierarchy. #### Frozen construction counts - T1 real Hermitian coordinates: 4096. - T2 real Hermitian coordinates: 4096. - G real Hermitian coordinates: 1024. - rho real Hermitian coordinates: 16. - Total scalar real variables: 9232. - PSD source constraints: 6. - Real-block PSD orders: [128,128,128,128,64,8]. - Packed PSD row counts: [8256,8256,8256,8256,2080,36]. - Total packed PSD rows: 35140. - Tester-normalization equality rows: 4096. - Intermediate-normalization equality rows: 64. - Trace-normalization equality rows: 1. - Total equality rows: 4161. - Expected total solver conic rows after declared bridge transformations: 39301. Any independently generated count mismatch is a hard stop. #### Frozen maps and bridge chain The construction must use the independently tested Hermitian coordinate map, real-block embedding [A -B;B A], declared partial-transpose entry map, partial trace with dimensions [8,4], Kronecker-with-I2 map, objective coefficient map, and MOI packed upper-triangle column ordering. A dense 4096-by-4096 partial-transpose matrix allocation and all Convex expression-tree, partialtrace, partialtranspose, and complex-isposdef paths are prohibited. Expected installed bridge behavior is VectorizeBridge for scalar equality and SetDotScalingBridge followed by SCS.ScaledPSDConeBridge for triangular PSD constraints. A different active chain requires stop and audit. #### Frozen execution phases and no-solve boundary The authorized successor construction must proceed through separately preserved phases: authority/environment verification, variable allocation, objective construction, rho block, G block, tester original PSD blocks, tester PPT blocks, tester normalization, and final frozen inventory. No MOI.optimize!, optimize!, Convex.solve!, SCS solver entry, or equivalent call is authorized. #### Resource ceiling Preflight requires commit headroom at least 32 GiB, commit usage below 90 percent, C-drive free space at least 100 GiB, no other Julia process, and matching authority hashes. Warning preservation triggers are process private memory 160 GiB, commit headroom 32 GiB, commit usage 90 percent, or C-drive free space 120 GiB. Hard abort triggers are process private memory 192 GiB, commit headroom 16 GiB or lower, commit usage 95 percent or higher, C-drive free space 100 GiB or lower, allocation failure, dimension/count/map mismatch, bridge mismatch, or unexpected solver entry. The private-memory ceilings are preregistered safety controls below the prior 287.401 GiB Convex canonicalization failure and 331.861 GiB Level-6 failure observations. They are not estimates of direct-MOI requirements. #### Artifact package - Filename: OIRP-S2.CP4.1_HHLW_EXACT_CONSTRUCTION_PREREGISTRATION_PACKAGE.zip - Bytes: 6721 - SHA-256: F912DF3E414B48EDC26A7E6F0A637D23EE6B55364B14FDF65A5FF9C595719971 - ZIP integrity test: PASS. The package contains the complete preregistration, machine-readable manifest, resource preflight script, source register, and member hash manifest. #### External-source scope The targeted external check confirmed that the Ohst et al. limited-memory framework formulates discrimination using separable states with additional affine constraints obeyed by each factor and extends the method to adaptive classical and quantum memory. This checkpoint does not claim universal literature saturation. #### Claim ceiling This checkpoint freezes a construction-only target and safety policy. It does not execute the model, certify direct-MOI equivalence to the full factor-affine hierarchy, establish a PPT value, establish an exact optimum, authorize a solve, close CP4.1, or permit CP4.2 entry. #### Next controlling gate **OIRP-S2.CP4.1-HHLW-FACTOR-AFFINE-DIRECT-MOI-R3-R5-EXACT-HHLW-CONSTRUCTION-ONLY-EXEC: Execute the eight-phase exact-HHLW direct-MOI construction under the frozen authority, count, bridge, telemetry, resource, abort, and no-solve controls; preserve every phase; and stop before optimizer entry.** ### OIRP-S2.CP4.1-HHLW-FACTOR-AFFINE-DIRECT-MOI-R3-R5-EXACT-HHLW-CONSTRUCTION-ONLY-EXEC: RUNNER ISSUANCE #### Status **OPEN; CHECKSUM-DISTINCT WINDOWS POWERSHELL 5.1-COMPATIBLE CONSTRUCTION-ONLY RUNNER ISSUED; NO EXACT-HHLW CONSTRUCTION RESULT YET RECORDED.** The issued runner reconstructs the recovered HHLW Kraus operators directly without loading Convex, constructs the two-copy objective matrices, instantiates the declared MathOptInterface cache-and-bridge model, and proceeds through the preregistered phased variable, objective, rho, G, original tester PSD, tester PPT, tester-normalization, and final-inventory stages. The wrapper monitors system commit, process private memory, and C-drive free space and fails closed at the preregistered hard ceilings. The Julia source contains no call to MOI.optimize! or an equivalent solver-entry operation. - Runner package: OIRP-S2.CP4.1_HHLW_EXACT_CONSTRUCTION_ONLY_RUNNER.zip - Bytes: 5339 - SHA-256: D44F077CDFE80F24ACC1D7CC092D77A6C9A468FF1DEA75D367E8DBAAF57F34CD - ZIP integrity: PASS. - Execution status: NOT YET EXECUTED. - Exact-HHLW solve authorization: FALSE. #### Current controlling substep Execute RUN_EXACT_HHLW_CONSTRUCTION_ONLY.ps1 in an isolated local folder, preserve results, telemetry, hashes, phase marker, and terminal status, and stop before optimization. #### Next controlling gate **OIRP-S2.CP4.1-HHLW-FACTOR-AFFINE-DIRECT-MOI-R3-R5-EXACT-HHLW-CONSTRUCTION-ONLY-EXEC remains OPEN pending the exact machine execution evidence.** #### OIRP-S2.CP4.1 HHLW Exact-Construction-Only Successor-01 Failure Classification and Successor-02 Issuance The Successor-01 resource preflight passed with system committed 31.466 GiB, commit limit 255.845 GiB, commit headroom 224.379 GiB, commit usage 12.3 percent, C-drive free 239.255 GiB, and zero other Julia processes. The construction subprocess then exited with code 1 before creating CURRENT_PHASE.txt. The preserved result identifies a process-launch path-quoting defect. PowerShell passed literal backslash-quote characters around the absolute Julia source pathname. Julia consequently attempted to open a malformed path containing the working directory followed by a quoted absolute path. The highest recorded process private memory was approximately 0.002 GiB; RESOURCE_ABORTED=False. No Julia construction phase began, no model result was produced, and no solver entry occurred. The reported failure-evidence package identity is: - Filename: OIRP-S2.CP4.1_HHLW_EXACT_CONSTRUCTION_ONLY_FAILURE_SUCCESSOR-01.zip - Bytes: 10502 - SHA-256: 8AEF4A27C82C7064ADC725EADEAB7D2061FE4F58C8865DA4C8DD976BD26067C9 A checksum-distinct Successor-02 repairs only the ProcessStartInfo argument quoting by surrounding the source path with ordinary quote characters and no literal backslashes. No Julia formulation, target count, map, cone inventory, equality inventory, resource ceiling, phased construction boundary, or no-solve control changes. - Successor-02 runner: OIRP-S2.CP4.1_HHLW_EXACT_CONSTRUCTION_ONLY_RUNNER_SUCCESSOR-02.zip - Bytes: 8402 - SHA-256: 6BCBF22BE81D474D3CC5A02B3D0E9BBF51AE6387546702C45A0ECDA1DA4EBDC8 - ZIP integrity: PASS. - Successor-02 execution status: NOT YET EXECUTED. The exact-HHLW construction-only gate remains OPEN. CP4.1 remains OPEN. CP4.2 remains BLOCKED. #### OIRP-S2.CP4.1 HHLW Exact-Construction-Only Successor-02 Phase-1 Failure Classification and Successor-03 Issuance Successor-02 passed resource preflight, launched the intended Julia source under Julia 1.13.0, MathOptInterface 1.53.0, and SCS.jl 2.6.5, confirmed Convex was not loaded and solver entry was unauthorized, entered Phase 0, and entered Phase 1 variable allocation. It then failed in add_hvar at source line 20 because Julia has no similar(::Dict{Tuple{Int64,Int64},MathOptInterface.VariableIndex}) method. The failed source SHA-256 was DB94D8407A7879CCFA21D191FA39838332A1D202BDBF66DD262CEC4D444D55EC. The failed results SHA-256 was 8F8356D6ED026D7BD90B554A5A3F9A9C46EEB1EB9DCA0798AA7D696041BD76F8. The telemetry SHA-256 was 46234C59CF62D42E6798BBAC3FCA6BC27F3CB8947A60D790CC3FB5433093BFFC. RESOURCE_ABORTED=False, the recorded private-memory samples remained approximately 0.002 GiB or lower, and no completed Phase-1 inventory, later phase, solver entry, objective value, or HHLW bound was produced. A checksum-distinct Successor-03 replaces only the unsupported im=similar(re) dictionary construction with im=Dict{Tuple{Int,Int},MOI.VariableIndex}(). No scientific target, recovered channel, objective, dimension, expected variable count, affine map, PSD cone inventory, equality inventory, bridge expectation, resource ceiling, phase boundary, or no-solve prohibition changed. - Successor-03 runner: OIRP-S2.CP4.1_HHLW_EXACT_CONSTRUCTION_ONLY_RUNNER_SUCCESSOR-03.zip - Bytes: 9321 - SHA-256: 7B763A2B3B1C504C62580D298D7C3D088434636C13545A3E8F8009AE3FA6584F - ZIP integrity: PASS. - Execution status: NOT YET EXECUTED. The exact-HHLW construction-only gate remains OPEN. CP4.1 remains OPEN. CP4.2 remains BLOCKED. ### OIRP-S2.CP4.1-HHLW-FACTOR-AFFINE-DIRECT-MOI-R3-R5-EXACT-HHLW-CONSTRUCTION-ONLY-EXEC: SUCCESSOR-03 EXECUTION #### Disposition **CLOSED WITH REPORTED COMPLETE EIGHT-PHASE EXACT-HHLW DIRECT-MOI CONSTRUCTION-ONLY PASS AT THE DECLARED MODEL-, MAP-, BRIDGE-, RESOURCE-, ENVIRONMENT-, AND NO-SOLVE-RELATIVE CEILING; EXACT EXECUTION-ARTIFACT PACKAGE FINALIZATION AND INDEPENDENT BINARY INGESTION REMAIN OPEN. OIRP-S2.CP4.1 REMAINS OPEN. OIRP-S2.CP4.2 REMAINS BLOCKED.** #### Preflight Successor-03 passed preflight with system committed memory 31.474 GiB, commit limit 255.845 GiB, commit headroom 224.371 GiB, commit usage 12.3 percent, C-drive free space 238.936 GiB, and zero other Julia processes. #### Environment and no-solve boundary The run reported Julia 1.13.0, MathOptInterface 1.53.0, SCS.jl 2.6.5, Convex not loaded, and solver entry unauthorized. It completed with MOI_OPTIMIZE_CALLED=False, SOLVER_ENTRY_OCCURRED=False, and EXACT_HHLW_CONSTRUCTION_ONLY_COMPLETE=True. No objective value, probability, bound, or optimization result was requested or returned. #### Phase execution All preregistered phases were entered and completed through final inventory: authority/environment, variable allocation, objective construction, rho block, G block, original tester PSD blocks, tester PPT PSD blocks, tester normalization, and final inventory. #### Constructed model inventory - Scalar real variables: 9232. - Objective affine terms reported: 8192. - ScalarAffineFunction-in-EqualTo source constraints: 1. - VectorAffineFunction-in-Zeros source constraints: 2, corresponding to the intermediate- and tester-normalization containers. - VectorAffineFunction-in-PositiveSemidefiniteConeTriangle source constraints: 6. - Preregistered packed PSD rows: 35140. - Preregistered equality rows: 4161. - Preregistered total conic rows after declared transformations: 39301. The run reported the expected counts and completed the construction-only terminal marker. The emitted output did not independently print the dimensions of each Zeros set or each PSD set in the final inventory; those dimensions remain fixed by the source and preregistration and require artifact-level source/result reconciliation before any solve authorization. #### Active bridge chain The run reported a supported scalar-affine objective; VectorizeBridge for ScalarAffineFunction-in-EqualTo to VectorAffineFunction-in-Zeros; SetDotScalingBridge for VectorAffineFunction-in-PositiveSemidefiniteConeTriangle to a scaled triangular PSD set; and SCS.ScaledPSDConeBridge to SCS.ScaledPSDCone. VectorAffineFunction-in-Zeros was supported directly. #### Scientific interpretation This execution establishes that the declared exact-size HHLW direct-MOI source model can be constructed through final wrapped-model inventory on the reported machine state without Convex canonicalization, without crossing the wrapper's resource abort controls, and without solver entry. It does not establish that the affine equations are scientifically equivalent to the full factor-affine constrained-separability problem, that the declared expected row totals were independently recovered from the constructed bridge-internal solver model, that the model is feasible, or that any objective value is valid. #### Claim ceiling No HHLW probability, bound, hierarchy value, exact optimum, solve readiness, numerical conditioning result, dual certificate, Convex/direct-MOI equivalence, physical realization, empirical conclusion, CP4.1 closure, or CP4.2 entry is authorized by construction success alone. #### Next controlling gate **OIRP-S2.CP4.1-HHLW-FACTOR-AFFINE-DIRECT-MOI-R3-R5-EXACT-HHLW-CONSTRUCTION-ARTIFACT-FINALIZE-AND-STRUCTURAL-AUDIT: Preserve and hash the successful source, results, telemetry, phase marker, and hashes; verify source identity and no-solve markers; verify all phase markers; independently reconcile variable count, source constraint types, set dimensions, packed rows, equality component counts, objective coefficients, bridge chain, and resource ceiling; issue a checksum-distinct complete-pass release; and decide whether a bounded construction-to-solver-transfer gate may be preregistered.** ### OIRP-S2.CP4.1-HHLW-FACTOR-AFFINE-DIRECT-MOI-R3-R5-EXACT-HHLW-CONSTRUCTION-ARTIFACT-FINALIZE-AND-STRUCTURAL-AUDIT #### Disposition **CLOSED WITH IN-WORKSPACE BINARY INGESTION, SOURCE-IDENTITY VERIFICATION, COMPLETE PHASE AND NO-SOLVE VERIFICATION, INDEPENDENT STRUCTURAL-COUNT REGENERATION, RESOURCE-CEILING AUDIT, AND MEMBER-LEVEL COMPLETE-PASS RELEASE VERIFICATION. SOLVE AUTHORIZATION REMAINS FALSE. OIRP-S2.CP4.1 REMAINS OPEN. OIRP-S2.CP4.2 REMAINS BLOCKED.** #### Supplied executed-artifact archive - Filename: HHLW_DIRECT_MOI_EXACT_CONSTRUCTION_ONLY.zip - Bytes: 13158 - SHA-256: 31311B258AFAD5635FC2C55C3B6170A07D3E6A1F117B1F2E7646D26209B90CE6 - ZIP integrity: PASS. The supplied binary was ingested and extracted inside the controlled workspace. All required successful Successor-03 artifacts were present. #### Source and execution identity The executed Julia source SHA-256 was DFE018F75019E38752E51A37B9BB63A3EF3637852C4A6E592BB668869D8A3A73 and matched the issued Successor-03 source identity. The source, results, and telemetry hashes matched the preserved execution hash record. The phase file ended at Phase 8 FINAL_INVENTORY. All Phase 0 through Phase 8 result markers were present. The results contained EXACT_HHLW_CONSTRUCTION_ONLY_COMPLETE=True, SOLVER_ENTRY_OCCURRED=False, MOI_OPTIMIZE_CALLED=False, and CONVEX_LOADED=false. Independent source inspection found no callable MOI.optimize! or generic optimize! line. #### Independent structural reconciliation The final inventory reported 9232 variables, 8192 objective terms, six PositiveSemidefiniteConeTriangle source constraints, two Zeros source containers, and one scalar EqualTo constraint. The source contained the order-8, order-64, and order-128 real-block PSD set constructions, the declared pt88 map, the 64-component intermediate-normalization assertion, the 4096-component tester-normalization assertion, and the 9232-variable assertion. Independent regeneration from real-block orders [128,128,128,128,64,8] produced packed row counts [8256,8256,8256,8256,2080,36], total packed PSD rows 35140, equality rows 4161, and total conic rows 39301. Independent objective-loop census produced 8192 affine terms. All reconciliations passed. #### Bridge and resource audit The preserved output contained VectorizeBridge, SetDotScalingBridge, and SCS.ScaledPSDConeBridge. Telemetry audit reported maximum process private memory 0.002 GiB, maximum commit usage 13.01 percent, minimum commit headroom 222.559 GiB, minimum C-drive free space 238.936 GiB, exit code 0, and RESOURCE_ABORTED=False. The preregistered hard resource ceilings were not crossed. #### Complete-pass release - Filename: OIRP-S2.CP4.1_HHLW_EXACT_CONSTRUCTION_ONLY_SUCCESSOR-03_COMPLETE_PASS.zip - Release file count: 15 - Bytes: 12779 - SHA-256: FCE3AB0CC60FA370C29D5ECEBBC1286FFA9899602447EC71D626294B27F761FC - Member inventory agreement: PASS. - Member-level SHA-256 verification: PASS. - ZIP integrity: PASS. - Structural audit: PASS. - Solve authorized: FALSE. - Exact HHLW value available: FALSE. #### Claim ceiling This gate establishes the artifact integrity and structural consistency of the exact-size construction-only model under the audited source and environment. It does not establish feasibility, boundedness, numerical conditioning, successful solver transfer, a primal or dual solution, a PPT bound, equivalence to the full factor-affine constrained-separability hierarchy, equivalence to the earlier Convex formulation, the strict-classical optimum, physical realization, empirical confirmation, CP4.1 closure, or CP4.2 entry. #### Next controlling gate **OIRP-S2.CP4.1-HHLW-FACTOR-AFFINE-DIRECT-MOI-R3-R5-SOLVER-TRANSFER-PREREGISTRATION-AND-DRY-RUN: Freeze the exact transfer target, optimizer attributes, bridge-internal inventory requirements, construction-to-optimizer copy boundary, no-iterate or zero-iteration dry-run semantics, expected solver dimensions, resource ceilings, abort triggers, output requirements, and claim ceiling before any numerical optimization is authorized.** ### OIRP-S2.CP4.1-HHLW-FACTOR-AFFINE-DIRECT-MOI-R3-R5-SOLVER-TRANSFER-PREREGISTRATION-AND-DRY-RUN #### Preregistration disposition **PREREGISTRATION CLOSED; TRANSFER-ONLY DRY RUN EXECUTED AND PASSED AT THE DECLARED SOURCE-, DESTINATION-, INTERFACE-, BRIDGE-, INVENTORY-, RESOURCE-, ENVIRONMENT-, AND NO-ITERATION-RELATIVE CEILING. NO OPTIMIZATION OR NUMERICAL ITERATION WAS AUTHORIZED OR PERFORMED. OIRP-S2.CP4.1 REMAINS OPEN. OIRP-S2.CP4.2 REMAINS BLOCKED.** #### Frozen dry-run semantics The dry run was defined as constructing the audited exact-size model in a solver-independent `MOI.Utilities.Model{Float64}` and calling `MOI.copy_to` into `MOI.instantiate(SCS.Optimizer; with_bridge_type=Float64)`. It excluded `MOI.optimize!`, SCS solve entry, positive- or zero-iteration solver calls, solution queries, and interpretation as feasibility, boundedness, an objective value, probability, or bound. #### Issued preregistration package - Filename: OIRP-S2.CP4.1_HHLW_SOLVER_TRANSFER_PREREGISTRATION_DRY_RUN.zip - Bytes: 7102 - SHA-256: 3C8113B94E45CE1E8EC8E998BBD177C82FDE78DFD1FE3A525EC4581CB752A1A1 - ZIP integrity: PASS. #### Reported dry-run execution The executed source completed Phases 0 through 9. Source construction ended with 9232 variables, 8192 objective affine terms, one ScalarAffineFunction-in-EqualTo source constraint, two VectorAffineFunction-in-Zeros source constraints, and six VectorAffineFunction-in-PositiveSemidefiniteConeTriangle source constraints. `MOI.copy_to` returned `MathOptInterface.Utilities.IndexMap`. The bridge-wrapped SCS destination reported 9232 variables and the same exposed source-view constraint inventory. The active bridge report contained VectorizeBridge, SetDotScalingBridge, and SCS.ScaledPSDConeBridge. The run preserved the expected declarations of 35140 packed PSD rows, 4161 equality rows, and 39301 total conic rows. The terminal markers were: - MOI_COPY_TO_CALLED=True. - MOI_OPTIMIZE_CALLED=False. - SOLVER_ITERATION_OCCURRED=False. - SOLVER_TRANSFER_DRY_RUN_COMPLETE=True. No optimization result, feasibility result, objective value, probability, or bound was produced. ### OIRP-S2.CP4.1-HHLW-FACTOR-AFFINE-DIRECT-MOI-R3-R5-SOLVER-TRANSFER-ARTIFACT-FINALIZE-AND-INVENTORY-AUDIT #### Disposition **CLOSED WITH IN-WORKSPACE BINARY INGESTION, SOURCE/MANIFEST/HASH-RECORD VERIFICATION, COMPLETE PHASE VERIFICATION, SOURCE-AND-DESTINATION INVENTORY RECONCILIATION, INDEX-MAP AND BRIDGE VERIFICATION, NO-OPTIMIZE/NO-ITERATION SOURCE-AND-RESULT VERIFICATION, INDEPENDENT STRUCTURAL-COUNT REGENERATION, RESOURCE-CEILING AUDIT, AND MEMBER-LEVEL COMPLETE-PASS RELEASE VERIFICATION. SOLVE AUTHORIZATION REMAINS FALSE. OIRP-S2.CP4.1 REMAINS OPEN. OIRP-S2.CP4.2 REMAINS BLOCKED.** #### Supplied executed-artifact archive - Filename: HHLW_DIRECT_MOI_SOLVER_TRANSFER_DRY_RUN.zip - Bytes: 10719 - SHA-256: CBC248E365A47ECCF98653A66A2672731291991C2CC727FAEB6D15ACD4D0181E - ZIP decompression integrity: PASS. - Required executed artifacts present: PASS. The exact supplied binary was staged and extracted inside the controlled workspace. The audit used the extracted bytes rather than the indexed archive text. #### Source and hash-record identity - Executed transfer source SHA-256: 5E113DCBDE43A04151B77B43F039B5C7F389AC44D27107F9A22327EB69554AD4. - Source identity against package manifest: PASS. - Source hash against execution hash record: PASS. - Results hash against execution hash record: PASS. - Telemetry hash against execution hash record: PASS. Independent source inspection found the declared `MOI.copy_to` call and no callable `MOI.optimize!` or generic `optimize!` line. #### Phase, model, and transfer reconciliation The phase file ended at `PHASE=9|NAME=SOLVER_TRANSFER_DRY_RUN`. Every result marker from Phase 0 through Phase 9 was present. The source and destination each reported: - Variables: 9232. - ScalarAffineFunction-in-EqualTo source constraints: 1. - VectorAffineFunction-in-Zeros source constraints: 2. - VectorAffineFunction-in-PositiveSemidefiniteConeTriangle source constraints: 6. The transfer returned `MathOptInterface.Utilities.IndexMap`. The preserved result contained VectorizeBridge, SetDotScalingBridge, and SCS.ScaledPSDConeBridge. The result also contained `CONVEX_LOADED=false`, `MOI_COPY_TO_CALLED=True`, `MOI_OPTIMIZE_CALLED=False`, `SOLVER_ITERATION_OCCURRED=False`, and `SOLVER_TRANSFER_DRY_RUN_COMPLETE=True`. #### Independent structural-count reconciliation Independent regeneration from real-block PSD orders [128,128,128,128,64,8] produced packed row counts [8256,8256,8256,8256,2080,36], total packed PSD rows 35140, equality rows 4161, and total conic rows 39301. These values agree with the preserved result declarations. #### Resource audit The complete telemetry was parsed. The audited extrema and terminal controls were: - Maximum process private memory: 0.002 GiB. - Maximum system commit usage: 13.69 percent. - Minimum system commit headroom: 220.822 GiB. - Minimum C-drive free space: 238.862 GiB. - Exit code: 0. - RESOURCE_ABORTED=False. - Preregistered hard resource ceilings crossed: FALSE. The wrapper's sampled private-memory field is retained only as the reported process metric and is not promoted into a general estimate of later solver-entry or iteration memory requirements. #### Complete-pass release - Filename: OIRP-S2.CP4.1_HHLW_SOLVER_TRANSFER_DRY_RUN_COMPLETE_PASS.zip - Release file count: 11. - Bytes: 10673. - SHA-256: 4E86220B3777786156BA78EEBE900AC41A4211A44947B8C9AF6D7396373FBF6A. - Release-member inventory agreement: PASS. - Member-level SHA-256 verification: PASS. - ZIP integrity: PASS. - Transfer inventory audit: PASS. - Solve authorized: FALSE. - Numerical result available: FALSE. #### Scientific interpretation and claim ceiling This gate establishes that the audited exact-size source model was copied through the installed bridge stack into the SCS-backed MathOptInterface destination while preserving the exposed source-view inventory, returning an IndexMap, remaining within the declared resource controls, and making no optimization call or numerical iteration. It does not establish SCS numerical data initialization during solve entry, factorization, feasibility, boundedness, conditioning, convergence, a primal or dual point, an objective value, a probability, a PPT bound, equality with the full factor-affine constrained-separability hierarchy, equality with the earlier Convex formulation, the exact strict-classical optimum, physical realization, empirical confirmation, CP4.1 closure, or CP4.2 entry. #### Next controlling gate **OIRP-S2.CP4.1-HHLW-FACTOR-AFFINE-DIRECT-MOI-R3-R5-SOLVER-ENTRY-PREREGISTRATION-AND-BOUNDED-INITIALIZATION-AUDIT: Before any numerical iteration is authorized, freeze the exact solver-entry semantics; distinguish data ingestion, cone assembly, normalization/scaling, factorization, and iteration; define whether SCS permits a noniterative initialization boundary; preregister solver attributes, expected solver-facing dimensions and cone inventory, memory ceilings, abort triggers, telemetry, artifact requirements, and claim ceiling; and prohibit interpretation of initialization or bounded execution as feasibility, convergence, or a physical bound without separately validated numerical evidence.** ### OIRP-S2.CP4.1-HHLW-FACTOR-AFFINE-DIRECT-MOI-R3-R5-SOLVER-ENTRY-PREREGISTRATION-AND-BOUNDED-INITIALIZATION-AUDIT #### Disposition **CLOSED AS A PREREGISTRATION AND INTERFACE-SEMANTICS AUDIT. NO EXACT-HHLW SOLVER ENTRY IS AUTHORIZED. NO NONITERATIVE SCS INITIALIZATION BOUNDARY HAS BEEN ESTABLISHED THROUGH THE INSTALLED MathOptInterface/SCS.jl OPTIMIZE PATH. A TINY-FIXTURE ENTRY-SEMANTICS PROBE IS REQUIRED BEFORE ANY EXACT-HHLW ITERATIVE CALL. OIRP-S2.CP4.1 REMAINS OPEN. OIRP-S2.CP4.2 REMAINS BLOCKED.** #### Interface decision The completed transfer dry run certifies source construction, bridge transformation, and MOI.copy_to transfer. It does not certify solver-facing data materialization, cone validation, scaling, workspace allocation, linear-system factorization, iterative solve entry, or solution extraction. Official SCS documentation separates solver-object initialization from solve invocation and documents max_iters as a solver option with a positive default. The retrieved documentation does not state that max_iters=0 is a supported initialization-only mode. Accordingly, max_iters=0 is not assumed safe, valid, or noniterative, and no exact-HHLW MOI.optimize! call is authorized by this gate. #### Frozen solver-entry layers The program distinguishes: source construction; bridge/copy transfer; solver-facing data materialization; cone validation and ordering; scaling and normalization; workspace and linear-system allocation; initialization/factorization; iterative solve loop; and status/solution extraction. Only source construction and bridge/copy transfer are certified for the exact HHLW model. #### Frozen exact solver-facing target The preregistered expected target remains 9232 variables, 4161 equality/zero-cone rows, 35140 PSD rows, 39301 total conic rows, and scaled PSD cone orders [128,128,128,128,64,8], with VectorizeBridge, SetDotScalingBridge, and SCS.ScaledPSDConeBridge. These are expected dimensions, not a native SCS matrix inventory independently extracted during solve setup. #### Safety envelope The first solver-entry probes require no other Julia process, commit headroom at least 64 GiB, commit usage below 80 percent, C-drive free space at least 150 GiB, and verified source and transfer hashes. Hard abort thresholds are 160 GiB process private memory, 64 GiB or less commit headroom, 80 percent or more commit usage, 150 GiB or less C-drive free space, any count/cone/order/objective-sign/bridge/environment mismatch, any unplanned positive iteration count, or loss of telemetry/process control. These are conservative preregistered controls, not memory estimates. #### Tiny-fixture requirement The next executable gate must use the smallest already validated direct-MOI fixture, never the exact HHLW instance. It must first test raw attribute acceptance without optimization; test max_iters=0 only if accepted and classify the exact result; and defer max_iters=1 to explicit separate authorization after the zero-iteration result is known. It must preserve versions, attributes, source/destination inventories, bridges, exit code, exceptions, termination/raw status, exposed iteration and timing fields, objective/result availability, telemetry, and hashes. #### Artifact package - Filename: OIRP-S2.CP4.1_HHLW_SOLVER_ENTRY_PREREGISTRATION_BOUNDED_INITIALIZATION_AUDIT.zip - Bytes: 4551 - SHA-256: E95AB5E53D37EA2C8EA219F670FAB4D8C54BDE5FC6251D8A3377CFA4BE6C65D9 - ZIP integrity: PASS. - Exact-HHLW optimize authorization: FALSE. - Numerical iteration authorization: FALSE. #### Claim ceiling This gate establishes a solver-entry constitution, expected inventory, safety envelope, and staged tiny-fixture probe requirement. It does not establish acceptance of zero iterations, isolation of setup from iteration, exact-model initialization, factorization memory safety, feasibility, boundedness, convergence, an objective value, a probability, or a physical HHLW bound. #### Next controlling gate **OIRP-S2.CP4.1-HHLW-FACTOR-AFFINE-DIRECT-MOI-R3-R5-SCS-ENTRY-SEMANTICS-TINY-FIXTURE-PROBE: Execute only the smallest validated direct-MOI fixture to determine installed SCS.jl/SCS attribute acceptance and whether max_iters=0 is rejected, accepted without iteration, or enters a solve path; preserve complete telemetry and interface evidence; and do not use the exact HHLW model.** ### OIRP-S2.CP4.1-HHLW-FACTOR-AFFINE-DIRECT-MOI-R3-R5-SCS-ENTRY-SEMANTICS-TINY-FIXTURE-PROBE #### Issuance and execution disposition **CLOSED WITH A DEFINITIVE INSTALLED-INTERFACE RESULT: `max_iters=0` IS ACCEPTED AND RETRIEVABLE BY THE MathOptInterface RAW-ATTRIBUTE LAYER BUT IS REJECTED BY NATIVE SCS VALIDATION WHEN `MOI.optimize!` ENTERS THE SOLVE PATH. ZERO ITERATIONS IS NOT A VALID INITIALIZATION-ONLY BOUNDARY IN THE TESTED JULIA 1.13.0 / MathOptInterface 1.53.0 / SCS.jl 2.6.5 ENVIRONMENT. NO POSITIVE ITERATION WAS AUTHORIZED OR EXECUTED IN THIS GATE. THE EXACT HHLW MODEL WAS ABSENT.** #### Issued probe package - Filename: OIRP-S2.CP4.1_HHLW_SCS_ENTRY_SEMANTICS_TINY_FIXTURE_PROBE.zip - Bytes: 4791 - SHA-256: 5352345F1EE2D9D1C706F84FBF19E533658A0D52DD116DCC9D2CE23AC6FF6FBB - ZIP integrity: PASS. - Exact-HHLW model permitted: FALSE. - `max_iters=1` execution permitted in this gate: FALSE. #### Fixture and bridge inventory The probe used only a real 2-by-2 density-matrix fixture with three packed-triangular variables, one ScalarAffineFunction-in-EqualTo constraint, one VectorAffineFunction-in-PositiveSemidefiniteConeTriangle constraint, trace one, and objective maximize rho[1,1]. The bridge report contained VectorizeBridge, SetDotScalingBridge, and SCS.ScaledPSDConeBridge. #### Case A: attribute-layer result Raw attributes `max_iters=0`, `max_iters=1`, and `time_limit_secs=1.0` were each accepted and retrieved even though `MOI.supports` returned false. Case A did not call `MOI.optimize!`, reported no solver iteration, and completed successfully. This establishes that raw-attribute storage and retrieval do not certify native-value validity at solve entry. #### Case B: native-validation result A fresh fixture accepted and retrieved `max_iters=0`, then called `MOI.optimize!`. Native SCS printed `max_iters must be positive`, followed by validation failure and missing-work messages. MathOptInterface reported `TERMINATION_STATUS=INVALID_MODEL`, an empty raw-status string, and `SOLVE_TIME_SEC=NaN`. The optimize path was entered, but no valid initialization-only state, workspace, factorization, numerical iterate, feasibility result, or objective result was established. The exposed `RESULT_COUNT=1` and `OBJECTIVE_VALUE=0.0` are retained only as invalid-state interface artifacts and are not promoted as numerical results. #### Harness-warning classification The predecessor probe source emitted Julia soft-scope warnings for `optimize_returned`, `optimize_error_type`, and `optimize_error_text`. Consequently, its printed return and exception fields are not reliable exception-capture evidence. This defect does not alter the controlling native-validation result because the native SCS messages and `INVALID_MODEL` status independently establish rejection of `max_iters=0` at solve entry. #### Claim ceiling This gate identifies installed-interface behavior on one tiny fixture only. It does not establish every SCS interface's behavior, exact-HHLW initialization safety, factorization memory, positive-iteration behavior, feasibility, convergence, or any HHLW value. ### OIRP-S2.CP4.1-HHLW-FACTOR-AFFINE-DIRECT-MOI-R3-R5-SCS-ONE-ITERATION-TINY-FIXTURE-PREREGISTRATION-AND-PROBE #### Preregistration and package identity **PREREGISTERED AND EXECUTED ONCE AT THE DECLARED TINY-FIXTURE, ONE-POSITIVE-ITERATION, ENVIRONMENT-, BRIDGE-, AND RESOURCE-RELATIVE CEILING. THE EXACT HHLW MODEL WAS ABSENT AND REMAINS PROHIBITED FROM SOLVER ENTRY.** - Filename: OIRP-S2.CP4.1_HHLW_SCS_ONE_ITERATION_TINY_FIXTURE_PROBE.zip - Bytes: 5173 - SHA-256: 18899FE4F1EC24F9E526C5D1AA4496ED5A89B3C32AFFE3788B97D2507B31C532 - ZIP integrity: PASS. - Authorized positive-iteration executions: 1. - Exact-HHLW model permitted: FALSE. The source placed execution inside `main()` to correct the predecessor soft-scope defect. It used only the same three-variable 2-by-2 density-matrix fixture, set `max_iters=1`, enabled native verbose SCS output, and preserved status and result fields. #### Environment and model inventory The execution reported Julia 1.13.0, MathOptInterface 1.53.0, SCS.jl 2.6.5, and native SCS 3.2.11. The fixture had three variables and four solver-facing conic rows: one zero-cone row and one three-entry PSD cone. Native SCS reported `nnz(A)=5`, `nnz(P)=0`, and the sparse-direct AMD-QDLDL linear-system path. #### Solver-entry and one-iteration result `max_iters=1` and `verbose=true` were accepted and retrieved. `MOI.optimize!` returned normally with no captured exception. Native SCS displayed iteration rows 0 and 1 and terminated with `solved (inaccurate - reached max_iters)`. MathOptInterface reported `TERMINATION_STATUS=ITERATION_LIMIT`. The timing report was total approximately 2.85e-3 seconds, setup approximately 1.19e-4 seconds, solve approximately 2.73e-3 seconds, linear-system approximately 3.50e-6 seconds, cone work approximately 5.70e-4 seconds, and acceleration approximately 1.00e-7 seconds. #### Residual and result-field audit At the final displayed iteration, native SCS reported primal residual approximately 1.16e1, dual residual approximately 7.96e-2, gap approximately 1.27e1, and native objective approximately -7.28e0. These values are far from the requested 1e-4 absolute and relative tolerances. MathOptInterface exposed `RESULT_COUNT=1`, `OBJECTIVE_VALUE=13.648391917581755`, `PRIMAL_STATUS=FEASIBLE_POINT`, and `DUAL_STATUS=FEASIBLE_POINT`. These are classified only as nonconverged one-iteration interface outputs. They are not promoted as feasibility, optimality, or objective certificates because termination was `ITERATION_LIMIT`, native status was explicitly inaccurate, residuals and gap were large, and the exposed objective exceeds the analytical fixture ceiling of one. #### Scientific and operational decision - Native positive-value validation: PASS for `max_iters=1`. - Native SCS setup and cone ingestion: ESTABLISHED for the tiny fixture. - Sparse-direct QDLDL initialization: ESTABLISHED for the tiny fixture. - Displayed positive iteration: ESTABLISHED through iteration row 1. - Numerical convergence: NOT ESTABLISHED. - Fixture feasibility certificate from this iterate: NOT ESTABLISHED. - Fixture optimality or objective certificate: NOT ESTABLISHED. - Exact-HHLW model present: NO. - Exact-HHLW solver entry authorized: NO. #### Artifact-finalization status The console record is sufficient for the restricted scientific classification above. Exact executed source, results, telemetry, status, and hash artifacts have not yet been ingested and independently finalized in the controlled workspace. Wrapper exit code, resource-abort status, exact telemetry extrema, source identity, and member-level release integrity therefore remain open artifact obligations. #### Claim ceiling This gate establishes setup and a single positive numerical iteration only for the declared tiny fixture. It does not establish exact-HHLW solver-facing matrix construction, exact-HHLW factorization or memory safety, exact-HHLW numerical iteration, feasibility, boundedness, convergence, a primal or dual point, an HHLW probability, a PPT bound, a strict-classical optimum, CP4.1 closure, or CP4.2 entry. #### Current program status **OIRP-S2.CP4.1 REMAINS OPEN. OIRP-S2.CP4.2 ENTRY REMAINS BLOCKED. CP4.R AND OIRP-S2 RETAIN THEIR PRIOR OPEN STATUS AND CLAIM CEILINGS.** #### Next controlling gate **OIRP-S2.CP4.1-HHLW-FACTOR-AFFINE-DIRECT-MOI-R3-R5-SCS-ONE-ITERATION-TINY-FIXTURE-ARTIFACT-FINALIZE-AND-ENTRY-BOUNDARY-AUDIT: Ingest and hash the exact executed tiny-fixture folder; verify source, manifest, results, telemetry, status, and hash records; confirm wrapper exit code and `RESOURCE_ABORTED` state; independently verify native dimensions, cone inventory, iterations 0 and 1, timing fields, `ITERATION_LIMIT`, inaccurate raw status, and nonconverged result-field classification; issue a checksum-distinct complete-pass release; and preregister the next exact-HHLW boundary without authorizing exact-HHLW numerical iteration.** ### OIRP-S2.CP4.1-HHLW-FACTOR-AFFINE-DIRECT-MOI-R3-R5-SCS-ONE-ITERATION-TINY-FIXTURE-ARTIFACT-FINALIZE-AND-ENTRY-BOUNDARY-AUDIT #### Status **OPEN; CHECKSUM-DISTINCT EXECUTED-ARTIFACT COLLECTOR ISSUED; FINAL BINARY INGESTION AND INDEPENDENT AUDIT PENDING. NO JULIA OR SOLVER RERUN IS REQUIRED FOR COLLECTION. EXACT-HHLW NUMERICAL ITERATION REMAINS UNAUTHORIZED.** #### Collector operation The collector verifies the presence of the executed source, wrapper, results, telemetry, status, hash record, package manifest, preregistration, and README. It requires the decisive result markers for exact-HHLW absence, one requested iteration, optimize entry, iteration-limit termination, and case completion. It also requires telemetry markers `EXIT_CODE=0` and `RESOURCE_ABORTED=False` before packaging. The collector creates `C:\OIRP\SCS_ONE_ITERATION_TINY_FIXTURE_PROBE_EXECUTED.zip`, extracts it independently to a temporary folder, and compares SHA-256 for every required member. It does not launch Julia, call MathOptInterface, instantiate SCS, or perform another numerical iteration. #### Collector package identity - Filename: OIRP-S2.CP4.1_HHLW_SCS_ONE_ITERATION_ARTIFACT_COLLECTOR.zip - Bytes: 2091 - SHA-256: 1E95B0BF1831810C5CDFC14B3501799F871DEA6C346E679C03645890E99B3F36 - ZIP integrity: PASS. - Collector execution status: NOT YET EXECUTED. #### Final-audit boundary The gate cannot be closed from console text alone because exact source identity, execution-hash reconciliation, wrapper exit code, resource-abort state, telemetry extrema, member inventory, and release integrity must be independently verified from the executed files. No such values are inferred before binary ingestion. #### Next controlling substep **Execute `COLLECT_ONE_ITERATION_TINY_FIXTURE_ARTIFACTS.ps1` once, supply `SCS_ONE_ITERATION_TINY_FIXTURE_PROBE_EXECUTED.zip`, and then complete the in-workspace source, result, telemetry, iteration, status, resource, and member-level release audit.** #### Final executed-artifact ingestion and audit result **OIRP-S2.CP4.1-HHLW-FACTOR-AFFINE-DIRECT-MOI-R3-R5-SCS-ONE-ITERATION-TINY-FIXTURE-ARTIFACT-FINALIZE-AND-ENTRY-BOUNDARY-AUDIT IS CLOSED WITH IN-WORKSPACE BINARY INGESTION, SOURCE/MANIFEST/HASH-RECORD VERIFICATION, NATIVE SOLVER-INVENTORY VERIFICATION, ITERATION-ROW VERIFICATION, RESOURCE-CEILING AUDIT, NONCONVERGED-RESULT CLASSIFICATION, AND MEMBER-LEVEL COMPLETE-PASS RELEASE VERIFICATION. EXACT-HHLW NUMERICAL ENTRY REMAINS UNAUTHORIZED.** ##### Supplied executed-artifact archive - Filename: SCS_ONE_ITERATION_TINY_FIXTURE_PROBE.zip - Bytes: 9024 - SHA-256: 82833FC0DE1E637A489CF7B879CC7A77A9AF522D533514856652E78C36301C31 - ZIP decompression integrity: PASS. - Required executed artifacts present: PASS. ##### Source and execution identity - Executed source SHA-256: ECA06899266785647EA5B194063FAC3580237CD2DE7C259533C10657C9D6FC20. - Source identity against package manifest: PASS. - Source, results, telemetry, and status hashes against execution hash record: PASS. - Function-scoped `main()` correction: PASS. - Exact HHLW model absent: PASS. - Exact HHLW solver-entry authorization false: PASS. ##### Native solver and iteration reconciliation The preserved native SCS record reports three variables, four conic rows, one zero-cone row, one three-entry PSD cone, `nnz(A)=5`, `nnz(P)=0`, and sparse-direct AMD-QDLDL. The bridge report contains VectorizeBridge, SetDotScalingBridge, and SCS.ScaledPSDConeBridge. Native iteration rows 0 and 1 are physically present in the result artifact. `MOI.optimize!` returned normally with no captured Julia exception. The termination status is ITERATION_LIMIT and the raw status is `solved (inaccurate - reached max_iters)`. ##### Resource audit - Maximum sampled process private memory: 0.002 GiB. - Maximum system commit usage: 13.62 percent. - Minimum system commit headroom: 220.992 GiB. - Minimum C-drive free space: 241.812 GiB. - Exit code: 0. - RESOURCE_ABORTED=False. - Hard resource threshold crossed: FALSE. The sampled private-memory value is retained only as the wrapper's reported process metric and is not promoted as an estimate for exact-HHLW setup or iteration. ##### Numerical-status audit The final displayed native values were primal residual 11.6, dual residual 0.0796, gap 12.7, and native objective approximately -7.28. The MathOptInterface objective field was 13.648391917581755, above the fixture's analytic ceiling of one. Therefore the exposed result count, primal status, dual status, and objective are nonconverged interface outputs only. Feasibility, optimality, and objective validity are not certified. ##### Complete-pass release - Filename: OIRP-S2.CP4.1_HHLW_SCS_ONE_ITERATION_TINY_FIXTURE_COMPLETE_PASS.zip - Release file count: 11. - Bytes: 9062. - SHA-256: 9C9936DB3D22D346978BDC7ACE7F9020212B1D7FAC0570D9D06965B05458E67C. - Release-member inventory agreement: PASS. - Member-level SHA-256 verification: PASS. - ZIP integrity: PASS. - Artifact and entry-boundary audit: PASS. - Exact-HHLW numerical entry authorized: FALSE. ##### Entry-boundary decision The tiny fixture establishes that the installed SCS path can materialize the solver-facing data, validate the cone inventory, initialize the sparse-direct QDLDL path, and execute one numerical iteration. It does not establish that the exact HHLW model can complete those operations within memory, that its factorization will succeed, that one iteration is scientifically useful, or that any returned exact-HHLW field would be valid. No exact-HHLW positive-iteration call is authorized. The next gate must first preregister a setup-dominant exact-model boundary with a single positive-iteration ceiling, strict resource-abort controls, native dimension and cone checks, complete stdout/stderr preservation, and a prohibition on interpreting any iterate as a bound. Execution authorization must remain separate from preregistration. ##### Claim ceiling This gate closes artifact finalization for the tiny fixture only. It does not establish exact-HHLW solver initialization, factorization memory safety, exact-HHLW iteration, feasibility, boundedness, convergence, a primal or dual point, a PPT bound, equivalence to the full factor-affine hierarchy, the exact strict-classical optimum, CP4.1 closure, or CP4.2 entry. ##### Next controlling gate **OIRP-S2.CP4.1-HHLW-FACTOR-AFFINE-DIRECT-MOI-R3-R5-EXACT-HHLW-ONE-ITERATION-ENTRY-PREREGISTRATION-AND-RESOURCE-ABORT-DESIGN: Freeze the exact source and transfer authorities, native expected dimensions and cone inventory, one-positive-iteration ceiling, solver attributes, direct versus indirect linear-system policy, setup/factorization telemetry, strict resource-abort controls, status and residual interpretation, artifact requirements, and claim ceiling; do not execute the exact HHLW solver until a checksum-distinct execution package is separately issued.** ### OIRP-S2.CP4.1-HHLW-FACTOR-AFFINE-DIRECT-MOI-R3-R5-EXACT-HHLW-ONE-ITERATION-ENTRY-PREREGISTRATION-AND-RESOURCE-ABORT-DESIGN #### Disposition **CLOSED AS A PREREGISTRATION AND RESOURCE-ABORT-DESIGN GATE. EXECUTION IS NOT AUTHORIZED BY THIS PACKAGE. A CHECKSUM-DISTINCT EXECUTION PACKAGE MUST PASS STATIC SOURCE AUDIT AND BE ISSUED SEPARATELY. OIRP-S2.CP4.1 REMAINS OPEN. OIRP-S2.CP4.2 ENTRY REMAINS BLOCKED.** #### Frozen authorities and inventory The gate freezes the audited exact construction source, transfer source, construction complete-pass release, transfer complete-pass release, and tiny one-iteration complete-pass release identities. Any mismatch is a hard stop. The expected exact native target is 9232 variables, 39301 conic rows, zero-cone length 4161, packed PSD rows 35140, and scaled PSD orders [128,128,128,128,64,8], with VectorizeBridge, SetDotScalingBridge, and SCS.ScaledPSDConeBridge. #### Frozen solver policy The first exact entry is limited to `max_iters=1`, verbose native output, normalization enabled, adaptive scaling disabled, acceleration disabled, and the installed sparse-direct AMD-QDLDL backend. No indirect, MKL, GPU, cuDSS, retry, second solve, or warm-start loop is authorized. Native banner disclosure and exact inventory agreement are mandatory. Official SCS API documentation states that native initialization performs validation, scaling, automatic parameter tuning when enabled, and linear-system setup; direct-solver KKT factorization occurs during initialization. The MathOptInterface/SCS.jl path may combine setup and solve behind `MOI.optimize!`, so the external parent monitor is an abort policy rather than a guaranteed in-process stop before factorization. #### Admission and abort policy Admission requires no other Julia process, exact hash agreement, at least 160 GiB commit headroom, commit use below 45 percent, at least 200 GiB C-drive free space, active telemetry, and writable output. Hard abort thresholds are 128 GiB Julia private memory, 112 GiB or less commit headroom, 55 percent or more commit use, 190 GiB or less C-drive free space, any authority/inventory/version/backend mismatch, more than one positive displayed iteration, telemetry loss, parent error, or unexpected child process. Monitor sampling must not exceed one second. These are conservative policy thresholds, not predictions of exact-HHLW memory requirements. A hard trigger must kill the Julia process tree, preserve evidence, set RESOURCE_ABORTED=True, and prohibit creation of a success package. #### Result firewall No one-iteration objective, result count, primal status, dual status, iterate, residual, raw status, or status containing `solved` is authorized as a probability, feasibility certificate, PPT bound, strict-classical result, or physical conclusion. Every numerical field remains diagnostic. #### Package identity - Filename: OIRP-S2.CP4.1_HHLW_EXACT_ONE_ITERATION_ENTRY_PREREGISTRATION_RESOURCE_ABORT_DESIGN.zip - Bytes: 5212 - SHA-256: 876FBE118DB460C94D5726E47AF6899926380A357E48C40003C79775A4CE47D3 - ZIP integrity: PASS. - Execution authorized: FALSE. #### Claim ceiling This gate establishes only an execution constitution and resource-abort design. It does not run the exact model, establish resource sufficiency, guarantee protection from abrupt allocation failure, establish successful factorization, produce a valid iterate or bound, close CP4.1, or permit CP4.2 entry. #### Next controlling gate **OIRP-S2.CP4.1-HHLW-FACTOR-AFFINE-DIRECT-MOI-R3-R5-EXACT-HHLW-ONE-ITERATION-ENTRY-STATIC-SOURCE-AUDIT-AND-EXECUTION-PACKAGE-ISSUANCE: Build the checksum-distinct source and parent monitor; prove by static audit that exactly one `MOI.optimize!` call exists, `max_iters=1` is set and retrieved, no retry or fallback exists, exact inventory assertions precede entry, resource controls fail closed, complete evidence is preserved, and no scientific interpretation is authorized; only then issue a separate execution package.** ### OIRP-S2.CP4.1 HHLW exact-entry UTF-8 recovery, construction-only finalization, and successor decision #### Exact predecessor and canonical succession The user-supplied `OIRP_PROGRAM_MASTER_LEDGER (14).md` is preserved unchanged as the exact binary predecessor for this update. - Predecessor bytes: 447743. - Predecessor SHA-256: A4F309EC35436E765F70FC50A491BFEB3E144B88611548750E5E3A0134D3F1CE. - Canonical successor filename: `OIRP_LEDGER.md`. The complete predecessor content is preserved unchanged as the prefix of this checksum-distinct canonical successor. #### Exact one-iteration transfer authority The local transfer archive was verified before execution: - Filename: `HHLW_DIRECT_MOI_SOLVER_TRANSFER_DRY_RUN.zip`. - Bytes: 10719. - SHA-256: `CBC248E365A47ECCF98653A66A2672731291991C2CC727FAEB6D15ACD4D0181E`. - Embedded transfer-source SHA-256: `5E113DCBDE43A04151B77B43F039B5C7F389AC44D27107F9A22327EB69554AD4`. #### Consumed exact-entry execution and post-run parent defect The first exact-entry successor passed its deterministic generated-source static audit. The built source SHA-256 was `9BCE9899B833489360C98C68A2DA58FC1DF36B5177EE6DCB70FA7CB733E6D68E`. The following checks reported `True`: transfer-source hash, single optimize-call count, `max_iters=1`, attribute retrieval, no loop around optimize, exact inventory assertion, interpretation firewall, exact-HHLW presence, and aggregate static-source audit. Julia then launched. The parent waited for the child to exit and failed during post-run artifact persistence because Windows PowerShell variables are case-insensitive: the stderr path variable `$Stderr` and captured stderr text variable `$stderr` were the same variable. The text assignment overwrote the path, and the subsequent `Set-Content` call failed. The execution authorization was therefore consumed and rerun was prohibited. The post-run collector produced: - Filename: `HHLW_EXACT_ONE_ITERATION_ENTRY_POSTRUN_FAILURE.zip`. - Bytes: 32919. - SHA-256: `73060D85F9E9D984DA3CA43A55D4ABD31BE504ED2A0E027D36894B6732378F1F`. - Rerun authorized: false. #### Phase-3 root-cause classification The recovered stdout established successful authority/environment entry, allocation of 9232 variables, construction of 8192 objective terms, and entry into Phase 3 `RHO_BLOCK`. It did not contain a Phase-3 completed inventory, later construction phase, transfer marker, solver-entry marker, native SCS banner, or numerical iteration. Binary inspection localized the child failure to source transcoding. The authority source contained the valid Julia integer-division code point U+00F7 (`÷`) at the two `psdfun` locations. The generated execution source contained the mojibake sequence U+00C3 U+00B7 (`÷`). The first runtime invocation of the corrupted `psdfun` body occurred in Phase 3. This was an operational source-transcoding failure, not a scientific-model, MathOptInterface, SCS, factorization, iteration, or resource failure. Resource evidence stayed far inside the preregistered ceilings. The displayed system commit use peaked at 13.46 percent and commit headroom remained at least 221.397 GiB. No numerical HHLW result existed. The checksum-distinct failure-evidence release was: - Filename: `OIRP-S2.CP4.1_HHLW_EXACT_ENTRY_PHASE3_FAILURE_EVIDENCE_RELEASE.zip`. - Bytes: 20308. - SHA-256: `4B14C8428DFB053EBFD357B64D9D117D4DC0E5168BE8DF7F35064F65EDA7701E`. #### UTF-8 source-preservation and post-run evidence redesign preregistration The corrective preregistration closed with execution unauthorized. It froze these requirements: - Read authority source bytes with `[System.IO.File]::ReadAllBytes`. - Decode with strict UTF-8 using `System.Text.UTF8Encoding(false,true)`. - Write generated source bytes with `[System.IO.File]::WriteAllBytes`. - Prohibit default-encoding `Get-Content` and `Set-Content` for Julia source transformation. - Preserve and audit BOM and line-ending policy. - Prove unchanged-prefix and unchanged-suffix identity around the sole gate-token substitution. - Require exactly two U+00F7 operators. - Reject U+00C3, U+00C2, U+FFFD, and known mojibake sequences. - Require strict UTF-8 byte round-trip identity and a non-ASCII code-point inventory. - Use unambiguous `$StdoutPath`, `$StdoutText`, `$StderrPath`, and `$StderrText` names. - Preserve stdout, stderr, child exit code, resource-abort state, telemetry, parent errors, status, and hashes independently on every terminal path. - Maintain an append-only execution-state ledger. - Require parser and construction-only Phase 0 through Phase 9 validation before any new numerical authorization. Preregistration package: - Filename: `OIRP-S2.CP4.1_HHLW_UTF8_SOURCE_PRESERVATION_POSTRUN_EVIDENCE_REDESIGN_PREREGISTRATION.zip`. - Bytes: 5510. - SHA-256: `5D8BE8993672C82D9281E62C3E1DC98FBEBA88BE460029755C179F06F745682E`. #### Initial construction-only package parser failure and correction The first construction-only package passed its container-side static audit but failed in Windows PowerShell parsing before authority verification. Literal non-ASCII mojibake test strings embedded in the PowerShell builder were themselves transcoded, generating parser errors. The execution-state ledger ended in `PACKAGE_FAILED`; the generated source and UTF-8 audit were absent; Julia did not launch; and the construction-only authorization was not consumed. The redesigned post-run evidence system nevertheless preserved the parent parser error, final telemetry, status, presence-aware hashes, and explicit terminal state. This validated the failure-path persistence architecture. A checksum-distinct Successor-01 made every PowerShell script ASCII-only and replaced literal Unicode tests with code-point checks for `0x00C3`, `0x00C2`, `0xFFFD`, and `0x00F7`. - Successor-01 filename: `OIRP-S2.CP4.1_HHLW_UTF8_CONSTRUCTION_ONLY_VALIDATION_PACKAGE_SUCCESSOR-01.zip`. - Bytes: 7433. - SHA-256: `01762FDDA87111D67115E1A972F50FC9D0BFB8460105D5D8FCE761C38899042C`. - All PowerShell scripts ASCII-only: pass. - Optimization authorized: false. #### Successful UTF-8 construction-only execution The ASCII-only successor verified the authority source and completed strict UTF-8 reconstruction. - Authority source SHA-256: `5E113DCBDE43A04151B77B43F039B5C7F389AC44D27107F9A22327EB69554AD4`. - Authority BOM present: false. - Authority LF count: 125. - Authority CRLF count: 0. - Unchanged-prefix SHA-256: `DD1F5CA0720045AAB5B409400D62B90BDD47997DEECD516FC0941569748A36CD`. - Unchanged-suffix SHA-256: `8B6ED5997C3630712BC204DC565B8EBAB3A97BFA78C47C89A99EFECB1588C51C`. - Gate-token occurrences: 1. - U+00F7 operator count: 2. - Mojibake firewall: pass. - Strict UTF-8 round trip: pass. - Non-ASCII code points: U+00F7 only. - Generated source SHA-256: `5A09268C37B61DC88A9448A03CFB762BD2D032C351670B12D269DED6ECB301D9`. The generated source completed Phases 0 through 9. It recovered 9232 variables, 8192 objective terms, one scalar-affine equality, two vector-zero constraints, and six triangular PSD constraints. The previously failed Phase-3 rho block completed. `MOI.copy_to` returned `MathOptInterface.Utilities.IndexMap`. The active bridge report contained `VectorizeBridge`, `SetDotScalingBridge`, and `SCS.ScaledPSDConeBridge`. The preserved dimensions remained: - Packed PSD rows: 35140. - Equality rows: 4161. - Total conic rows: 39301. The terminal markers were: - `MOI_COPY_TO_CALLED=True`. - `MOI_OPTIMIZE_CALLED=False`. - `SOLVER_ITERATION_OCCURRED=False`. - `SOLVER_TRANSFER_DRY_RUN_COMPLETE=True`. - `PACKAGE_COMPLETED`. - `EXIT_CODE=0`. - `RESOURCE_ABORTED=False`. The executed archive was independently ingested: - Filename: `HHLW_UTF8_CONSTRUCTION_ONLY_VALIDATION_EXECUTED.zip`. - Bytes: 33784. - SHA-256: `48511A06A4F19F250DBD1E1E361DCB2EF6D3EBB385FA9555D391DE4AC53711E1`. - ZIP integrity: pass. - Empty stderr: pass. - Empty parent-persistence error record: pass. Telemetry extrema were: - Maximum sampled process private memory: 0.002 GiB. - Maximum commit usage: 13.61 percent. - Minimum commit headroom: 221.027 GiB. - Minimum C-drive free space: 241.293 GiB. #### Hash-manifest ordering limitation The construction runner generated `CONSTRUCTION_ONLY_HASHES.txt` before appending `ARTIFACT_PERSISTENCE_COMPLETED` and `PACKAGE_COMPLETED` to `EXECUTION_STATE.txt`. The original state-ledger hash therefore describes a valid preterminal snapshot, not the final state-ledger bytes. Immutable artifacts matched the original manifest. The final complete-pass release independently hashes the terminal state ledger. Any numerical successor must append and close the terminal execution state before generating the final hash manifest. #### Finalized complete-pass release The checksum-distinct finalized release is: - Filename: `OIRP-S2.CP4.1_HHLW_UTF8_CONSTRUCTION_ONLY_COMPLETE_PASS.zip`. - Bytes: 13312. - SHA-256: `7AA26DE6A1BE3FCFDB0A012AD9E97CD2B4E977EF19AD5667AD1D8DA15FE8389C`. - ZIP integrity: pass. - Construction-only finalization: pass. - Final terminal state independently hashed: pass. - One-iteration successor eligibility: true. - One-iteration execution authorization: false. #### Scientific decision The UTF-8-safe construction and transfer boundary is certified at a source-, authority-, code-point-, unchanged-region-, inventory-, bridge-, environment-, resource-, artifact-, and no-optimize-relative ceiling. The Phase-3 source-transcoding defect is closed. The post-run variable-collision defect is closed in the redesigned runner. Construction through `MOI.copy_to` is artifact-finalized. This work does not establish native SCS initialization for the exact HHLW model, direct QDLDL factorization, factorization memory safety, one exact numerical iteration, feasibility, boundedness, convergence, a primal or dual point, an objective value, an HHLW probability, a PPT bound, equality with the full Definition-23 factor-affine hierarchy, the exact strict-classical optimum, physical realization, empirical confirmation, CP4.1 closure, or CP4.2 entry. #### Program status - OIRP-S2.CP4.1: OPEN. - OIRP-S2.CP4.2 entry: BLOCKED. - CP4.R: OPEN at its previously recorded scope. - OIRP-S2: OPEN. - Saturation counter: unchanged by this operational recovery and construction-only finalization; no closure is authorized. #### Next controlling gate **OIRP-S2.CP4.1-HHLW-FACTOR-AFFINE-DIRECT-MOI-R3-R5-UTF8-SAFE-EXACT-ONE-ITERATION-SUCCESSOR-PREREGISTRATION-AND-STATIC-PACKAGE-AUDIT: Freeze and audit the corrected UTF-8-safe one-iteration source; derive it from the finalized source lineage; preserve unchanged-region identity; add exactly one `MOI.optimize!` call; set and retrieve `max_iters=1`; retain the backend, inventory, resource, no-retry, and interpretation firewalls; use unambiguous evidence variables; append terminal state before final hashing; issue a checksum-distinct package; and keep execution authorization separate from preregistration.** ### OIRP-S2.CP4.1 UTF-8-Safe Exact One-Iteration Successor, Local Authorization, Native SCS Entry, and Artifact Finalization #### Exact predecessor and canonical succession The user-supplied `OIRP_PROGRAM_MASTER_LEDGER (15).md` is preserved unchanged as the exact binary predecessor for this update. - Predecessor bytes: 458699. - Predecessor SHA-256: F2B4F9296F88992D8D1DCAE8467FBFB38CF1F9418CE9F44A99D3D245F51BF4EC. - Canonical successor filename: `OIRP_LEDGER.md`. - Predecessor-prefix identity in the canonical successor: PASS. The complete predecessor content is preserved unchanged as the prefix of this checksum-distinct canonical successor. #### UTF-8-safe exact one-iteration successor preregistration and static package audit The construction-only authority source was frozen at SHA-256 `5A09268C37B61DC88A9448A03CFB762BD2D032C351670B12D269DED6ECB301D9`. A checksum-distinct successor builder and parent monitor were issued. The package required byte-level source input and output, strict UTF-8 decoding, exactly two U+00F7 operators, exclusion of U+00C3, U+00C2, and U+FFFD, exactly one `MOI.optimize!(destination)` call, `max_iters=1` set and retrieval controls, no retry or fallback, unambiguous stdout and stderr variable names, terminal execution state before final hashing, resource admission and hard-abort controls, and an explicit scientific-interpretation firewall. The preregistration package identity was: - Filename: `OIRP-S2.CP4.1_HHLW_UTF8_SAFE_EXACT_ONE_ITERATION_SUCCESSOR_PREREGISTRATION.zip`. - Bytes: 8663. - SHA-256: `8B2A33B883B1EFA2F8098D488FAA01E0618E09C08BAF8420873392F5A8475FE8`. - ZIP integrity: PASS. - Static package audit: PASS. - Execution authorized by preregistration alone: FALSE. #### Local source-generation audit and execution-authorization decision A checksum-distinct Windows-host audit package was issued and run without launching Julia. It generated and audited the exact numerical-entry source. The local audit established: - Authority SHA-256: `5A09268C37B61DC88A9448A03CFB762BD2D032C351670B12D269DED6ECB301D9`. - Unchanged-prefix SHA-256: `DD1F5CA0720045AAB5B409400D62B90BDD47997DEECD516FC0941569748A36CD`. - Unchanged-middle SHA-256: `7729988D6B5A17C8ED93F8C5768B707BB9AF651B7398C52649DC4211D9B90B3C`. - U+00F7 operator count: 2. - Mojibake firewall: PASS. - Strict UTF-8 round trip: PASS. - Optimize-call count: 1. - `max_iters=1` check: PASS. - Attribute-retrieval check: PASS. - No-retry-or-loop check: PASS. - Interpretation firewall: PASS. - Generated source bytes: 8289. - Generated source SHA-256: `AF77DD559B56FAD5B229564D2B56670A52046C52CDDDB2ECC05936CC02CD220E`. - Local source-generation audit: PASS. The local decision authorized exactly one execution and prohibited automatic retry. The local-audit package identity was: - Filename: `OIRP-S2.CP4.1_HHLW_UTF8_SAFE_ONE_ITERATION_LOCAL_GENERATION_AUDIT.zip`. - Bytes: 12402. - SHA-256: `9BC046753E19926C5CB5968EA6F7B23C74AB7922FA1450AE08421918364CACF6`. - ZIP integrity: PASS. #### Single authorized exact-HHLW execution The single authorized execution regenerated the exact approved source and completed Phases 0 through 10. The authorization was consumed and no rerun is authorized. The source-side construction and transfer inventory remained: - Variables: 9232. - Objective affine terms: 8192. - Scalar-affine equality constraints: 1. - Vector-zero constraint containers: 2. - Triangular PSD source constraints: 6. - Packed PSD rows: 35140. - Equality rows: 4161. - Total conic rows: 39301. - Transfer index-map type: `MathOptInterface.Utilities.IndexMap`. - Active bridge chain: `VectorizeBridge`, `SetDotScalingBridge`, and `SCS.ScaledPSDConeBridge`. Phase 10 set and retrieved `max_iters=1` and entered the sole optimize call. Native SCS 3.2.11 reported: - Variables n: 9232. - Constraints m: 39301. - Zero-cone rows: 4161. - PSD rows: 35140. - PSD block count: 6. - `nnz(A)=45380`. - `nnz(P)=0`. - Linear-system path: `sparse-direct-amd-qdldl`. - Normalization enabled. - Adaptive scaling disabled. - Acceleration lookback disabled. - Maximum iterations: 1. The native transcript contained displayed iteration rows 0 and 1. The optimize call returned normally. MathOptInterface reported `TERMINATION_STATUS=ITERATION_LIMIT` and raw status `solved (inaccurate - reached max_iters)`. The native timing record reported approximately 0.0323 seconds total, including approximately 0.0208 seconds setup and 0.0115 seconds solve. These timings are execution-relative observations only and are not projections for a longer solve. #### Numerical interpretation firewall The final displayed native diagnostics were approximately: - Primal residual: 1.57. - Dual residual: 0.170. - Gap: 16.4. - Native objective: -8.991423, marked inaccurate. The executed source explicitly recorded `RESULT_INTERPRETATION_AUTHORIZED=False`. The `solved` substring is part of an inaccurate iteration-limit status and is not a convergence or scientific-solution certificate. No primal feasibility, dual feasibility, boundedness, convergence, valid primal or dual point, trustworthy objective, HHLW discrimination probability, PPT upper bound, strict-classical optimum, or physical conclusion is established by this one-iteration probe. #### Terminal-state, hash, and resource audit The archived execution-state ledger records: - `PACKAGE_START`. - `SOURCE_AUDIT_PASSED`. - `PREFLIGHT_PASSED`. - `CHILD_STARTED`. - `CHILD_EXITED`. - `ARTIFACT_PERSISTENCE_STARTED`. - `PACKAGE_COMPLETED`. The terminal status was `EXIT_CODE=0` and `RESOURCE_ABORTED=False`. The stderr and parent-persistence-error artifacts were empty. The final hash manifest was generated after terminal-state creation, closing the prior state-hash ordering defect. Telemetry extrema were: - Maximum sampled process private memory: 0.002 GiB. - Maximum system commit usage: 13.61 percent. - Minimum system commit headroom: 221.018 GiB. - Minimum C-drive free space: 241.25 GiB. The sampled private-memory field is retained only as the wrapper-reported process metric and is not generalized into a precise native factorization-memory measurement. #### Executed archive and finalized native-entry release The collected execution archive was independently ingested and verified: - Filename: `HHLW_UTF8_SAFE_EXACT_ONE_ITERATION_EXECUTED.zip`. - Bytes: 15465. - SHA-256: `706B7529FFB134C4BC98EFE96FE78670DA1DB193A17F14AAF9A270E9D925A510`. - Member count: 16. - ZIP integrity: PASS. - Required artifacts: PASS. - Member-level hash reconciliation: PASS. The checksum-distinct finalized evidence release is: - Filename: `OIRP-S2.CP4.1_HHLW_UTF8_SAFE_EXACT_ONE_ITERATION_NATIVE_ENTRY_COMPLETE_PASS.zip`. - Bytes: 17188. - SHA-256: `A4C63FCC84F8C73594A0DD538A7CDF2F668208AC1AC039ABC5EDCBDC9EB4F7AD`. - ZIP integrity: PASS. - Input archive identity: PASS. - Source and execution hashes: PASS. - UTF-8 audit: PASS. - Phases 0 through 10: PASS. - Native inventory and direct-QDLDL path: PASS. - One requested iteration: PASS. - Terminal state and final hashing: PASS. - Valid numerical bound established: FALSE. - Rerun authorized: FALSE. #### Scientific advance and claim ceiling This sequence establishes, at the declared source, environment, model, bridge, resource, and one-requested-iteration scope: - exact UTF-8-safe successor generation; - exact authorized source identity; - construction and transfer through Phases 0 through 9; - native SCS acceptance of the 9232-variable, 39301-row exact model; - direct disclosure of the zero-cone, PSD, and sparse-matrix inventories; - reported native setup completion; - entry into the sparse-direct AMD-QDLDL path; - and completion of one requested numerical iteration followed by `ITERATION_LIMIT`. It does not establish numerical convergence, a valid optimization result, a certified HHLW probability or bound, equality with the complete Ohst factor-affine constrained-separability hierarchy, the exact strict-classical optimum, physical realization, empirical confirmation, definite-event generation, substrate ontology, CP4.1 closure, or CP4.2 entry. #### Program status - UTF-8 source defect: CLOSED. - Post-run evidence-variable defect: CLOSED. - Construction-only boundary: CLOSED. - Native SCS entry boundary: CLOSED. - One-requested-iteration evidence: CLOSED. - Longer numerical convergence path: NOT AUTHORIZED. - Valid objective or bound: NOT ESTABLISHED. - Rerun authorization: FALSE. - OIRP-S2.CP4.1: OPEN. - OIRP-S2.CP4.2 entry: BLOCKED. - CP4.R: OPEN at its previously recorded scope. - OIRP-S2: OPEN. #### Next controlling gate **OIRP-S2.CP4.1-HHLW-NATIVE-SCS-CONVERGENCE-PATH-PREREGISTRATION-AND-SCIENTIFIC-NECESSITY-DECISION: Determine whether a longer native SCS solve is scientifically necessary given the existing exact rational coarse-PPT upper certificate and the distinct full factor-affine obligations; establish whether this exact model is quantity-identical to the already certified coarse-PPT formulation; assess whether further iteration would add decision-relevant evidence or merely reproduce an existing outer bound; freeze any residual, gap, status, certificate, iteration, time, resource, checkpoint, resume, failure-preservation, and no-retry conditions; and keep any future execution authorization separate from preregistration. No longer solve is authorized by this ledger update.** ### OIRP-S2.CP4.1-HHLW-FACTOR-AFFINE-SOURCE-GROUNDED-MODEL-RECOVERY-AND-EXECUTION-PATH-DECISION #### Exact predecessor and canonical succession The exact predecessor is OIRP_LEDGER.md, 468079 bytes, SHA-256 30CC584CB587EE60646421A102712F7A86D4BF5A9DB9AC8B6A6BA52D762FBC7D. Its complete content is preserved unchanged as the prefix of this checksum-distinct canonical successor. #### Disposition **CLOSED WITH A SOURCE-GROUNDED RECOVERY MAP AND A NONEXECUTION DECISION. THE COMPLETE TWO-USE DEFINITION-23 FACTOR-AFFINE MODEL IS SCIENTIFICALLY DISTINCT FROM THE CERTIFIED COARSE ADAPTIVE-PPT MODEL. EXACT SOURCE INGEST AND MAP-AUTHORITY REGISTRATION ARE REQUIRED BEFORE CONSTRUCTION. NO FACTOR-AFFINE MODEL CONSTRUCTION OR NUMERICAL EXECUTION IS AUTHORIZED.** #### Recovered target and nonidentity decision The complete two-use classically adaptive target has finite history-factor form T_i = sum_h R_h tensor S_{i|h}, together with explicit history projection, system permutation, factor-block embedding, and factor-level affine trace-and-replace constraints. The executed direct-MOI model instead uses aggregate adaptive normalization and round-cut tester-element PPT constraints. The direct-MOI program is the reconstructed coarse adaptive-PPT outer relaxation at its audited scope and is not the complete factor-affine constrained-separability model. The existing exact rational coarse adaptive-PPT upper enclosure remains 122898671115429/125000000000000 = 0.983189368923432 at its prior inclusion scope. Another coarse-PPT convergence solve is not authorized and cannot substitute for the factor-affine obligation. #### Executable-workspace and authority decision The exact publication repository archive or clone, commit identity, software-license record, projection source, permutation and block-embedding source, factor-affine trace-and-replace source, tensor-order crosswalk, exact HHLW objective binding, fixed-history count manifest, and deterministic map-test suite were not present as a complete checksum-registered local authority set. Historical enterprise records and project discovery do not replace exact binary source ingest. The smallest source-grounded targets are fixed history alphabet L=1 for map and construction-only unit testing, followed by L=2 as a restricted subclass benchmark. Neither is a bound for the arbitrary-finite-history class without a certified reduction or alphabet-independent formulation. #### Authorized staged path 1. Exact repository binary ingest, archive/member hashing, commit registration, and license disposition. 2. Construction-free publication-to-source notation and tensor-order crosswalk. 3. Deterministic projection, permutation, factor-affine, normalization, reconstruction, and objective tests. 4. Fixed-L=1 construction-only inventory audit with no optimizer call. 5. Fixed-L=2 construction-only subclass audit with no optimizer call. 6. Separate solver-entry preregistration only after all prior stages pass. 7. Complete-class promotion only through a certified history reduction or alphabet-independent construction. #### Prohibited actions No guessed projection, guessed permutation, snippet-based source reconstruction, coarse-PPT relabeling, L=2 complete-class promotion, coarse-PPT convergence rerun, factor-affine solver execution before map certification, or inferred factor-affine value is authorized. #### Recoverability release - Filename: OIRP-S2.CP4.1_HHLW_FACTOR_AFFINE_SOURCE_GROUNDED_RECOVERY_DECISION.zip. - Bytes: 4740. - SHA-256: E1E594BB89C88B350E441DE445A90101D88D23114079305FEAC88948BDBCA7F1. - ZIP integrity: PASS. - Factor-affine model construction authorized: FALSE. - Factor-affine solver execution authorized: FALSE. - Coarse-PPT convergence rerun authorized: FALSE. #### Claim ceiling This gate identifies the source-grounded factor-affine target and the exact authorities required before implementation. It does not execute the hierarchy, establish a fixed-history value, determine the exact strict-classical optimum, prove coarse-PPT tightness, close CP4.1, or unblock CP4.2. #### Program status - OIRP-S2.CP4.1: OPEN. - OIRP-S2.CP4.2 entry: BLOCKED. - CP4.R: OPEN at its prior scope. - OIRP-S2: OPEN. #### Next controlling gate **OIRP-S2.CP4.1-HHLW-FACTOR-AFFINE-EXACT-SOURCE-INGEST-AND-MAP-AUTHORITY-REGISTRATION: Stage the exact publication repository archive or clone; register archive, commit, member, and license identities; extract and hash the projection, permutation, history-block, trace-and-replace, and hierarchy sources; bind the exact HHLW construction; issue the tensor-order and notation crosswalk; and authorize only deterministic map tests, with no model construction or solver execution until the source authority passes.** ### OIRP-S2.CP4.1-HHLW-FACTOR-AFFINE-EXACT-SOURCE-INGEST-AND-MAP-AUTHORITY-REGISTRATION #### Exact predecessor The exact canonical predecessor was 472850 bytes with SHA-256 29D6523219C4A234086EB8168E4A448B00CF1DA1915850E255AB64CC7CFF79FB. Its complete bytes are preserved unchanged as the prefix of this successor. #### Disposition **GATE REMAINS OPEN AT THE EXACT-BINARY INGEST BOUNDARY. A SOURCE-BEARING ENTERPRISE PACKAGE WAS LOCATED AND ITS INDEXED CONTENT CONFIRMED THE EXPECTED UPSTREAM REPOSITORY TREE AND CORE JULIA SOURCE FAMILIES, BUT THE EXACT PACKAGE BINARY WAS NOT MATERIALIZED IN THE EXECUTABLE WORKSPACE. ARCHIVE, MEMBER, COMMIT, LICENSE, AND BYTE-LEVEL SOURCE AUTHORITY ARE NOT CERTIFIED. NO MAP TEST, MODEL CONSTRUCTION, OR SOLVER EXECUTION IS AUTHORIZED.** #### Located package and indexed evidence Enterprise search located OIRP-S2.CP4.1-HHLW-PATCH-VERIFY-EXEC-INGEST_PACKAGE.zip. Its indexed content identifies an embedded quantum-channel-discrimination-with-limited-memory-master.zip and the core repository members README.md, SDP_lib.jl, lib.jl, process_matrix_lib.jl, memory_detection_sym_extension.jl, adaptive_cd.jl, classically_adaptive_cd.jl, parallel_cd.jl, single_copy_cd.jl, channel_discrimination.jl, and example scripts. Indexed content exposes relevant map symbols including MultiState, PermuteSystems, PermuteProcess, trace_and_replace, swap, LocalIndex, LinearIndex, partialtrace, partialtranspose, Multi_partialtrace, link_product, Choi_matrix, and adaptive_copy_ensemble. These names establish relevance only. Indexed extraction is not an exact binary and cannot certify exact bytes, archive integrity, checksums, encoding, line endings, commit, license, or executable identity. #### Authority status - Source-bearing package location: PASS. - Embedded upstream ZIP name: PASS. - Exact outer package staged locally: FAIL. - Exact embedded ZIP staged locally: FAIL. - Outer and embedded SHA-256 identities: NOT ESTABLISHED. - Member-level hash registry: NOT ESTABLISHED. - Commit and license evidence: NOT ESTABLISHED. - Tensor-order and notation crosswalk: NOT CERTIFIED. - Deterministic map tests: NOT AUTHORIZED. - Model construction: NOT AUTHORIZED. - Solver execution: NOT AUTHORIZED. #### Claim ceiling This checkpoint locates the source-bearing package and registers named source families visible in indexed content. It does not certify exact source authority or any factor-affine mathematical or numerical result. #### Next controlling gate **OIRP-S2.CP4.1-HHLW-FACTOR-AFFINE-EXACT-SOURCE-BINARY-MATERIALIZATION-AND-HASH-REGISTRATION: Materialize the exact OIRP-S2.CP4.1-HHLW-PATCH-VERIFY-EXEC-INGEST_PACKAGE.zip binary or its exact embedded quantum-channel-discrimination-with-limited-memory-master.zip in /mnt/data; compute outer and embedded SHA-256 identities; test ZIP integrity; inventory and hash every member; register commit and license evidence if present; and stop before map testing, model construction, or solver execution.** ### OIRP-S2.CP4.1-HHLW-FACTOR-AFFINE-EXACT-SOURCE-BINARY-MATERIALIZATION-AND-HASH-REGISTRATION #### Exact predecessor The exact canonical predecessor was 475847 bytes with SHA-256 BF5AF5D2D73A238EA2E601902B346A0AB9B7D32E490D54AC91F7DFD99D123591. Its complete content is preserved unchanged as the prefix of this checksum-distinct successor. #### Disposition **CLOSED WITH PASS FOR EXACT BINARY MATERIALIZATION, ZIP INTEGRITY, EMBEDDED REPOSITORY IDENTITY, COMPLETE MEMBER HASH REGISTRATION, ONE-LINE PATCH IDENTITY, AND EXPLICIT COMMIT/LICENSE ABSENCE.** #### Binary identities - Outer package: OIRP-S2.CP4.1-HHLW-PATCH-VERIFY-EXEC-INGEST_PACKAGE.zip; 153093 bytes; SHA-256 5CC8256EE24941D8F1E0B1B3B00AAA3AC4372EDB9775DCDC7214275808057055; file members 17; ZIP integrity PASS. - Embedded repository archive: quantum-channel-discrimination-with-limited-memory-master.zip; 19406 bytes; SHA-256 5D17D8A483A1DC34D93153863E4E85CCFF4B4964E8D7F412E0EBA414D6C36A56; file members 13; ZIP integrity PASS. - Embedded-to-current ledger relation before this update: EMBEDDED_IS_PREFIX_OF_CURRENT. #### Source and lineage decision The exact original and DIMFIX source hashes match the registered identities. The DIMFIX source differs from the original by exactly one changed source line. The embedded repository archive contains no .git metadata and no LICENSE, COPYING, or NOTICE file. Exact commit identity and software-license lineage remain unresolved and are not inferred from the publication license. #### Authorization Deterministic nonsolver map tests are authorized. Factor-affine model construction and solver execution remain unauthorized. #### Claim ceiling This gate certifies source binary and checksum identities only. It does not certify mathematical correctness of every source routine, the publication-to-code tensor order, Eq. 61 or Eq. 65 equivalence, a factor-affine model, a hierarchy level, a numerical value, or CP4.1 closure. #### Next controlling gate **OIRP-S2.CP4.1-HHLW-FACTOR-AFFINE-DETERMINISTIC-MAP-TESTS-AND-TENSOR-ORDER-CROSSWALK: Execute source-grounded, nonsolver tests of indexing, permutation, trace-and-replace, partial trace, partial transpose, link product, Choi convention, adaptive-copy ordering, and history/block mappings; issue the publication-to-source tensor-order crosswalk; and stop before factor-affine model construction or optimization.** ### OIRP-S2.CP4.1-HHLW-FACTOR-AFFINE-DETERMINISTIC-MAP-TESTS-AND-TENSOR-ORDER-CROSSWALK #### Exact predecessor The exact predecessor was 478241 bytes with SHA-256 352349960E6BB797B982892149AA2552710A76539F48776FF81386EAD63E49B5. Its complete content is preserved unchanged as the prefix of this successor. #### Disposition **CLOSED WITH PASS FOR THE RECOVERED GENERIC INDEX, PERMUTATION, TRACE-AND-REPLACE, PARTIAL-TRACE, PARTIAL-TRANSPOSE, LINK-PRODUCT, CHOI-CONVENTION, ADAPTIVE-COPY DIMENSION, AND DIMFIX-TYPING TESTS. THE PUBLICATION-SPECIFIC EQ. 61 HISTORY PROJECTION, EQ. 65 PERMUTATION/BLOCK EMBEDDING, AND COMPLETE EQS. 66-68 FACTOR-AFFINE EMITTER REMAIN OPEN.** All 28 deterministic nonsolver checks passed. The repository convention is Input tensor Output, with one-based mixed-radix indexing and the last subsystem varying fastest. The DIMFIX role assignment is type-correct for unequal dimensions. The two-copy and adaptive-copy source orders are recorded in the crosswalk. Generic utilities do not establish the exact publication-specific factor-affine maps. No factor-affine model was constructed and no optimizer was called. #### Authorization Factor-affine model construction and solver execution remain unauthorized. #### Next controlling gate **OIRP-S2.CP4.1-HHLW-FACTOR-AFFINE-PUBLICATION-MAP-SPECIFICATION-AND-L1-CONSTRUCTION-PREREGISTRATION: Extract the exact Eq. 61 projection, Eq. 65 permutation/block embedding, Eqs. 66-68 factor-affine maps, and HHLW objective pullback from the publication authority; bind them to certified repository conventions; independently test basis actions; issue an L=1 construction-only specification and exact count manifest; and keep model construction and optimization unauthorized until the specification passes.** ### OIRP-S2.CP4.1-HHLW-FACTOR-AFFINE-PUBLICATION-MAP-SPECIFICATION-AND-L1-CONSTRUCTION-PREREGISTRATION #### Exact predecessor The exact predecessor was 480024 bytes with SHA-256 45EC35DC617D977B104212E79D67C9428DEE7CBA2559B3081828214E674D6128. Its complete content is preserved unchanged as the prefix of this successor. #### Disposition **CLOSED WITH A CORRECTED PUBLICATION-EQUATION CROSSWALK, AN L=1 CARRIER/COUNT SPECIFICATION, AND A FAIL-CLOSED CONSTRUCTION-ONLY PREREGISTRATION.** #### Publication numbering correction The published v2 article controls. The matched-history projection is Eq. 60, not Eq. 61. Definition 23 product form is Eq. 63. The lifted classically adaptive decomposition is Eq. 64, not Eq. 65. The factor-affine constraints are Eqs. 65 and 66, and trace-and-replace is Eq. 67. Eq. 68 belongs to the appendix tester-realization proof and is not a factor-affine map. #### Map specification Eq. 60 retains matched history sectors by summing the partial trace against |jj>