# Source extract: FA-HCOD-02.docx

Hidden-Control False Positives in Quantum Darwinism

A common-record preservation diagnostic for unresolved channel variation

Scott Muniz

Dr. Ware Technology Services, Charleston, SC, United States | scott@drware.com

Research Article submitted for editorial consideration at PRX Quantum

Popular Summary

Quantum systems can look classical when their surroundings store many copies of the same information. But if the interaction that creates those copies is partly hidden, ordinary signs of copying can be misleading. Different hidden interactions may each store a clear record, but not the same record. We introduce a two-step test: first check that all hidden channels preserve the same record, then check that the environment contains enough information about that record. This prevents false positives when experiments or simulations claim that a quantum record has become objective.

Keywords

Quantum Darwinism; spectrum broadcast structures; hidden-control channels; environmental objectivity; common-record preservation; Holevo information; open quantum systems; relational quantum foundations.

Abstract

Environmental redundancy is often used as evidence that a quantum record has become objective. This paper identifies a hidden-control failure mode: if an inaccessible channel label selects different record bases, each channel can exhibit sectorwise decoherence and redundancy while the integrated observer has no single commonly preserved record. We formulate Hidden-Control Objectivity Diagnostics (HCOD), an ETP-based theorem package for certifying objective records under unresolved channel variation. For bounded finite-dimensional Hamiltonian channels, a record-sector projector is preserved for every active hidden channel if and only if the lifted projector commutes with each channel generator. We then define a normalized record-misalignment diagnostic Delta_rec over declared admissible record classes, prove monotonicity, unitary covariance, and perturbation continuity, and add a first- and second-order Duhamel stability expansion. A class-relative no-go corollary states that exact objectivity for records in a declared class is impossible when Delta_rec is nonzero for that class. We connect this algebraic gate to a second fragment-information gate based on integrated Holevo information and show two independent failure modes: sectorwise false-positive objectivity and common-record preservation without sufficient redundancy. We also state measurable-family and CPTP-map versions of the diagnostic and provide deterministic scripts for reproducing the examples. The result refines, rather than replaces, strong Quantum Darwinism and spectrum-broadcast-structure criteria by adding an explicit hidden-control common-record check.

Claim-interface status. HCOD establishes a bounded common-record and fragment-information certification architecture. It does not derive intrinsic record support, an intrinsic observer, an intrinsic operational boundary, a complete physical record channel, a metric, causal geometry, or Lorentzian structure. Intrinsic S1 and intrinsic S2 remain open in the broader research program.

Methodological Scope and Input Boundary

Authority and role. This journal-facing successor is synchronized with ETP Final Synthesis Draft 13, Ultimate Provenance and Conditional Reconstruction Protocol Version 06, Local Relational Time Version 58, and the Local Relational Geometry Version 7 architecture. This manuscript remains a bounded Layer 1 and Target III diagnostic for common-record preservation and fragment information under unresolved channel variation. It does not select a basement, derive physical instantiation, or derive definite events from a merely formal structure.

• Relational potentiality remains a candidate basement, not an established premise or conclusion of this manuscript.

• Physical systems, controls, channels, Hamiltonians, fragments, pointer alternatives, instruments, access structures, outcome registers, probabilities, and records are supplied physical or model inputs whose provenance must be declared.

• Formal states, process matrices, commutators, entropies, mutual informations, Holevo quantities, causal witnesses, postselection identities, and numerical simulations do not establish physical instantiation.

• Objectivity, common-record preservation, redundancy, recoverability, accessibility, causal nonseparability, operational boundaries, topology, and geometry remain distinct claims.

• Target I concerns basement instantiation. Target II concerns definite-event generation. This paper addresses a bounded Target III reconstruction or certification question and does not establish Targets I or II.

• Every conclusion remains indexed to its candidate class, complete carrier, witness or instrument family, selected output, access structure, comparator, tolerance, and analytic or computational status.

Inherited Input Certificate and Claim Ceiling

1. Introduction: Hidden-Control Objectivity Diagnostics

Quantum Darwinism and spectrum-broadcast-structure approaches explain how multiple independent observers can infer the same classical record from environmental fragments. In many theoretical and experimental settings, however, the observer may not know which interaction channel created the fragment records. HCOD asks whether objectivity claims remain valid when a hidden channel label selects among possible record-forming dynamics.

The central failure mode is false-positive objectivity. A Z-channel may decohere and redundantly record the Z basis, while an X-channel may decohere and redundantly record the X basis. If the hidden label is inaccessible, a sectorwise check can report success even though the integrated observer has no one record algebra preserved across the active channels.

The contribution is therefore not the elementary mathematical fact that invariant projectors commute with a Hamiltonian. The contribution is a certification package for hidden-control objectivity claims: specify the admissible record class, compute the common-record obstruction Delta_rec, test fragment information for the same record, and classify exact, approximate, false-positive, or failed objectivity.

HCOD follows a broader methodological principle: operational resources require independent certification. Fragment redundancy certifies information accessibility, while common-record preservation certifies compatibility of the record across unresolved channels. Neither certification route substitutes for the other.

This positioning follows the author’s submission strategy: the Environmental Objectivity and Causal Nonseparability companion is treated as the planned PRXQ anchor paper, while the present ETP/HCOD paper develops the general diagnostic-theorem framework explaining why unresolved control matters.

1.1 Contributions and assumptions roadmap

1.2 Literature positioning and what is new

Zurek’s Quantum Darwinism program identifies information redundancy in environmental fragments as a route to objectivity; HCOD retains the redundancy question but adds a prior common-record gate for unresolved channel variation.

Le and Olaya-Castro prove that strong Quantum Darwinism and strong independence are equivalent to spectrum broadcast structure, and that strong Quantum Darwinism can signal state objectivity without requiring strong independence. HCOD is complementary: it asks whether the same record algebra is preserved across hidden channels before fragment information is interpreted as objectivity.

Korbicz reviews Quantum Darwinism, spectrum broadcast structures, and strong Quantum Darwinism as roads to objectivity. HCOD adds a diagnostic for a hidden-control setting in which roads verified sectorwise may not agree after the channel label is forgotten.

Chisholm, Palma, and Innocenti show that noncommuting evolutions can still allow objective states through a relaxed pointer-state definition. HCOD addresses a different obstruction: even if each channel admits a relaxed pointer or record structure, an observer who cannot access the channel label needs one common record algebra across the active family.

Doucet and Deffner classify two-body Hamiltonians for Quantum Darwinism. HCOD uses a different lens: it does not classify all objectivizing Hamiltonians, but diagnoses whether multiple hidden objectivizing channels preserve a common record once mixed.

2. The Hidden-Control Setting

Let A be a finite set of hidden channels with p_a>0. Channel a has bounded self-adjoint Hamiltonian H(a) on H_S tensor H_E and unitary U_a(t)=exp(-itH(a)). The observer lacks access to a and therefore describes the accessible evolution as Phi_t(rho)=sum_a p_a U_a(t)rho U_a(t)^dagger.

A candidate record class C is a nonempty set of nontrivial finite projective decompositions R={Q_r} of H_S. The trivial decomposition {I_S} is excluded. Three useful choices are C_rank1, all rank-one PVMs; C_coarse, all nontrivial finite coarse-grained projective decompositions; and C_phys, a model-declared set of physically motivated pointer or record algebras.

Complete-carrier declaration. For each asserted objectivity result, the task-relative carrier includes the system, active environment, hidden-channel label or its physically inaccessible implementation, retained record fragments, references and synchronization used by the certification protocol, instrument outputs, any discarded carriers, and correlations relevant to later use. Omitting any admitted component restricts the conclusion to the selected view. Common-record preservation on the declared carrier is not complete physical record-channel closure.

3. Common-Record Preservation Theorem

Proof. Preservation implies U_a(t)(Q_r tensor I_E)U_a(t)^dagger=Q_r tensor I_E. Differentiating at t=0 gives the lifted commutator condition. Conversely, the commutator condition makes the lifted projector invariant under functional calculus of H(a).

4. The Delta_rec Diagnostic

For nonzero channel generators, define

delta_rec(R;H)=max_{a:p_a>0} max_r ||[H(a),Q_r tensor I_E]|| / ||H(a)||.

If zero generators are included, use the regularized denominator ||H(a)||+epsilon_H and report epsilon_H. The unregularized ratio is used in all nonzero examples. For a declared admissible class C, define Delta_rec(C;H)=inf_{R in C} delta_rec(R;H).

Witness-family discipline. Delta_rec is complete only for the declared record class and generator family addressed by the theorem. Failure to find a separator outside a proved-complete family supports RESTRICTED-NULL or UNDERDETERMINED, not complete physical equivalence.

4.1 Structural properties of Delta_rec

5. Stability and Approximate Preservation

The first inequality follows by integrating dQ(t)/dt=i exp(itH)[H,Q]exp(-itH). The second follows by applying the same integral argument to the first derivative and bounding the nested commutator term.

6. Two-Gate Hidden-Control Objectivity Certification

HCOD certifies objectivity using two gates. Gate 1 is common-record preservation: Delta_rec(C;H)=0 for exact claims or Delta_rec(C;H)<=epsilon for approximate claims. Gate 2 is integrated fragment information: many disjoint fragments must carry sufficient information about the same record algebra R that passed Gate 1.

Preservation of a common record algebra does not by itself guarantee exact recoverability, redundancy, or objectivity. Those properties remain distinct and must be evaluated through their own declared operational tests.

7. False-Positive Quantum Darwinism Under Hidden Channel Variation

Figure 1. Hidden channel Z and hidden channel X can each produce sectorwise redundancy while the integrated observer has no common record.

8. Worked Benchmarks Beyond the Z/X Toy Model

Spin-star benchmark. A system qubit interacts with many environmental spins through an axis selected by an unresolved hidden label. If all axes are Z, Delta_rec=0 and the question reduces to fragment information. If the hidden family contains noncommuting axes, Delta_rec becomes positive for the rank-one class and sectorwise redundancy is not enough.

Collisional benchmark. Sequential environmental fragments interact with the system through a hidden channel label selecting the record basis. HCOD classifies whether a redundancy plateau reflects one integrated record or a mixture of channel-conditioned records.

Noncommuting-evolution benchmark. Chisholm-Palma-Innocenti-style relaxed pointer identification can be analyzed within each channel, while HCOD asks whether the relaxed structures agree across the hidden family. This makes the relation between noncommuting within-channel dynamics and hidden-control across-channel compatibility explicit.

9. Measurable-Family and CPTP Generalizations

OIRP Conditional-Closure Interface

Program status. The core Observer-Invariant Reconstruction Program (OIRP) is conditionally closed as a restricted truth-first constitution for conditional reconstruction. This closure does not establish a substrate theory, physical-instantiation bridge, definite-event selector, universal ontological core, intrinsic observer, or positive empirical ETP result. Physical actuality remains admitted rather than derived, ultimate provenance remains unresolved and reopenable, and no common-record or fragment-information result may retroactively justify the supplied systems, controls, channels, Hamiltonians, fragments, pointer alternatives, instruments, probabilities, records, access structures, or physical equivalences on which it depends.

Manuscript effect. The common-record theorem, Delta_rec diagnostic, structural properties, Duhamel stability estimates, class-relative no-go corollary, two-gate certification, false-positive examples, measurable-family extension, CPTP-map formulation, and CPR5.2-validated reproduction artifacts retain their existing scopes. OIRP closure adds governance only; it does not promote class-relative common-record certification into intrinsic objectivity, complete physical record-channel closure, an intrinsic observer or boundary, geometry, definite-event generation, or physical implementation.

Inherited OIRP Constitutional Kernel

K1. Admitted actuality: physical actuality, events, systems, channels, and carriers are admitted for reconstruction, not derived from downstream certification.

K2. Typed target and scope: each claim remains indexed to its record class, channel family, carrier, selected outputs, access structure, comparator, tolerance, and exact, approximate, analytic, or computational status.

K3. Complete carrier and boundary: active environments, hidden labels or implementations, fragments, references, controls, outputs, discarded carriers, resources, and relevant correlations must be declared.

K4. Witness and access: record classes, measurements, instruments, fragment access, and witness-completeness status must be explicit.

K5. Equivalence before identity: class-relative preservation, observer access, record equivalence, representation covariance, and physical equivalence must be typed before objectivity, identity, or nullity promotion.

K6. Transformations, composition, and history: Hamiltonian or CPTP dynamics, hidden mixtures, fragment composition, sequential interactions, and histories must be declared; channelwise certification does not certify the integrated observer description.

K7. Criteria and uncertainty: Delta_rec normalization, regularization, Holevo or mutual-information thresholds, tolerances, perturbation bounds, and numerical error must be explicit.

K8. Provenance, rivals, falsifiers, and ceilings: inputs, Quantum Darwinism and SBS comparators, alternative hidden-control explanations, falsifiers, evidence class, reopening triggers, and nonretroactivity must be preserved.

K9. Plural and null admissibility: exact, approximate, sectorwise false-positive, information-failure, restricted-null, uncertified, and underdetermined outcomes remain legitimate when correctly typed.

Reopening and Successor-Research Control

This manuscript should be reopened or promoted only by qualifying evidence, including a new physical bridge, complete-record-channel theorem, witness-completeness theorem or counterexample, newly relevant hidden carrier or correlation, mixture or composition theorem or failure, revised physical-equivalence result, approximation failure or stronger bound, measured rival discrimination, theorem contradiction, or artifact-integrity failure. Future work otherwise proceeds through restricted successor programs for recoverability and witness completeness, composition and boundary closure, physical realization and empirical discrimination, or separate provenance and definite-event research.

Publication statement. OIRP provides the governing methodology for future HCOD revisions: truth-first, carrier-complete, witness-explicit, equivalence-controlled, composition-aware, provenance-preserving, falsifiable, and nonretroactive.

10. Scope, Relationship to the Anchor Companion, and Future Work

The Environmental Objectivity and Causal Nonseparability companion studies the independence of environmental objectivity and causal nonseparability, whereas HCOD studies the independence of fragment redundancy and common-record preservation under unresolved control. The companion serves as the planned PRXQ anchor paper because it supplies a concrete boundary result and numerical operational quantity; the present ETP/HCOD paper supplies the general hidden-control diagnostic and theorem framework.

This paper does not derive the Born rule, first-person definiteness, continuum spacetime, Lorentz invariance, a microscopic quantum-gravity Hamiltonian, or Einstein dynamics. Those claims are not needed for HCOD. The Mokoena comparison remains interpretive scaffolding only: incomplete relational resolution motivates vocabulary, not new gravitational equations or cosmological claims.

Scope interface. HCOD supplies common-record compatibility criteria and hidden-control falsifiers for already admitted interaction and record families. It does not supply an instantiation bridge or geometric reconstruction map. The controlling corpus authorities are ETP Final Synthesis Draft 13, Ultimate Provenance and Conditional Reconstruction Protocol Version 06, Local Relational Time Version 58, Local Relational Geometry Version 7, and Manuscript Authority Register Version 9.

Future work should implement the CPTP diagnostic in realistic open-system models, estimate Delta_rec experimentally in randomized or adaptive simulators, and quantify observer-disagreement probability as a function of Delta_rec and integrated fragment information.

11. Conclusion

ETP/HCOD reframes the manuscript around a narrow PRXQ-relevant claim: hidden-control variation can create false-positive Quantum Darwinism when objectivity is verified only channel by channel. The common-record theorem, Delta_rec structural properties, Duhamel stability expansion, class-relative no-go corollary, two-gate certification protocol, and CPTP/measurable-family versions together make the paper a diagnostic framework for objective-record certification under unresolved channel variation.

The broader lesson is methodological rather than model specific: integrated objectivity claims require certification of a common record before redundancy diagnostics are interpreted as evidence of objectivity. Hidden control therefore provides a concrete instance of the general principle that operational resources cannot be identified solely from sectorwise evidence.

These conclusions are operational and class-relative. They neither select an intrinsic observer partition nor convert hidden-control compatibility into a claim of emergent geometry or physical-instantiation closure.

Statements and Declarations

Competing interests. The author declares no competing interests.

Funding. The author received no specific funding for this work.

Data availability. The verified deterministic scripts, expected outputs, claim-to-artifact map, and validation runner are supplied with this submission as supplementary material. CPR5.2 validated the archive checksums, executed python scripts/run_all.py --verify, and ran the packaged pytest suite successfully. No public Zenodo DOI or public GitHub URL is claimed for this submission-stage supplement.

Use of AI assistance. Microsoft 365 Copilot based on the GPT-5 reasoning model assisted with language editing, consistency review, literature-positioning synthesis, code drafting, and reproducibility-package drafting. The author directed the work, reviewed the mathematical statements, verified the numerical scripts and references, and remains solely responsible for the content, correctness, and conclusions. No AI system is an author of this manuscript.

Author contributions. S.M. is the sole author and conceived, carried out, and wrote up the work.

Ethics approval. Not applicable.

Appendix A: Proof Details

The proof of Theorem 1 is finite-dimensional and bounded. The preserved object is the lifted projector Q_r tensor I_E or its range. No unbounded-generator claim is made.

The optional linear-independence assumption is per channel. It is required only when decomposed interaction terms are used to infer [A_j(a),Q_r]=0 term by term. The lifted commutator theorem does not require it.

The Duhamel stability expansion is standard. It is included to connect Delta_rec to finite-time record drift, not to claim novelty in operator-dynamics perturbation theory.

Appendix B: Reproducibility Package Contents

The verified HCOD reproducibility supplement includes deterministic scripts, expected outputs, a one-command validation runner, a smoke-test suite, a claim-to-artifact map, release notes, requirements, codemeta, CITATION.cff, and SHA256SUMS.txt. The command python scripts/run_all.py --verify reproduces the expected outputs. Public repository identifiers are intentionally omitted because none has been independently verified.

References

Zurek, W. H. Quantum Darwinism. Nature Physics 5, 181-188 (2009). DOI: 10.1038/nphys1202.

Le, T. P., and Olaya-Castro, A. Strong Quantum Darwinism and Strong Independence are Equivalent to Spectrum Broadcast Structure. Physical Review Letters 122, 010403 (2019). DOI: 10.1103/PhysRevLett.122.010403.

Korbicz, J. K. Roads to objectivity: Quantum Darwinism, Spectrum Broadcast Structures, and Strong quantum Darwinism - a review. Quantum 5, 571 (2021). DOI: 10.22331/q-2021-11-08-571.

Chisholm, D. A., Palma, G. M., and Innocenti, L. Emergence of quantum Darwinism and pointer states for noncommuting evolutions. APS Open Science 1, 000024 (2026). DOI: 10.1103/75jr-ltct.

Doucet, E., and Deffner, S. Classifying Two-Body Hamiltonians for Quantum Darwinism. Physical Review X 14, 041064 (2024). DOI: 10.1103/PhysRevX.14.041064.

Bratteli, O., and Robinson, D. W. Operator Algebras and Quantum Statistical Mechanics 1. Springer, second edition.

Nachtergaele, B., and Sims, R. Lieb-Robinson Bounds in Quantum Many-Body Physics. Contemporary Mathematics 529, 141-176 (2010). arXiv:1004.2086.

Rovelli, C. Relational Quantum Mechanics. International Journal of Theoretical Physics 35, 1637-1678 (1996). DOI: 10.1007/BF02302261.

Muniz, S. Environmental Objectivity and Causal Nonseparability. Unpublished companion manuscript; no public identifier is claimed in this working release.

Muniz, S. Uniform and Sector-Weighted Locality Diagnostics for Topology-Controlled Quantum Dynamics. Unpublished companion manuscript; no public identifier is claimed in this working release.

Muniz, S. HCOD/ETP Version 8 Reproducibility Package. Author-controlled archive; no public persistent identifier is claimed in this working release.

OIRP-S2.MS1 Corpus Synchronization Addendum

Status: SUCCESSOR CANDIDATE. Scientific cutoff: verified record through HHLWBUILD2F Level 5. HHLW Level 6 excluded because no completed raw result was available.

Authority and scope

This checksum-distinct manuscript successor is synchronized through OIRP-S2.MS1 using the verified OIRP-S2 record available on September 18, 2026. The core OIRP program remains conditionally closed only as a truth-first constitution for conditional reconstruction. OIRP-S2 remains open. Physical actuality is admitted rather than derived, ultimate provenance remains unresolved and reopenable, and no downstream reconstruction may retroactively justify its admitted physical inputs.

OIRP-S2 composition update

The current successor program separates constituent certification from composite certification. Channel, instrument, process, comb, superchannel, adaptive-network, controller-inclusive, and memory-bearing claims require their own complete carriers, interfaces, histories, witnesses, equivalence relations, metrics, tolerances, and composition laws. Equality or recoverability under restricted access does not establish complete physical equivalence, and a finite-dimensional computation does not establish physical realization or a nonfinite theorem.

Current CP4.1 numerical and theorem status

CP4.1 has established a restricted finite-dimensional CPTP telescoping theorem for compatible channel sequences, genuine diamond-norm semidefinite-program executions on declared finite-dimensional cases, noncommuting-channel tests, dimension-changing examples, and an ancilla-advantage benchmark. These results do not establish a universal physical composition law, arbitrary process composition, unrestricted adaptive equivalence, nonfinite closure, or OIRP-S2 closure.

HHLWBUILD2F status firewall

The patched repository hierarchy record is L1 = 0.9268200938227155, L2 = 0.9998804689772093, L3 = 1.0000370777829688, L4 = 1.00015286168964, and L5 = 1.0000000197695689. Values slightly above one are treated only as solver-tolerance-compatible with probability one, not as literal probabilities. Level 6 was not available for this synchronization. Formal patch correctness, formal convergence, exact probability one, equality with the strict-classical optimum, equality with the Definition-23 factor-affine hierarchy, CP4.1 closure, and CP4.2 entry are not established.

External relationship and prohibited inference

The external constrained-separability literature formulates limited-memory and classically adaptive channel discrimination using separable variables with additional affine constraints and discusses PPT and constrained symmetric-extension outer approximations. That framework supports keeping the repository patched hierarchy distinct from the full factor-affine constrained hierarchy unless an explicit equivalence and implementation audit is completed. No external source is used here to replace proof, raw execution, or authority-grade numerical certification.

Evidence and release classification

This addendum is a manuscript-synchronization action. It changes cross-program status language and interfaces but does not alter previously proved theorem statements, raw calculations, figures, datasets, or experimental status except where this addendum explicitly narrows a claim. No physical-device experiment, definite-event selector, substrate ontology, universal witness completeness, or ultimate-provenance result is claimed.

Objectivity-composition boundary

Common-record preservation for each declared channel and fragment-information sufficiency remain separate gates. Their satisfaction on constituents does not establish common-record preservation for a composed, adaptive, feedback-controlled, or memory-bearing process. Hidden controller states, outcome registers, retained environments, branch histories, and access changes must be included in the complete carrier.

Source note

Internal authority: OIRP_LEDGER.md and the applicable OIRP/OIRP-S1/OIRP-S2 reproducibility and correction packages in the Recovery corpus. External relationship checked against T.-A. Ohst, S. Zhang, H. C. Nguyen, M. Plavala, and M. T. Quintino, “Characterising memory in quantum channel discrimination via constrained separability problems,” arXiv:2411.08110. Publication status must be verified independently before journal submission.

OIRP-S2 CP4.1-CP4.3 Interface Addendum

This hidden-control objectivity manuscript retains its common-record and fragment-information scope. CP4.1-CP4.3 add only the branch-register, controller, memory, tester, postselection, tomography, operational-quotient, and composite-certification restrictions governing downstream use.

OIRP-S2 remains open. These closures do not establish physical realization, laboratory confirmation, empirical confirmation, indefinite-causal-order closure, a universal process-matrix composition law, a universal operational-memory formula, definite-event generation, substrate ontology, or ultimate physical provenance.

Physical actuality, events, carriers, interactions, records, instruments, calibrations, and empirical inputs remain admitted rather than derived. Ultimate provenance remains unresolved and reopenable. No downstream result may retroactively justify an admitted input.

Restricted closure status

• CP4.1 is closed at a restricted channel-level and HHLW claim ceiling. The exact strict-classical optimum, complete arbitrary-history factor-affine hierarchy, physical realization, and empirical confirmation remain excluded.

• CP4.2 is closed at a restricted instrument, comb, superchannel, adaptive-memory, postselection, tomography, identifiability, implementation, and empirical-preregistration ceiling.

• CP4.3 is closed at a restricted operational-quotient, extension, tensor-descent, operational-memory, fixed-context composite-certification, and general-process no-go ceiling.

Composite-certification firewall

Certified constituents do not automatically certify a composite. Composite use requires matching typed interfaces, complete carriers, causal order, controllers, interleavings, memory and environment access, branch and history treatment, tester class, normalization, success floors, equivalence or gauge, uncertainty model, and implementation class.

The restricted fixed-context hybrid theorem does not imply a universal composition rule for arbitrary process matrices or indefinite causal order. Direct operational tensors must be defined on declared operator-system domains or proved extension independent.

Operational-memory firewall

Operational memory is defined only relative to a fixed realization class by minimizing over all admitted realizations of one operational quotient. Selected ambient-extension Choi rank, selected Stinespring multiplicity, and nonminimal dilation size are not automatically operational-memory invariants.

Authority and reopening

Detailed theorem, numerical, execution, dataset, figure, and empirical authority remains package specific. This manuscript successor does not replace the certified research packages or the canonical OIRP program ledger.

The affected branch reopens if a new carrier, environment, branch, controller, tester, causal architecture, tensor structure, gauge, identifiability result, correction, retraction, counterexample, hardware result, or empirical dataset changes the restricted claim ceiling.