@prefix : . @prefix cor: . @prefix fa: . @prefix owl: . @prefix rdf: . @prefix xml: . @prefix xsd: . @prefix rdfs: . @prefix dc: . a owl:Ontology ; rdfs:label "Foundations Audit & COR Theory Dual Architecture Ontology" ; rdfs:comment "A formal, typed OWL 2 ontology specifying the strict architectural dichotomy and operational bridges between the Foundations Audit (epistemological observatory, Constitutional Kernel K1–K9, P.E.N. definability boundaries, and claim-ceiling governance) and COR Theory (Conditional Operational Reconstruction 5-layer physics stack, complete carrier accounting, HCOD two-gate diagnostics, and countermodel boundaries)." ; owl:versionInfo "v2.1.0-COR" ; dc:creator "Scott Muniz" ; dc:publisher "Dr. Ware Technology Services — FoundationsAudit.org" ; dc:date "2026-10-28" . ################################################################# # Annotation Properties (Governance & Site Integration) ################################################################# fa:claimStatus a owl:AnnotationProperty ; rdfs:label "Claim Status Tier" ; rdfs:comment "Standardized 10-tier Foundations Audit status ceiling assigned to an ontological entity." . fa:evidenceClass a owl:AnnotationProperty ; rdfs:label "Evidence Class" ; rdfs:comment "Epistemological evidence category supporting the entity (e.g., Constitutional / Protocol, Analytic Theorem, Model-Theoretic Boundary)." . fa:siteRoute a owl:AnnotationProperty ; rdfs:label "Canonical Site Route" ; rdfs:comment "Authoritative URL path on FoundationsAudit.org where this ontological concept is documented and audited." . fa:sourceDocument a owl:AnnotationProperty ; rdfs:label "Controlling Source Document" ; rdfs:comment "Verified corpus artifact ID(s) establishing the authority of this class or property." . fa:formalExpression a owl:AnnotationProperty ; rdfs:label "Formal Mathematical / Logical Expression" ; rdfs:comment "Canonical symbolic formula, commutator condition, or algebraic law associated with the entity." . fa:claimCeilingExclusion a owl:AnnotationProperty ; rdfs:label "Claim Ceiling Exclusion (What Is NOT Claimed)" ; rdfs:comment "Explicit nonretroactive boundary preventing ontological overreach or concept smuggling." . fa:domainGroup a owl:AnnotationProperty ; rdfs:label "Ontological Module Group" ; rdfs:comment "Thematic cluster within the dual Foundations Audit / COR Theory architecture." . ################################################################# # Object Properties ################################################################# fa:auditsClaim a owl:ObjectProperty ; rdfs:label "audits claim" ; rdfs:domain fa:FoundationsAuditEngine ; rdfs:range cor:PhysicalClaim ; rdfs:comment "Connects the Foundations Audit Engine to a typed proposition in the COR physics stack for carrier, witness, and nondefinability verification." ; fa:siteRoute "/foundations-audit/audit-engine" . fa:enforcesTargetDomain a owl:ObjectProperty ; rdfs:label "enforces target domain" ; rdfs:domain cor:PhysicalClaim ; rdfs:range fa:TargetDomain ; rdfs:comment "Requires every physical claim to explicitly declare which of the three mutually disjoint epistemological targets (Target I, II, or III) it addresses." ; fa:siteRoute "/foundations-audit/truth-first-method" . cor:requiresCompleteCarrier a owl:ObjectProperty ; rdfs:label "requires complete carrier" ; rdfs:domain cor:PhysicalClaim ; rdfs:range cor:CompleteCarrier ; rdfs:comment "Mandates under Kernel K3 that any physical proposition declare its full substrate ledger (primary system, environment fragment, control line, and work battery)." ; fa:siteRoute "/foundations-audit/constitutional-kernel" . cor:dependsOnLayer a owl:ObjectProperty , owl:TransitiveProperty ; rdfs:label "depends on layer" ; rdfs:domain cor:DependencyLayer ; rdfs:range cor:DependencyLayer ; rdfs:comment "Transitive constructive dependency ordering across the 5-layer COR Theory hierarchy (Layer 4 -> Layer 3 -> Layer 2 -> Layer 1 -> Layer 0)." ; fa:siteRoute "/cor-theory/overview" . fa:evaluatesDiagnosticGate a owl:ObjectProperty ; rdfs:label "evaluates diagnostic gate" ; rdfs:domain fa:FoundationsAuditEngine ; rdfs:range cor:OperationalDiagnostic ; rdfs:comment "Links the Audit Engine to quantitative operational diagnostics such as HCOD, Fisher clock adequacy, and Lieb-Robinson sector envelopes." ; fa:siteRoute "/research/hcod" . cor:preservesPointerAlgebra a owl:ObjectProperty ; rdfs:label "preserves pointer algebra" ; rdfs:domain cor:InteractionChannel ; rdfs:range cor:PointerRecordAlgebra ; rdfs:comment "Specifies that an interaction channel or channel family commutes with and preserves the orthogonal pointer projectors of a candidate record algebra." ; fa:siteRoute "/research/quantum-darwinism" . cor:hasSubstrateComponent a owl:ObjectProperty ; rdfs:label "has substrate component" ; rdfs:domain cor:CompleteCarrier ; rdfs:range cor:SubstrateComponent ; rdfs:comment "Associates a Complete Carrier declaration with its retained and discarded physical degrees of freedom, ancillas, controls, and batteries." ; fa:siteRoute "/cor-theory/core-concepts" . fa:evaluatesGate1 a owl:ObjectProperty ; rdfs:label "evaluates Gate 1 (Common Record Preservation)" ; rdfs:domain cor:HCODDiagnostic ; rdfs:range cor:Gate1_CommonRecordPreservation ; rdfs:comment "First certification gate of the HCOD protocol verifying zero common-record commutator misalignment across all active channels." ; fa:siteRoute "/research/hcod" . fa:evaluatesGate2 a owl:ObjectProperty ; rdfs:label "evaluates Gate 2 (Integrated Fragment Information)" ; rdfs:domain cor:HCODDiagnostic ; rdfs:range cor:Gate2_IntegratedFragmentInformation ; rdfs:comment "Second certification gate of the HCOD protocol verifying Holevo information redundancy across disjoint environment fragments." ; fa:siteRoute "/research/hcod" . fa:governedByKernelRule a owl:ObjectProperty ; rdfs:label "governed by Constitutional Kernel rule" ; rdfs:domain cor:PhysicalClaim ; rdfs:range fa:ConstitutionalKernel ; rdfs:comment "Subjects every physical claim and audit decision to the nine theory-neutral governance rules (K1–K9)." ; fa:siteRoute "/foundations-audit/constitutional-kernel" . cor:requiresPhysicalBridge a owl:ObjectProperty ; rdfs:label "requires physical bridge" ; rdfs:domain cor:PhysicalClaim ; rdfs:range cor:PhysicalBridge ; rdfs:comment "Connects a formal mathematical reduct to physical instantiation via an explicitly admitted operational bridge J_phys." ; fa:siteRoute "/cor-theory/core-concepts" . fa:boundedByCountermodel a owl:ObjectProperty ; rdfs:label "bounded by countermodel" ; rdfs:domain cor:PhysicalClaim ; rdfs:range cor:Countermodel ; rdfs:comment "Identifies explicit mathematical or computational counterexamples that prove the necessity of a theorem's hypotheses and mark its no-go boundary." ; fa:siteRoute "/research/countermodels" . fa:reopenedByTrigger a owl:ObjectProperty ; rdfs:label "reopened by constitutional trigger" ; rdfs:domain cor:Layer_4_HigherSpacetime ; rdfs:range fa:ReopeningTrigger ; rdfs:comment "Specifies the mandatory empirical or formal conditions required to reopen provisionally closed higher-geometry and gravity claims." ; fa:siteRoute "/cor-theory/limits" . cor:supersedesFramework a owl:ObjectProperty ; rdfs:label "universally supersedes framework" ; rdfs:domain cor:CORTheoryStack ; rdfs:range fa:ETP_HistoricalLineage ; rdfs:comment "Formalizes ADR-11: COR Theory universally replaces Emergent Timeless Potentiality (ETP) as the controlling theory stack while preserving ETP for provenance." ; fa:siteRoute "/cor-theory/evolution" . ################################################################# # 1. FOUNDATIONS AUDIT DOMAIN (fa:) # Epistemological Observatory, Rules & Governance Firewall ################################################################# fa:FoundationsAuditEngine a owl:Class ; rdfs:label "Foundations Audit Engine" ; rdfs:comment "The judicial scientific observatory and operational audit engine enforcing non-circularity, P.E.N. definability limits, claim ceilings, and complete carrier accounting." ; fa:domainGroup "Audit Engine & Provenance" ; fa:claimStatus "Exact result" ; fa:evidenceClass "Constitutional / Protocol" ; fa:siteRoute "/foundations-audit/audit-engine" ; fa:sourceDocument "FA-AUTH-01, OIRP_LEDGER" ; fa:formalExpression "Intake -> Carrier(K3) -> P.E.N.(L_0, L_1) -> Witness(K4) -> Ceiling(K8)" ; fa:claimCeilingExclusion "Does not propose a speculative physical substrate; PUB-03 internal repository tooling is strictly firewalled from public scientific claims." . fa:ConstitutionalKernel a owl:Class ; rdfs:label "Constitutional Kernel (K1–K9)" ; rdfs:comment "Governing 9-point theory-neutral epistemological inspection rules (K1–K9) situated above both the Audit Engine and COR Theory." ; fa:domainGroup "Constitutional Kernel" ; fa:claimStatus "Admission" ; fa:evidenceClass "Constitutional / Protocol" ; fa:siteRoute "/foundations-audit/constitutional-kernel" ; fa:sourceDocument "FA-AUTH-01" ; fa:formalExpression "K = {K1, K2, K3, K4, K5, K6, K7, K8, K9}" ; fa:claimCeilingExclusion "The Kernel is methodological and epistemic governance, not a dynamical equation of motion or physical law." . fa:Rule_K1_AdmittedActuality a owl:Class ; rdfs:label "K1: Admitted Actuality" ; rdfs:subClassOf fa:ConstitutionalKernel ; rdfs:comment "K1: Physical actuality, events, and state carriers are admitted as factual starting points for conditional reconstruction, never derived as ultimate ontology." ; fa:domainGroup "Constitutional Kernel" ; fa:claimStatus "Admission" ; fa:evidenceClass "Constitutional / Protocol" ; fa:siteRoute "/foundations-audit/constitutional-kernel" ; fa:sourceDocument "FA-AUTH-01" ; fa:formalExpression "Actuality(A_0) := Admitted; not Derived(L_0 |- A_0)" ; fa:claimCeilingExclusion "Downstream operational success cannot retroactively prove or derive ultimate ontological existence." . fa:Rule_K2_TypedScope a owl:Class ; rdfs:label "K2: Typed Target and Scope" ; rdfs:subClassOf fa:ConstitutionalKernel ; rdfs:comment "K2: All claims remain strictly indexed to target, domain, task, regime, and exact/approximate status." ; fa:domainGroup "Constitutional Kernel" ; fa:claimStatus "Definition" ; fa:evidenceClass "Constitutional / Protocol" ; fa:siteRoute "/foundations-audit/constitutional-kernel" ; fa:sourceDocument "FA-AUTH-01" ; fa:formalExpression "Claim := (Target, Domain, Task, Regime, Exactness)" ; fa:claimCeilingExclusion "Results certified within a finite-dimensional or task-relative regime cannot be extrapolated to unbounded continuum regimes without separate proof." . fa:Rule_K3_CompleteCarrierDeclaration a owl:Class ; rdfs:label "K3: Complete Carrier and Boundary Declaration" ; rdfs:subClassOf fa:ConstitutionalKernel ; rdfs:comment "K3: Forces complete declaration of primary systems, discarded and retained environments, ancillas, controls, references, and work batteries." ; fa:domainGroup "Constitutional Kernel" ; fa:claimStatus "Definition" ; fa:evidenceClass "Constitutional / Protocol" ; fa:siteRoute "/foundations-audit/constitutional-kernel" ; fa:sourceDocument "FA-AUTH-01" ; fa:formalExpression "C_complete = H_S x H_E x H_C x H_B x H_ref" ; fa:claimCeilingExclusion "Tracing out an environment or control line restricts operational access but does not erase its physical correlations." . fa:Rule_K4_WitnessAndAccess a owl:Class ; rdfs:label "K4: Witness and Access Discipline" ; rdfs:subClassOf fa:ConstitutionalKernel ; rdfs:comment "K4: Measurement testers, readouts, access restrictions, and witness-completeness status must be explicitly declared." ; fa:domainGroup "Constitutional Kernel" ; fa:claimStatus "Definition" ; fa:evidenceClass "Constitutional / Protocol" ; fa:siteRoute "/foundations-audit/constitutional-kernel" ; fa:sourceDocument "FA-AUTH-01, FA-LRT-01" ; fa:formalExpression "WitnessFamily W = {M_alpha}; Nullity typed by Completeness(W)" ; fa:claimCeilingExclusion "Failure to detect a difference under restricted access establishes Restricted-Null status, never ontic identity." . fa:Rule_K5_EquivalenceBeforeIdentity a owl:Class ; rdfs:label "K5: Equivalence Before Identity" ; rdfs:subClassOf fa:ConstitutionalKernel ; rdfs:comment "K5: Operational, representational, gauge, and physical equivalences must be formally typed before asserting identity or invariance." ; fa:domainGroup "Constitutional Kernel" ; fa:claimStatus "Definition" ; fa:evidenceClass "Constitutional / Protocol" ; fa:siteRoute "/foundations-audit/constitutional-kernel" ; fa:sourceDocument "FA-AUTH-01" ; fa:formalExpression "x ~_op y =/= x ===_phys y" ; fa:claimCeilingExclusion "Quotient equivalence under a limited observable algebra does not imply ontological identity of underlying states." . fa:Rule_K6_TransformationsCompositionAndHistory a owl:Class ; rdfs:label "K6: Transformations, Composition, and History" ; rdfs:subClassOf fa:ConstitutionalKernel ; rdfs:comment "K6: Constituent certification does not automatically certify composite systems, sequential histories, or open-system continuations." ; fa:domainGroup "Constitutional Kernel" ; fa:claimStatus "Restricted result" ; fa:evidenceClass "Constitutional / Protocol" ; fa:siteRoute "/foundations-audit/constitutional-kernel" ; fa:sourceDocument "FA-AUTH-01, OIRP_LEDGER" ; fa:formalExpression "Certified(A) & Certified(B) =/=> Certified(A (x) B)" ; fa:claimCeilingExclusion "Prevents silent aggregation of local subsystem bounds into global composite guarantees without holonomy and cross-talk audits." . fa:Rule_K7_CriteriaAndUncertainty a owl:Class ; rdfs:label "K7: Criteria, Calibration, and Uncertainty" ; rdfs:subClassOf fa:ConstitutionalKernel ; rdfs:comment "K7: Error models, tolerances, calibration protocols, solver budgets, and resource bounds must be explicitly stated." ; fa:domainGroup "Constitutional Kernel" ; fa:claimStatus "Definition" ; fa:evidenceClass "Constitutional / Protocol" ; fa:siteRoute "/foundations-audit/constitutional-kernel" ; fa:sourceDocument "FA-AUTH-01, FA-LRT-01" ; fa:formalExpression "Tolerance(epsilon_calib, epsilon_solver) >= 0" ; fa:claimCeilingExclusion "Numerical SDP solver tolerances (e.g., values 1.0 + 1e-8) are numerical artifacts, never super-quantum physical probabilities." . fa:Rule_K8_NonretroactivityFirewall a owl:Class ; rdfs:label "K8: Provenance, Rivals, Falsifiers, and Nonretroactivity Firewall" ; rdfs:subClassOf fa:ConstitutionalKernel ; rdfs:comment "K8: Downstream operational success cannot retroactively justify or prove upstream basement instantiation; rivals and falsifiers must be preserved." ; fa:domainGroup "Constitutional Kernel" ; fa:claimStatus "Admission" ; fa:evidenceClass "Constitutional / Protocol" ; fa:siteRoute "/foundations-audit/constitutional-kernel" ; fa:sourceDocument "FA-AUTH-01" ; fa:formalExpression "Success(Layer_k) =/=> Proof(Layer_0)" ; fa:claimCeilingExclusion "Blocks retroactive ontological boot-strapping from effective operational models." . fa:Rule_K9_PluralAndNullAdmissibility a owl:Class ; rdfs:label "K9: Plural and Null Admissibility" ; rdfs:subClassOf fa:ConstitutionalKernel ; rdfs:comment "K9: Preserves null results, refutations, countermodels, Pareto frontiers, and underdetermination as valid, successful scientific outcomes." ; fa:domainGroup "Constitutional Kernel" ; fa:claimStatus "Admission" ; fa:evidenceClass "Constitutional / Protocol" ; fa:siteRoute "/foundations-audit/constitutional-kernel" ; fa:sourceDocument "FA-AUTH-01" ; fa:formalExpression "Outcome in {Exact, Restricted, Countermodel, Null, Plural, Open}" ; fa:claimCeilingExclusion "Refusal to force a unique closure where evidence underdetermines the outcome is mandatory scientific rigor, not failure." . ### The Three-Target Firewall (Strictly Disjoint Classes) fa:TargetDomain a owl:Class ; rdfs:label "Epistemological Target Domain" ; rdfs:comment "Epistemological targets separating physical existence (Target I), single definite event occurrence (Target II), and conditional operational reconstruction (Target III)." ; fa:domainGroup "Three-Target Firewall" ; fa:claimStatus "Definition" ; fa:evidenceClass "Constitutional / Protocol" ; fa:siteRoute "/foundations-audit/truth-first-method" ; fa:sourceDocument "FA-AUTH-01, FA-SYN-01" ; fa:formalExpression "Target_I (+) Target_II (+) Target_III (Pairwise Disjoint)" ; fa:claimCeilingExclusion "Progress in Target III operational reconstruction never resolves Target I existence or Target II single-outcome selection." . fa:Target_I_BasementInstantiation a owl:Class ; rdfs:label "Target I: Basement Instantiation (What Exists)" ; rdfs:subClassOf fa:TargetDomain ; owl:disjointWith fa:Target_II_DefiniteEventGeneration , fa:Target_III_OperationalReconstruction ; rdfs:comment "Target I: What exists fundamentally (Basement instantiation / K1 Admitted Actuality). Treated as admitted input, never derived from syntax." ; fa:domainGroup "Three-Target Firewall" ; fa:claimStatus "Admission" ; fa:evidenceClass "Constitutional / Protocol" ; fa:siteRoute "/foundations-audit/truth-first-method" ; fa:sourceDocument "FA-AUTH-01" ; fa:formalExpression "Target_I : Physical Instantiation Predicate P_phys" ; fa:claimCeilingExclusion "Blocked from formal derivation by the Paired-Expansion Nondefinability (P.E.N.) Theorem." . fa:Target_II_DefiniteEventGeneration a owl:Class ; rdfs:label "Target II: Definite Event Generation (What Happens)" ; rdfs:subClassOf fa:TargetDomain ; owl:disjointWith fa:Target_III_OperationalReconstruction ; rdfs:comment "Target II: What actually happens in a single run (Single definite event token generation and non-null physical outcome registration)." ; fa:domainGroup "Three-Target Firewall" ; fa:claimStatus "Admission" ; fa:evidenceClass "Constitutional / Protocol" ; fa:siteRoute "/physics-explained/measurement-problem" ; fa:sourceDocument "FA-AUTH-01, FA-SYN-01" ; fa:formalExpression "Target_II : Single-Run Event Token e_k in E_admitted" ; fa:claimCeilingExclusion "Decoherence and Quantum Darwinism explain pointer selection and broadcast (Target III), not single-outcome actualization (Target II)." . fa:Target_III_OperationalReconstruction a owl:Class ; rdfs:label "Target III: Conditional Operational Reconstruction" ; rdfs:subClassOf fa:TargetDomain ; rdfs:comment "Target III: How observers reconstruct objective records, operational duration, calibrated clocks, causal latency, and geometry from admitted events." ; fa:domainGroup "Three-Target Firewall" ; fa:claimStatus "Exact result" ; fa:evidenceClass "Analytic Theorem" ; fa:siteRoute "/cor-theory/overview" ; fa:sourceDocument "FA-SYN-01, FA-LRT-01, FA-LRG-01" ; fa:formalExpression "Target_III : (A_0, J_phys, C_complete) |-> {Records, Duration, CausalBounds}" ; fa:claimCeilingExclusion "Strictly conditional on admitted Target I/II packages; cannot be inverted to derive Target I or Target II." . ### Basement Provenance Protocol & Model-Theoretic Boundaries fa:BasementProvenanceProtocol a owl:Class ; rdfs:label "Basement Provenance Protocol (BNP)" ; rdfs:comment "Formal logic auditing physical inputs vs. outputs (0 + X = X, 0 + X != 0 => X != 0) to prevent smuggling physical structure through pure syntax." ; fa:domainGroup "Audit Engine & Provenance" ; fa:claimStatus "Exact result" ; fa:evidenceClass "Model-Theoretic Boundary" ; fa:siteRoute "/foundations-audit/truth-first-method" ; fa:sourceDocument "FA-AUTH-01, FA-LRT-01" ; fa:formalExpression "0 + X = X ; (0 + X != 0) => (X != 0)" ; fa:claimCeilingExclusion "Zero physical input combined with formal transformations yields zero physical instantiation without an admitted bridge X != 0." . fa:NonNullProvenancePrinciple a owl:Class ; rdfs:label "Non-Null Provenance Principle" ; rdfs:subClassOf fa:BasementProvenanceProtocol ; rdfs:comment "Proves non-null physical outcomes strictly require non-null physical input provenance." ; fa:domainGroup "Audit Engine & Provenance" ; fa:claimStatus "Exact result" ; fa:evidenceClass "Model-Theoretic Boundary" ; fa:siteRoute "/foundations-audit/truth-first-method" ; fa:sourceDocument "FA-AUTH-01" ; fa:formalExpression "Prov_phys(Output) != 0 => Prov_phys(Input) != 0" ; fa:claimCeilingExclusion "Refutes any claim of 'emergence from nothing' or purely mathematical genesis of physical reality." . fa:PEN_NondefinabilityTheorem a owl:Class ; rdfs:label "Paired-Expansion Nondefinability Theorem (P.E.N.)" ; rdfs:subClassOf fa:BasementProvenanceProtocol ; rdfs:comment "Model-theoretic theorem: when a formal reduct L_0 admits two expansions agreeing on L_0 but differing in physical instantiation P_phys, instantiation is neither implicitly nor explicitly definable from L_0." ; fa:domainGroup "Audit Engine & Provenance" ; fa:claimStatus "Exact result" ; fa:evidenceClass "Model-Theoretic Boundary" ; fa:siteRoute "/foundations-audit/audit-engine" ; fa:sourceDocument "FA-AUTH-01" ; fa:formalExpression "M_1|L_0 = M_2|L_0 & P_phys(M_1) != P_phys(M_2) => L_0 |/|- P_phys" ; fa:claimCeilingExclusion "Establishes scoped model-theoretic nondefinability over declared languages, not universal mystic unknowability." . fa:TypedNullityProtocol a owl:Class ; rdfs:label "Typed Nullity Protocol (BNP-C3)" ; rdfs:subClassOf fa:BasementProvenanceProtocol ; rdfs:comment "Classifies operational indistinguishability into NULL (proved-complete witness family), RESTRICTED-NULL (task/access limited), and UNDETERMINED." ; fa:domainGroup "Audit Engine & Provenance" ; fa:claimStatus "Definition" ; fa:evidenceClass "Constitutional / Protocol" ; fa:siteRoute "/evidence/glossary" ; fa:sourceDocument "FA-LRT-01" ; fa:formalExpression "Nullity in {NULL_complete, RESTRICTED-NULL_task, UNDETERMINED}" ; fa:claimCeilingExclusion "Prevents conflating lack of observed difference under restricted instruments with true physical absence." . fa:ClaimStatusTier a owl:Class ; rdfs:label "Claim Status System (10 Tiers)" ; rdfs:comment "Standardized 10-tier taxonomy enforcing explicit epistemic ceilings: Admission, Definition, Exact result, Restricted result, Countermodel, Empirical result, Conjecture, Open question, Internal diagnostic, Historical." ; fa:domainGroup "Program Lineage & Status" ; fa:claimStatus "Definition" ; fa:evidenceClass "Constitutional / Protocol" ; fa:siteRoute "/foundations-audit/claim-status" ; fa:sourceDocument "FA-AUTH-01" ; fa:formalExpression "Status in {ADM, DEF, EXA, RES, CNT, EMP, CNJ, OPN, INT, HIS}" ; fa:claimCeilingExclusion "No positive Empirical Result [EMP] on quantum hardware is claimed for ETP/COR; PUB-03 is strictly [INT]." . fa:ReopeningTrigger a owl:Class ; rdfs:label "Constitutional Reopening Trigger (10 Triggers)" ; rdfs:comment "Pre-registered formal and empirical conditions required to reopen provisionally closed questions such as Layer 4 spacetime dynamics and gravity." ; fa:domainGroup "Program Lineage & Status" ; fa:claimStatus "Open question" ; fa:evidenceClass "Constitutional / Protocol" ; fa:siteRoute "/cor-theory/limits" ; fa:sourceDocument "FA-AUTH-01, FA-LRG-01" ; fa:formalExpression "Reopen(Layer_4) <=> Verified(Trigger_i), i in {1..10}" ; fa:claimCeilingExclusion "Until a registered trigger is satisfied, higher geometry and gravity remain closed at their documented underdetermination ceiling." . fa:ProgramLineage a owl:Class ; rdfs:label "Foundations Triad & Program Lineage" ; rdfs:comment "Architectural separation between the immutable research ledger (OIRP), retained historical manuscript lineage (ETP), and sole controlling theory stack (COR)." ; fa:domainGroup "Program Lineage & Status" ; fa:claimStatus "Definition" ; fa:evidenceClass "Historical Ledger" ; fa:siteRoute "/cor-theory/evolution" ; fa:sourceDocument "FA-AUTH-01, OIRP_LEDGER" ; fa:formalExpression "Triad = (OIRP_Ledger [HIS], ETP_Corpus [HIS], COR_Theory [CONTROLLING])" ; fa:claimCeilingExclusion "Preserving ETP and OIRP archives maintains cryptographic provenance and never overrides COR Theory's controlling authority." . fa:OIRP_ResearchLedger a owl:Class ; rdfs:label "OIRP Master Research Ledger" ; rdfs:subClassOf fa:ProgramLineage ; rdfs:comment "Observer-Invariant Reconstruction Program immutable historical checkpoint record (OIRP-11 through CP4.R2C)." ; fa:domainGroup "Program Lineage & Status" ; fa:claimStatus "Historical" ; fa:evidenceClass "Historical Ledger" ; fa:siteRoute "/research/oirp" ; fa:sourceDocument "OIRP_LEDGER" ; fa:formalExpression "Checkpoints = {OIRP-11..17, OIRP-S1, OIRP-S2: CP4.1..CP4.R2C}" ; fa:claimCeilingExclusion "Closed as a restricted constitutional program; HHLW Level 6 is explicitly excluded as unverified." . fa:ETP_HistoricalLineage a owl:Class ; rdfs:label "ETP Historical Manuscript Lineage" ; rdfs:subClassOf fa:ProgramLineage ; rdfs:comment "Emergent Timeless Potentiality predecessor manuscript archive permanently retained for derivation traceability and SHA-256 provenance." ; fa:domainGroup "Program Lineage & Status" ; fa:claimStatus "Historical" ; fa:evidenceClass "Historical Ledger" ; fa:siteRoute "/cor-theory/evolution" ; fa:sourceDocument "FA-AUTH-01, FA-SYN-01" ; fa:formalExpression "ETP --[Universally Superseded By K1-K9]--> COR Theory" ; fa:claimCeilingExclusion "Retained strictly for historical provenance; all speculative ontological emergence language is superseded by COR Theory." . ################################################################# # 2. COR THEORY DOMAIN (cor:) # Conditional Operational Reconstruction Physics Stack ################################################################# cor:CORTheoryStack a owl:Class ; rdfs:label "COR Theory Stack (Conditional Operational Reconstruction)" ; rdfs:comment "The sole controlling, authoritative positive physics framework reconstructing operational records, duration, and locality conditionally from admitted physical packages." ; rdfs:subClassOf [ a owl:Restriction ; owl:onProperty cor:supersedesFramework ; owl:someValuesFrom fa:ETP_HistoricalLineage ] ; fa:domainGroup "COR Layer Hierarchy" ; fa:claimStatus "Exact result" ; fa:evidenceClass "Constitutional / Protocol" ; fa:siteRoute "/cor-theory" ; fa:sourceDocument "FA-SYN-01, FA-AUTH-01" ; fa:formalExpression "COR : Admitted(A_0, J_phys, C_complete) |-> OperationalStack(L_0..L_4)" ; fa:claimCeilingExclusion "Not a 'theory of everything'; does not derive physical actuality, the Born rule, or quantum mechanics from pure logic." . cor:PhysicalClaim a owl:Class ; rdfs:label "Typed Physical Claim" ; rdfs:comment "A typed scientific proposition within the COR physics framework subject to target indexing, complete carrier declaration, and claim-ceiling audit." ; fa:domainGroup "Audit Engine & Provenance" ; fa:claimStatus "Definition" ; fa:evidenceClass "Constitutional / Protocol" ; fa:siteRoute "/foundations-audit" ; fa:sourceDocument "FA-AUTH-01, FA-SYN-01" ; fa:formalExpression "Proposition P : (Target_k, C_complete, W_access, StatusCeiling)" ; fa:claimCeilingExclusion "Unconditioned or untyped assertions fail intake verification under K2 and K3." . cor:PhysicalBridge a owl:Class ; rdfs:label "Admitted Physical Bridge (J_phys)" ; rdfs:subClassOf cor:CORTheoryStack ; rdfs:comment "Explicitly declared operational mapping connecting formal mathematical terms in a reduct to admitted physical instruments, readouts, and state carriers." ; fa:domainGroup "Complete Carrier Schema" ; fa:claimStatus "Admission" ; fa:evidenceClass "Constitutional / Protocol" ; fa:siteRoute "/cor-theory/core-concepts" ; fa:sourceDocument "FA-SYN-01, FA-LRT-01" ; fa:formalExpression "J_phys : L_0_Syntax --> AdmittedPhysicalOperations" ; fa:claimCeilingExclusion "A bridge is an admitted operational stipulation (K1/K3), never an automatic consequence of pure mathematics." . ### 5-Layer Reconstruction Hierarchy cor:DependencyLayer a owl:Class ; rdfs:label "COR Constructive Dependency Layer" ; rdfs:subClassOf cor:CORTheoryStack ; rdfs:comment "Stratified constructive layer within the COR Theory hierarchy ordered by transitive dependency (Layer 0 through Layer 4)." ; fa:domainGroup "COR Layer Hierarchy" ; fa:claimStatus "Definition" ; fa:evidenceClass "Constitutional / Protocol" ; fa:siteRoute "/cor-theory/overview" ; fa:sourceDocument "FA-SYN-01" ; fa:formalExpression "L_0 < L_1 < L_2 < L_3 < L_4 (Transitive Dependency)" ; fa:claimCeilingExclusion "Upper layers depend transitively on lower layers but cannot retroactively validate lower-layer premises (K8)." . cor:Layer_0_BasementProvenance a owl:Class ; rdfs:label "Layer 0: Admitted Actuality & Basement Provenance" ; rdfs:subClassOf cor:DependencyLayer ; rdfs:comment "Layer 0: Admitted physical actuality, complete carrier declarations, and the non-null provenance protocol (BNP)." ; fa:domainGroup "COR Layer Hierarchy" ; fa:claimStatus "Admission" ; fa:evidenceClass "Constitutional / Protocol" ; fa:siteRoute "/cor-theory/core-concepts" ; fa:sourceDocument "FA-AUTH-01, FA-SYN-01" ; fa:formalExpression "Layer 0 : (A_0 != 0, J_phys, C_complete)" ; fa:claimCeilingExclusion "Ultimate metaphysical provenance of physical existence is unresolved and explicitly not derived." . cor:Layer_1_EventsAndRecords a owl:Class ; rdfs:label "Layer 1: Events, Pointer Algebras & Relational Records" ; rdfs:subClassOf cor:DependencyLayer , [ a owl:Restriction ; owl:onProperty cor:dependsOnLayer ; owl:someValuesFrom cor:Layer_0_BasementProvenance ] ; rdfs:comment "Layer 1: Instantiated events, orthogonal pointer states, Quantum Darwinism broadcast channels, HCOD diagnostics, and plural memory structures." ; fa:domainGroup "COR Layer Hierarchy" ; fa:claimStatus "Exact result" ; fa:evidenceClass "Analytic Theorem" ; fa:siteRoute "/research/quantum-darwinism" ; fa:sourceDocument "FA-SYN-01, FA-QD-ST-01, FA-HCOD-02" ; fa:formalExpression "Layer 1 : [H(a), Q_r (x) I_E] = 0 & I_Holevo(R : E_f) >= (1 - delta) H(R)" ; fa:claimCeilingExclusion "Explains conditional broadcast of pointer records; does not derive wave-function collapse or the Born rule." . cor:Layer_2_LocalRelationalTime a owl:Class ; rdfs:label "Layer 2: Local Relational Time & Fisher Clocks" ; rdfs:subClassOf cor:DependencyLayer , [ a owl:Restriction ; owl:onProperty cor:dependsOnLayer ; owl:someValuesFrom cor:Layer_1_EventsAndRecords ] ; rdfs:comment "Layer 2: Operational duration, Accessible Fisher Information, Fisher-clock correspondence, comparison transducers, and loop holonomy synchronization." ; fa:domainGroup "COR Layer Hierarchy" ; fa:claimStatus "Exact result" ; fa:evidenceClass "Analytic Theorem" ; fa:siteRoute "/cor-theory/time" ; fa:sourceDocument "FA-LRT-01, FA-SYN-01" ; fa:formalExpression "Layer 2 : d_tau_op = sqrt(I_F^(acc)(theta)) d_theta ; Holonomy(gamma) = id" ; fa:claimCeilingExclusion "Establishes conditional clock correspondence; does not derive metaphysical, cosmological, or universal absolute time." . cor:Layer_3_LocalRelationalGeometry a owl:Class ; rdfs:label "Layer 3: Local Relational Geometry & Propagation Bounds" ; rdfs:subClassOf cor:DependencyLayer , [ a owl:Restriction ; owl:onProperty cor:dependsOnLayer ; owl:someValuesFrom cor:Layer_2_LocalRelationalTime ] ; rdfs:comment "Layer 3: Graph interaction topology, sector-family Lieb-Robinson propagation diagnostics (C_inf, C_1, C_bar), and recoverability metrics." ; fa:domainGroup "COR Layer Hierarchy" ; fa:claimStatus "Restricted result" ; fa:evidenceClass "Analytic Theorem" ; fa:siteRoute "/cor-theory/causality-topology" ; fa:sourceDocument "FA-CB-02, FA-LRG-01" ; fa:formalExpression "Layer 3 : C_bar(x,t) <= C_1(x,t) <= C_inf(x,t)" ; fa:claimCeilingExclusion "Lieb-Robinson velocity is a lattice-convention bound parameter, not a derived relativistic invariant speed of light c." . cor:Layer_4_HigherSpacetime a owl:Class ; rdfs:label "Layer 4: Higher Spacetime & Gravity (Provisionally Closed / Open)" ; rdfs:subClassOf cor:DependencyLayer , [ a owl:Restriction ; owl:onProperty cor:dependsOnLayer ; owl:someValuesFrom cor:Layer_3_LocalRelationalGeometry ] , [ a owl:Restriction ; owl:onProperty fa:reopenedByTrigger ; owl:someValuesFrom fa:ReopeningTrigger ] ; rdfs:comment "Layer 4: Provisional higher continuum geometry, Lorentzian signature emergence, and Einstein spacetime dynamics (currently closed at underdetermination ceiling and reopenable via 10 triggers)." ; fa:domainGroup "COR Layer Hierarchy" ; fa:claimStatus "Open question" ; fa:evidenceClass "Constitutional / Protocol" ; fa:siteRoute "/cor-theory/geometry" ; fa:sourceDocument "FA-LRG-01, FA-AUTH-01" ; fa:formalExpression "Layer 4 : Status = UNRESOLVED_AND_REOPENABLE (Triggers 1..10)" ; fa:claimCeilingExclusion "Does NOT establish an intrinsic Lorentzian metric, continuum manifold, Levi-Civita uniqueness without metric inputs, or emergent gravity." . ### Complete Carrier Schema (K3 Class Requirements) cor:SubstrateComponent a owl:Class ; rdfs:label "Physical Substrate Component" ; rdfs:subClassOf cor:CORTheoryStack ; rdfs:comment "A declared physical subsystem, bath, control register, or energy reservoir within the Complete Carrier ledger." ; fa:domainGroup "Complete Carrier Schema" ; fa:claimStatus "Definition" ; fa:evidenceClass "Constitutional / Protocol" ; fa:siteRoute "/cor-theory/core-concepts" ; fa:sourceDocument "FA-AUTH-01, FA-SYN-01" ; fa:formalExpression "H_component subseteq C_complete" ; fa:claimCeilingExclusion "No component may be silently traced out while retaining claims that depend on its coherence or work supply." . cor:CompleteCarrier a owl:Class ; rdfs:label "Complete Carrier (K3 Ledger)" ; rdfs:comment "Full physical substrate ledger required by Kernel K3: intersection of Primary System with declared Environment Fragment, Control Line, and Work Battery." ; owl:equivalentClass [ a owl:Class ; owl:intersectionOf ( cor:PrimarySystem [ a owl:Restriction ; owl:onProperty cor:hasSubstrateComponent ; owl:someValuesFrom cor:EnvironmentFragment ] [ a owl:Restriction ; owl:onProperty cor:hasSubstrateComponent ; owl:someValuesFrom cor:ControlLine ] [ a owl:Restriction ; owl:onProperty cor:hasSubstrateComponent ; owl:someValuesFrom cor:WorkBattery ] ) ] ; fa:domainGroup "Complete Carrier Schema" ; fa:claimStatus "Definition" ; fa:evidenceClass "Constitutional / Protocol" ; fa:siteRoute "/foundations-audit/constitutional-kernel" ; fa:sourceDocument "FA-AUTH-01, FA-SYN-01" ; fa:formalExpression "C_complete === PrimarySystem & exists hasSubstrateComponent.(EnvironmentFragment & ControlLine & WorkBattery)" ; fa:claimCeilingExclusion "Omitting any active carrier component downgrades an audited claim to an incomplete or restricted view." . cor:PrimarySystem a owl:Class ; rdfs:label "Primary System (H_S)" ; rdfs:subClassOf cor:SubstrateComponent ; rdfs:comment "The target physical system carrying the candidate pointer observable or clock parameter under investigation." ; fa:domainGroup "Complete Carrier Schema" ; fa:claimStatus "Definition" ; fa:evidenceClass "Constitutional / Protocol" ; fa:siteRoute "/cor-theory/core-concepts" ; fa:sourceDocument "FA-SYN-01" ; fa:formalExpression "H_S (System Hilbert Space / State Space)" ; fa:claimCeilingExclusion "Cannot be treated as isolated when environmental broadcast or control conditioning is invoked." . cor:EnvironmentFragment a owl:Class ; rdfs:label "Environment Fragment (H_E_k)" ; rdfs:subClassOf cor:SubstrateComponent ; rdfs:comment "Sub-partition of the surrounding environment sampled by independent observers to test redundant classical record broadcast." ; fa:domainGroup "Complete Carrier Schema" ; fa:claimStatus "Definition" ; fa:evidenceClass "Constitutional / Protocol" ; fa:siteRoute "/research/quantum-darwinism" ; fa:sourceDocument "FA-QD-ST-01, FA-HCOD-02" ; fa:formalExpression "H_E = (x)_{k=1}^N H_{E_k}, F subset {1..N}" ; fa:claimCeilingExclusion "Environment partition structure is an admitted operational decomposition, not derived from pure spectrum alone." . cor:ControlLine a owl:Class ; rdfs:label "Quantum/Classical Control Line (H_C)" ; rdfs:subClassOf cor:SubstrateComponent ; rdfs:comment "Ancilla or switch register governing channel selection, interaction topology, or superposed causal order." ; fa:domainGroup "Complete Carrier Schema" ; fa:claimStatus "Definition" ; fa:evidenceClass "Constitutional / Protocol" ; fa:siteRoute "/research/hcod" ; fa:sourceDocument "FA-HCOD-02, FA-QD-PRXQ-01, FA-QD-PS-01" ; fa:formalExpression "H_C = span{|a>_C} (Control / Sector Register)" ; fa:claimCeilingExclusion "Unresolved or traced-out control lines can induce false-positive sectorwise redundancy unless Gate 1 (Delta_rec = 0) holds." . cor:WorkBattery a owl:Class ; rdfs:label "Thermodynamic Work Battery & Reference (H_B)" ; rdfs:subClassOf cor:SubstrateComponent ; rdfs:comment "Explicit energy reservoir, phase reference, and refresh resource required for clock calibration, memory stabilization, and transducer readout." ; fa:domainGroup "Complete Carrier Schema" ; fa:claimStatus "Definition" ; fa:evidenceClass "Constitutional / Protocol" ; fa:siteRoute "/cor-theory/records-memory-agency" ; fa:sourceDocument "FA-LRT-01, OIRP_LEDGER" ; fa:formalExpression "H_B (Resource & Calibration Ledger)" ; fa:claimCeilingExclusion "Prevents perpetual-motion or zero-cost memory refresh assumptions in autonomous clock and memory models." . ### Relational State & Quantum Darwinism cor:RelationalStateAssignment a owl:Class ; rdfs:label "Relational State Assignment" ; rdfs:subClassOf cor:Layer_1_EventsAndRecords ; rdfs:comment "Non-ontic conditional mathematical state assignment tracking operational access statistics relative to declared carrier and witness restrictions." ; fa:domainGroup "Relational Records & HCOD" ; fa:claimStatus "Definition" ; fa:evidenceClass "Constitutional / Protocol" ; fa:siteRoute "/cor-theory/core-concepts" ; fa:sourceDocument "FA-SYN-01" ; fa:formalExpression "rho_{S|W,C} : Conditional Operational State Catalog" ; fa:claimCeilingExclusion "State assignments represent conditional operational expectations, not reified ontic matter waves." . cor:InteractionChannel a owl:Class ; rdfs:label "Controlled Interaction Channel Family" ; rdfs:subClassOf cor:Layer_1_EventsAndRecords ; rdfs:comment "Indexed family of system-environment Hamiltonians H(a) or CPTP maps Phi_a acoplando pointer observables to environment fragments." ; fa:domainGroup "Relational Records & HCOD" ; fa:claimStatus "Definition" ; fa:evidenceClass "Analytic Theorem" ; fa:siteRoute "/research/quantum-darwinism" ; fa:sourceDocument "FA-QD-ST-01, FA-HCOD-02" ; fa:formalExpression "H_tot = sum_a |a> Survival of Redundant Broadcast" ; fa:claimCeilingExclusion "Certifies record broadcast stability; does not derive single-outcome collapse or the Born rule." . cor:PostselectionInformationBudget a owl:Class ; rdfs:label "Postselection Information Budget Theorem" ; rdfs:subClassOf cor:Layer_1_EventsAndRecords ; rdfs:comment "Finite-dimensional theorem proving that average postselection Holevo gain over a control readout Y is bounded by the conditional mutual information I(Lambda : T | F)." ; fa:domainGroup "Relational Records & HCOD" ; fa:claimStatus "Exact result" ; fa:evidenceClass "Analytic Theorem" ; fa:siteRoute "/research/postselection" ; fa:sourceDocument "FA-QD-PS-01" ; fa:formalExpression "sum_y p_y (chi_y - chi) = I(Lambda:Y|F) - I(Lambda:Y) <= I(Lambda:T|F)" ; fa:claimCeilingExclusion "Postselection redistributes existing correlation budget; it cannot manufacture free objective information." . cor:CausalNonseparabilityIndependence a owl:Class ; rdfs:label "Causal Nonseparability vs. Objectivity Independence Theorem" ; rdfs:subClassOf cor:Layer_1_EventsAndRecords ; rdfs:comment "Proves in the declared composite class that environmental objectivity (redundant records) and indefinite causal order (e.g., quantum switch) are logically independent properties." ; fa:domainGroup "Relational Records & HCOD" ; fa:claimStatus "Exact result" ; fa:evidenceClass "Analytic Theorem" ; fa:siteRoute "/cor-theory/causality-topology" ; fa:sourceDocument "FA-QD-PRXQ-01" ; fa:formalExpression "Objectivity =/=> CausalNonseparability ; CausalNonseparability =/=> Objectivity" ; fa:claimCeilingExclusion "Analytical and computational result; does not claim laboratory spacetime superposition." . ### Operational Diagnostics & HCOD Two-Gate Protocol cor:OperationalDiagnostic a owl:Class ; rdfs:label "Operational Diagnostic Protocol" ; rdfs:subClassOf cor:CORTheoryStack ; rdfs:comment "Quantitative mathematical and computational diagnostic evaluated by the Foundations Audit Engine to certify or refute operational claims." ; fa:domainGroup "Relational Records & HCOD" ; fa:claimStatus "Definition" ; fa:evidenceClass "Diagnostic Taxonomy" ; fa:siteRoute "/research" ; fa:sourceDocument "FA-HCOD-02, FA-CB-02, FA-LRT-01" ; fa:formalExpression "Diagnostic D : ModelPackage |-> {Pass, Fail, RestrictedCeiling}" ; fa:claimCeilingExclusion "Passing an operational diagnostic certifies scoped compatibility, not metaphysical necessity." . cor:HCODDiagnostic a owl:Class ; rdfs:label "HCOD (Hidden-Control Objectivity Diagnostic)" ; rdfs:subClassOf cor:OperationalDiagnostic ; rdfs:comment "Hidden-Control Objectivity Diagnostic evaluating channel-varying record compatibility via a mandatory two-gate certification architecture." ; rdfs:subClassOf [ a owl:Restriction ; owl:onProperty fa:evaluatesGate1 ; owl:someValuesFrom cor:Gate1_CommonRecordPreservation ] , [ a owl:Restriction ; owl:onProperty fa:evaluatesGate2 ; owl:someValuesFrom cor:Gate2_IntegratedFragmentInformation ] ; fa:domainGroup "Relational Records & HCOD" ; fa:claimStatus "Exact result" ; fa:evidenceClass "Diagnostic Taxonomy" ; fa:siteRoute "/research/hcod" ; fa:sourceDocument "FA-HCOD-02" ; fa:formalExpression "HCOD_Pass <=> (Gate_1: Delta_rec = 0) & (Gate_2: I_Holevo >= (1 - delta)H(R))" ; fa:claimCeilingExclusion "Detects false-positive sectorwise objectivity when control labels are inaccessible; does not derive intrinsic observer boundaries." . cor:Gate1_CommonRecordPreservation a owl:Class ; rdfs:label "HCOD Gate 1: Common-Record Preservation" ; rdfs:subClassOf cor:OperationalDiagnostic ; rdfs:comment "Gate 1: Checks normalized commutator [H(a), Q_r x I_E] = 0 (Delta_rec = 0) across all active interaction channels a." ; fa:domainGroup "Relational Records & HCOD" ; fa:claimStatus "Exact result" ; fa:evidenceClass "Analytic Theorem" ; fa:siteRoute "/research/hcod" ; fa:sourceDocument "FA-HCOD-02" ; fa:formalExpression "Delta_rec(R; H) = max_a max_r ||[H(a), Q_r (x) I_E]|| / ||H(a)|| = 0" ; fa:claimCeilingExclusion "If Delta_rec > 0, sectorwise Holevo plateaus are false positives because different sectors record incompatible bases." . cor:Gate2_IntegratedFragmentInformation a owl:Class ; rdfs:label "HCOD Gate 2: Integrated Fragment Information" ; rdfs:subClassOf cor:OperationalDiagnostic ; rdfs:comment "Gate 2: Verifies redundant Holevo fragment information for that exact common record across many disjoint environment subfractions." ; fa:domainGroup "Relational Records & HCOD" ; fa:claimStatus "Exact result" ; fa:evidenceClass "Analytic Theorem" ; fa:siteRoute "/research/hcod" ; fa:sourceDocument "FA-HCOD-02" ; fa:formalExpression "chi(R : E_F) >= (1 - delta) H(R) for all |F| >= f_delta N" ; fa:claimCeilingExclusion "Gate 2 alone is insufficient under hidden control variation unless Gate 1 is simultaneously satisfied." . ### Temporal & Geometric Reconstruction Diagnostics (Layers 2 & 3) cor:FisherClockCorrespondenceTheorem a owl:Class ; rdfs:label "Dynamical-Time / Fisher-Clock Correspondence Theorem" ; rdfs:subClassOf cor:Layer_2_LocalRelationalTime , cor:OperationalDiagnostic ; rdfs:comment "Proves that operational duration agrees affinely with dynamical parameter T iff accessible Fisher information is positive and constant almost everywhere after calibration." ; fa:domainGroup "Temporal & Geometric Reconstruction" ; fa:claimStatus "Exact result" ; fa:evidenceClass "Analytic Theorem" ; fa:siteRoute "/cor-theory/time" ; fa:sourceDocument "FA-LRT-01" ; fa:formalExpression "tau_op(T) = a T + b <=> I_F^(acc)(T) = c > 0 a.e. (sqrt(I_F) integrable at endpoints)" ; fa:claimCeilingExclusion "Clock adequacy is an operational correspondence theorem, not a derivation of fundamental metaphysical time." . cor:LoopHolonomySynchronization a owl:Class ; rdfs:label "Loop Holonomy Clock Synchronization Theorem" ; rdfs:subClassOf cor:Layer_2_LocalRelationalTime , cor:OperationalDiagnostic ; rdfs:comment "Establishes that a connected network of local clocks linked by comparison transducers admits a global time calibration iff every closed comparison loop has identity holonomy." ; fa:domainGroup "Temporal & Geometric Reconstruction" ; fa:claimStatus "Exact result" ; fa:evidenceClass "Analytic Theorem" ; fa:siteRoute "/cor-theory/time" ; fa:sourceDocument "FA-LRT-01" ; fa:formalExpression "GlobalCalibration(G) <=> forall cycle gamma in pi_1(G), Hol(gamma) = id" ; fa:claimCeilingExclusion "Separates local clock duration from global synchronization; does not assert a universal cosmic time coordinate." . cor:LiebRobinsonSectorDiagnostics a owl:Class ; rdfs:label "Sector-Family Lieb-Robinson Propagation Diagnostics (C_inf, C_1, C_bar)" ; rdfs:subClassOf cor:Layer_3_LocalRelationalGeometry , cor:OperationalDiagnostic ; rdfs:comment "Separates uniform essential-supremum commutator norm (C_inf), sector-weighted norm (C_1), and averaged commutator norm (C_bar) in topology-controlled lattice dynamics." ; fa:domainGroup "Temporal & Geometric Reconstruction" ; fa:claimStatus "Restricted result" ; fa:evidenceClass "Analytic Theorem" ; fa:siteRoute "/cor-theory/causality-topology" ; fa:sourceDocument "FA-CB-02" ; fa:formalExpression "C_bar(x,t) <= C_1(x,t) <= C_inf(x,t) ; Piecewise Uniform Sector Envelope" ; fa:claimCeilingExclusion "Graph propagation bounds are convention-dependent lattice diagnostics, not relativistic Lorentzian light cones." . ### Countermodels & Obstruction Boundaries cor:Countermodel a owl:Class ; rdfs:label "Certified Countermodel / No-Go Boundary" ; rdfs:subClassOf cor:CORTheoryStack ; rdfs:comment "Explicit mathematical model or finite-dimensional construction demonstrating hypothesis necessity, nonuniqueness, or breakdown of unconditioned claims." ; fa:domainGroup "Countermodels & Boundaries" ; fa:claimStatus "Countermodel" ; fa:evidenceClass "Finite-Dimensional Calculation" ; fa:siteRoute "/research/countermodels" ; fa:sourceDocument "FA-AUTH-01, FA-LRT-01, FA-HCOD-02, FA-CB-02" ; fa:formalExpression "exists Model M : Hypotheses_reduced(M) & ~Conclusion(M)" ; fa:claimCeilingExclusion "Countermodels are positive scientific achievements under K9 that prevent false theorems." . cor:DephasingClockCountermodel a owl:Class ; rdfs:label "Dephasing Clock Adequacy Breakdown Countermodel" ; rdfs:subClassOf cor:Countermodel ; rdfs:comment "Explicit nonunitary dephasing model where accessible Fisher information vanishes, proving that record growth or parameter evolution alone does not guarantee an adequate operational clock." ; fa:domainGroup "Countermodels & Boundaries" ; fa:claimStatus "Countermodel" ; fa:evidenceClass "Finite-Dimensional Calculation" ; fa:siteRoute "/research/countermodels" ; fa:sourceDocument "FA-LRT-01" ; fa:formalExpression "I_F^(acc)(t) -> 0 => Breakdown of Affine Clock Correspondence" ; fa:claimCeilingExclusion "Refutes claims that any irreversible entropy or record increase automatically defines a valid clock." . cor:HiddenControlFalsePositiveModel a owl:Class ; rdfs:label "Hidden-Control False-Positive Objectivity Countermodel" ; rdfs:subClassOf cor:Countermodel ; rdfs:comment "Demonstrates a channel family where each individual control sector exhibits high Holevo redundancy in rotated bases (Gate 2 per sector), but Gate 1 fails (Delta_rec > 0), destroying common objective records when the control is inaccessible." ; fa:domainGroup "Countermodels & Boundaries" ; fa:claimStatus "Countermodel" ; fa:evidenceClass "Finite-Dimensional Calculation" ; fa:siteRoute "/research/hcod" ; fa:sourceDocument "FA-HCOD-02" ; fa:formalExpression "chi_a(R_a : E_F) high forall a, but Delta_rec > 0 => Consensus Failure" ; fa:claimCeilingExclusion "Proves sectorwise redundancy cannot be averaged into consensus without common-pointer preservation." . cor:LowerFrontSectorObstruction a owl:Class ; rdfs:label "Lower-Front Sector Obstruction Countermodel" ; rdfs:subClassOf cor:Countermodel ; rdfs:comment "Proves that when active control sectors have essentially unbounded propagation velocities, no single uniform exponential Lieb-Robinson envelope can bound C_inf." ; fa:domainGroup "Countermodels & Boundaries" ; fa:claimStatus "Countermodel" ; fa:evidenceClass "Analytic Theorem" ; fa:siteRoute "/research/countermodels" ; fa:sourceDocument "FA-CB-02" ; fa:formalExpression "ess sup_a v(a) = infinity => No Uniform Exponential Envelope for C_inf" ; fa:claimCeilingExclusion "Demonstrates why C_bar (averaged) cannot substitute for C_inf (uniform) in superposed topologies." . ################################################################# # Axioms & Rules ################################################################# # Non-Null Provenance Axiom: A valid physical claim MUST declare a complete carrier and target. cor:ValidPhysicalClaim a owl:Class ; rdfs:label "Valid Audited Physical Claim" ; rdfs:comment "Non-Null Provenance Axiom: A valid physical claim within the Foundations Audit & COR Theory architecture MUST be a PhysicalClaim that enforces a declared TargetDomain (K2) and requires a CompleteCarrier (K3)." ; owl:equivalentClass [ a owl:Class ; owl:intersectionOf ( cor:PhysicalClaim [ a owl:Restriction ; owl:onProperty fa:enforcesTargetDomain ; owl:someValuesFrom fa:TargetDomain ] [ a owl:Restriction ; owl:onProperty cor:requiresCompleteCarrier ; owl:someValuesFrom cor:CompleteCarrier ] ) ] ; fa:domainGroup "Audit Engine & Provenance" ; fa:claimStatus "Exact result" ; fa:evidenceClass "Constitutional / Protocol" ; fa:siteRoute "/foundations-audit/audit-engine" ; fa:sourceDocument "FA-AUTH-01, FA-SYN-01" ; fa:formalExpression "ValidPhysicalClaim === PhysicalClaim & exists enforcesTargetDomain.TargetDomain & exists requiresCompleteCarrier.CompleteCarrier" ; fa:claimCeilingExclusion "Any proposition lacking either a typed TargetDomain or a CompleteCarrier fails constitutional intake." .