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久那斗 Kunato Core Ver.5.0.0: Ontological Admission, Typed Representation Transport, and Effective-Structure Validation

Scheduler4861

Published Aug 19, 2026• 0 citations
Publisher

Abstract

Abstract We present Kunato Core Ver.5.0.0, a general framework for ontological admission, typed representation transport, empirical identifiability, effective-structure validation, and provenance-preserving epistemic state transition. The framework addresses a recurrent inferential problem across mathematical physics, statistical inference, inverse problems, effective theories, information theory, complex systems, quantum theory, and scientific realism: mathematical definability, empirical adequacy, model identification, and physical realization are distinct achievements and must not be silently promoted into one another. Kunato formalizes this separation through the constraint Formal(M) AND Emp(M; O) DOES NOT IMPLY Ontic(M). No representation receives automatic ontological privilege. Finite observation provides a first source of non-identification. Distinct formal models can agree exactly on a finite empirical record; in particular, uncountably many models can be constructed that coincide on any prescribed finite set of sample points. This establishes non-uniqueness within the relevant formal model class without promoting mathematical alternatives into claims about distinct physical causal histories. Finite measurement precision is treated through fibers of explicit resolution maps rather than by identifying metric neighborhoods with equivalence classes. The framework further distinguishes finite-dimensional state spaces from finite-state ontologies: finite-dimensional complex Hilbert spaces can contain a continuum of pure-state rays, whereas finite operational distinguishability requires additional assumptions such as a uniform positive separation scale on a compact state space. For stochastic observations, Kunato separates distributional identifiability, asymptotic inference, finite-sample discrimination, and zero-error identification. Positive overlap between competing observational laws prevents zero-error discrimination from the corresponding finite record. Increasing statistical evidence can therefore strengthen discrimination without automatically supplying an ontological realization warrant. Identification within a declared candidate class likewise remains conditional on that class and does not establish that physical reality belongs to it. The mathematical core is a typed property-transport calculus. Given a representation map Phi: X -> Y and a property P: X -> Z, P factors through Phi precisely when P is constant on every fiber of Phi. Equivalently, the kernel equivalence relation induced by Phi is contained in the kernel equivalence relation induced by P. This criterion separates state identification from property identification: a non-injective representation may fail to recover individual source states while still determining every property invariant on its fibers. Representation types, identified by their induced fiber equivalence relations, are organized by refinement within the complete lattice of equivalence relations on X. This provides a common mathematical structure for coarse-graining, quotient representations, projections, information loss, recoverability, and comparison of effective descriptions. Refinement is a partial order, so representations may also be incomparable. Effective structures consequently require property-specific transport warrants. Compression of a unitary parent operator, for example, need not preserve unitarity or normality. Conversely, non-normality alone does not entail a non-real spectrum, irreversibility, non-Markovianity, or absence of characteristic timescales. Observable symmetry, effective geometry, statistical regularity, entropy, information structure, temporal scales, and other representation-dependent properties cannot be transported automatically to a parent ontology. Kunato operationalizes these restrictions through methodological admission protocols. The Metric Admission Protocol regulates inference from effective metric structure to fundamental geometry. The Statistical-Invariant Admission Protocol separates existence of a mean from typicality, concentration, and self-averaging. The Timescale Admission Protocol distinguishes observed decay and hazard structure from claims about fundamental temporal dynamics. The Informational-Semantic Admission Protocol constrains inference from probability, entropy, information geometry, and semantic structure to latent ontology. The Criticality Admission Protocol separates phenomenological scaling from stronger claims of critical structure by requiring appropriately scoped diagnostics such as finite-size behavior, exponent stability, data collapse, robustness analysis, and negative controls. These protocols are methodological admission criteria rather than asserted laws of nature. Ontological admission is governed by differentiated semantic, fit, identification, scope, realization, revocation, and provenance warrants. These warrant types prevent empirical fit, interpretation, candidate-class identification, physical realization, and evidential history from being collapsed into an undifferentiated notion of support. Epistemic judgments are represented as contextual and versioned states, allowing changes in evidence, candidate classes, semantics, scope, and warrants to be reconstructed as explicit state transitions rather than hidden revisions. A central distinction is that UNRESOLVED is not REJECTED. Failure to establish an adequate promotion warrant blocks the requested inference but does not establish falsity or nonexistence. Rejection requires an independent refutation condition. Revocation acts on claims and accepted epistemic states while retaining their provenance; it does not imply any operation on authors or other persons. Self-application closes the framework. Continuum models, discrete models, cellular automata, XOR-based constructions, effective theories, quantum representations, and Kunato itself receive no exemption from the admission rules. Failure to identify a continuum ontology does not identify a discrete ontology, empirical adequacy of a constructive model does not establish its fundamental realization, and formal validity of Kunato does not confer physical ontological status on Kunato. The framework therefore entails neither a privileged fundamental model nor ontological nihilism. Not identified does not imply false, and not admitted does not imply nonexistent. Kunato Core Ver.5.0.0 provides a unified formal and computational vocabulary for ontological admission, finite-data non-identification, finite-record discrimination, inverse problems, coarse-graining, property factorization, representation refinement, effective dynamics, statistical invariants, temporal inference, information-theoretic interpretation, criticality assessment, model-class identification, provenance, epistemic-state revision, and scientific realism. Its objective is not to determine a preferred ontology by methodological fiat, but to make the inferential boundaries between representation, observation, identification, and physical realization explicit and auditable. The framework is summarized by four constraints: no hidden epistemic transition; no hidden ontological promotion; no untyped representational transport; and no self-exemption. Its terminal methodological principle is: no representation receives automatic ontological privilege.

DOI
10.5281/zenodo.22005910

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Abstract We present Kunato Core Ver.5.0.0, a general framework for ontological admission, typed representation transport, empirical identifiability, effective-structure validation, and provenance-preserving epistemic state transition. The framework addresses a recurrent inferential problem across mathematical physics, statistical inference, inverse problems, effective theories, information theory, complex systems, quantum theory, and scientific realism: mathematical definability, empirical adequacy, model identification, and physical realization are distinct achievements and must not be silently promoted into one another. Kunato formalizes this separation through the constraint Formal(M) AND Emp(M; O) DOES NOT IMPLY Ontic(M). No representation receives automatic ontological privilege. Finite observation provides a first source of non-identification. Distinct formal models can agree exactly on a finite empirical record; in particular, uncountably many models can be constructed that coincide on any prescribed finite set of sample points. This establishes non-uniqueness within the relevant formal model class without promoting mathematical alternatives into claims about distinct physical causal histories. Finite measurement precision is treated through fibers of explicit resolution maps rather than by identifying metric neighborhoods with equivalence classes. The framework further distinguishes finite-dimensional state spaces from finite-state ontologies: finite-dimensional complex Hilbert spaces can contain a continuum of pure-state rays, whereas finite operational distinguishability requires additional assumptions such as a uniform positive separation scale on a compact state space. For stochastic observations, Kunato separates distributional identifiability, asymptotic inference, finite-sample discrimination, and zero-error identification. Positive overlap between competing observational laws prevents zero-error discrimination from the corresponding finite record. Increasing statistical evidence can therefore strengthen discrimination without automatically supplying an ontological realization warrant. Identification within a declared candidate class likewise remains conditional on that class and does not establish that physical reality belongs to it. The mathematical core is a typed property-transport calculus. Given a representation map Phi: X -> Y and a property P: X -> Z, P factors through Phi precisely when P is constant on every fiber of Phi. Equivalently, the kernel equivalence relation induced by Phi is contained in the kernel equivalence relation induced by P. This criterion separates state identification from property identification: a non-injective representation may fail to recover individual source states while still determining every property invariant on its fibers. Representation types, identified by their induced fiber equivalence relations, are organized by refinement within the complete lattice of equivalence relations on X. This provides a common mathematical structure for coarse-graining, quotient representations, projections, information loss, recoverability, and comparison of effective descriptions. Refinement is a partial order, so representations may also be incomparable. Effective structures consequently require property-specific transport warrants. Compression of a unitary parent operator, for example, need not preserve unitarity or normality. Conversely, non-normality alone does not entail a non-real spectrum, irreversibility, non-Markovianity, or absence of characteristic timescales. Observable symmetry, effective geometry, statistical regularity, entropy, information structure, temporal scales, and other representation-dependent properties cannot be transported automatically to a parent ontology. Kunato operationalizes these restrictions through methodological admission protocols. The Metric Admission Protocol regulates inference from effective metric structure to fundamental geometry. The Statistical-Invariant Admission Protocol separates existence of a mean from typicality, concentration, and self-averaging. The Timescale Admission Protocol distinguishes observed decay and hazard structure from claims about fundamental temporal dynamics. The Informational-Semantic Admission Protocol constrains inference from probability, entropy, information geometry, and semantic structure to latent ontology. The Criticality Admission Protocol separates phenomenological scaling from stronger claims of critical structure by requiring appropriately scoped diagnostics such as finite-size behavior, exponent stability, data collapse, robustness analysis, and negative controls. These protocols are methodological admission criteria rather than asserted laws of nature. Ontological admission is governed by differentiated semantic, fit, identification, scope, realization, revocation, and provenance warrants. These warrant types prevent empirical fit, interpretation, candidate-class identification, physical realization, and evidential history from being collapsed into an undifferentiated notion of support. Epistemic judgments are represented as contextual and versioned states, allowing changes in evidence, candidate classes, semantics, scope, and warrants to be reconstructed as explicit state transitions rather than hidden revisions. A central distinction is that UNRESOLVED is not REJECTED. Failure to establish an adequate promotion warrant blocks the requested inference but does not establish falsity or nonexistence. Rejection requires an independent refutation condition. Revocation acts on claims and accepted epistemic states while retaining their provenance; it does not imply any operation on authors or other persons. Self-application closes the framework. Continuum models, discrete models, cellular automata, XOR-based constructions, effective theories, quantum representations, and Kunato itself receive no exemption from the admission rules. Failure to identify a continuum ontology does not identify a discrete ontology, empirical adequacy of a constructive model does not establish its fundamental realization, and formal validity of Kunato does not confer physical ontological status on Kunato. The framework therefore entails neither a privileged fundamental model nor ontological nihilism. Not identified does not imply false, and not admitted does not imply nonexistent. Kunato Core Ver.5.0.0 provides a unified formal and computational vocabulary for ontological admission, finite-data non-identification, finite-record discrimination, inverse problems, coarse-graining, property factorization, representation refinement, effective dynamics, statistical invariants, temporal inference, information-theoretic interpretation, criticality assessment, model-class identification, provenance, epistemic-state revision, and scientific realism. Its objective is not to determine a preferred ontology by methodological fiat, but to make the inferential boundaries between representation, observation, identification, and physical realization explicit and auditable. The framework is summarized by four constraints: no hidden epistemic transition; no hidden ontological promotion; no untyped representational transport; and no self-exemption. Its terminal methodological principle is: no representation receives automatic ontological privilege.
This preprint introduces the concept of an observer-relative undifferentiated probability envelope(观察者相对的未分化概率包络) as a minimal operational description for situations in which a family of candidate underlying states cannot yet be distinguished by a specified observer, interface, or intervention set. Rather than treating “undifferentiated” as an absolute absence of structure, the framework defines it through an observer-induced equivalence relation on a candidate state space. When all candidate states belong to a single operational equivalence class, the observer has access only to a coarse probability-level description. The paper distinguishes two interpretations that must remain separate. Model A(模型A), adopted as the current operational description, treats the probability distribution itself as the minimal empirically justified state description. Model B(模型B) is retained as an open ontological hypothesis in which each individual realization may already possess a unique underlying actual state, while the observer has only incomplete knowledge of that state. Model B is neither accepted nor rejected; it is reserved for future tests that could produce predictions distinguishable from Model A. The analysis formalizes the first-distinction boundary using equivalence classes and partition refinement, shows that a minimal nontrivial refinement naturally produces two distinguishable classes without implying physical binary ontology, and emphasizes the distinction between operational indistinguishability and ontological identity. Quantum coherent superposition is deliberately not assumed as the deepest interpretation of the undifferentiated layer. Instead, quantum-state descriptions are treated provisionally as higher-level effective operational representations whose deeper interpretation remains open. This work freezes a temporary lower boundary in a broader research chain connecting observer-relative distinguishability, admissible state spaces, relational structure, dynamics, projection, coarse-graining, and finite observational readout. The next stage is to determine whether a deeper ontological completion can generate experimentally distinguishable consequences, or whether the probability-envelope description is operationally complete.
This work develops a mathematical and computational investigation of the Einstein–Bohr boundary problem by reformulating it as a problem of representation, projection, reconstruction, and empirical identifiability. Rather than beginning with a predetermined interpretation of quantum mechanics, the study asks a more constrained question: what mathematical structure would be required for an observer-independent carrier of physical states to be describable, reconstructable, and empirically distinguishable from standard quantum-mechanical explanations? A generalized carrier, denoted by Ω, is introduced as an algebraic-dynamical structure whose observable consequences arise through context-dependent projections. This formulation permits mathematical description without requiring a global, context-independent assignment of classical values. The resulting framework is examined against quantum contextuality, Bell/CHSH constraints, incomplete witness bases, information loss under projection, reconstruction ambiguity, dynamical consistency, and observational equivalence. A sequence of computational Model-Lab investigations then addresses a stronger problem: even if such a carrier can be mathematically represented, can it be empirically identified? History dependence, hidden memory, non-Markovian dynamics, causal breaks, system resets, and latent-state models are tested against increasingly strong quantum countermodels. These investigations show that several apparently distinctive signatures are insufficient by themselves. In particular, history dependence and memory can be reproduced by enlarged system–environment quantum models, and strong statistical evidence for memory does not automatically constitute evidence for an additional ontology. The analysis therefore proceeds to possible post-quantum escape routes. No-signalling supra-quantum correlations, nonlinear dynamics, complete-positivity boundaries, ancilla consistency, process-tensor descriptions, and higher-order quantum-process alternatives are examined as successive admissibility tests. These investigations motivate a hierarchy of constraints that any empirically meaningful extension must survive before a deviation from standard quantum modeling can reasonably be interpreted as evidence for additional physical structure. The final part develops a resource-bounded empirical discrimination program. Instead of allowing hidden environments or memory resources to grow without limit, the admissible quantum countermodel class is constrained by independently established physical resources. A synthetic memory-dimension experiment demonstrates how temporal process complexity can, under explicitly stated representation-dependent assumptions, provide a witness against a bounded-memory null class. Finite-sample simulations and adversarial null-model stress tests are used to explore the statistical behavior of this approach. The central conclusion is deliberately limited: Ω can be mathematically described within the developed model class, but mathematical describability does not establish its physical existence or unique empirical identification. Memory, history dependence, non-Markovianity, and unusual correlations are likewise insufficient on their own. Independent empirical warrant would require observations that cannot be reproduced by any admissible standard quantum model after environment, memory, causal, higher-order, and other relevant resources have been independently constrained. The work consequently transforms the original ontological question into a more precise experimental one: what observation would remain outside the equivalence class of all resource-bounded quantum-process explanations while continuing to satisfy the required probabilistic, causal, compositional, and physical consistency conditions? The accompanying computational artifacts document the Model-Lab simulations, identifiability tests, post-quantum model campaign, resource-bounded experiment, and adversarial null-model analysis. These numerical investigations are computational experiments and should not be interpreted as laboratory evidence for physics beyond quantum mechanics.
This paper develops a framework-relative ontology of determinacy. Its core question is not what the world is made of, but what must minimally be accounted for if a stable deter- minate identity is internally self-representing. The primitive and functional core of Version 3.8 is retained: Being, the possibility of distinction, and domain-relative realizability define the sparse primitive basis; coherent self-representation then requires three non-equivalent func- tional questions—Support, Internal Encoding, and Correspondence. Explicit finite witness pairs establish uniform non-determination of each role from the other two in the unrestricted baseline class, while stronger canonical or equivariant subclasses remain open. Version 4.1.1 is a corrective consolidation of Version 4.1 rather than a new upstream on- tology step. It retains the Version 4.0 bridge revision and the Version 4.1 constructional layer. That layer adds the reverse evaluative direction Physics ⇒ Mathematics ⇒ Ontology and records where downstream structures constrain, but do not retroactively constitute, the ontol- ogy. Several previous bridge claims are weakened or rejected. Symmetry classification, tensor factorization, entanglement of a state, and path-dependent dynamics are kept as four distinct mathematical layers. A conditional expectation is treated as a localization map rather than as actualization; a branch instrument defines possible conditional events but does not select one realized branch; and a projection onto admissible spectral sectors is not called conservative dynamics without an independently derived dilation. The causal and propagation bridge is sharpened in two directions. First, a previous can- didate definition of a null relation by vanishing accumulated interval volume is proved degen- erate: every comparable pair admits a chain of links, so that criterion vanishes throughout the causal order. Link ensembles remain useful near-null approximants, but the null sector is therefore a limiting or measure-relative object rather than a pair-local primitive in the de- clared causal-set model. Second, the long-range free-chain calculation at 𝛼 = 2 is separated into two non-commuting limits. The infinite-range spectral symbol has maximal group veloc- ity 𝜋𝐽𝑎, whereas the envelope of finite-cutoff maxima tends to 2𝐽𝑎 Si(𝜋). These are spectral group-velocity statements; a causal signal cone still requires separate Lieb–Robinson-type hy- potheses. Isotropy and a unique physical Lorentz cone remain open. The defect bridge is updated with the completed 𝐾 = 512 data layer of the frozen ratio campaign. All 903 prescribed values of 𝜃 are present with eight branches each; 897 aggregate points are admissible and six lie in a short rejected interval. Neither √ 2 nor 𝜙 is a local or global minimum. The original preregistered primary ratio test nevertheless remains non- evaluable because its 𝐾 = 64 training gate is universally degenerate. Thus 𝐾 = 512 completes a characterization block; it does not retrospectively repair the primary estimator. Provenance registration and cross-platform verification remain pending. Version 4.0 turned Test 28A into an explicit reconstruction audit, and Version 4.1 retains that audit unchanged. For the standard three one-body extractions on ℋ = (C 3 ) ⊗3 , the combined linear map has exact rank 25 and kernel dimension 704. The hidden space splits as 192 two-body plus 512 fully traceless three-body directions; even the full 𝑆3-invariant class retains an exact 156-dimensional hidden sector. The preregistered continuation identifies an exact energy-selected fixed point, the totally antisymmetric state |𝜀⟩, while holonomy and variance objectives yield set-valued argmin correspondences. The historical non-triviality gate is therefore preserved but shown not to be a universal criterion, and no retroactive 𝑉28.4 verdict is declared. A prospectively frozen two-local QPH family provides an exact computer-assisted existence witness: its cycle-phase differential has rank 704/704 on the marginal kernel for the primary family and two preregistered replications, so marginals plus relational cycle phases are locally in- formationally complete in the fixed regularity stratum. Canonical modular-mismatch selectors are then audited rather than assumed. Identical additive qutrit references and every single pure mismatch under exact 𝑆3 protection obey strict capacity/rank no-go bounds. On the protected 156-dimensional domain a physically generated mixed mismatch has sufficient raw capacity but standard phase-only QPH remains incomplete. Exact cumulant analysis explains why order three is the natural next layer: the 𝑆3-hidden sector decomposes as 156 = 36 + 120, and the third connected cumulant is a complete affine coordinate on fibres of fixed proper marginals. A historical preregistered cubic-moment completion is retained only as a delicate T-NUM wit- ness, not as a theorem premise. This is the declared stopping point of the arity/cubic line: selecting one specific cubic observable would require a new independent physical law. Test 28B remains suspended. Version 4.0 added one further macro-level correction, retained in Version 4.1. Causal and conformal structure, transport geometry, stable matter sectors, and quantum correlations are treated as parallel downstream representations of one substrate model, not as a serial matter– space–time chain. A proposed identification of the matter admissibility projector Πadm with spacetime volume is rejected in its literal form: the projector is matter-branch specific, need not be nested under generative updates, and has no canonical finite trace in a type-III con- tinuum. In its place a conditional causal–transport conformal closure theorem is proved. If a causal reconstruction supplies a Lorentzian conformal class and an independent transport limit supplies a positive spatial metric on the same spacelike distribution, the conformal factor is fixed pointwise exactly when the two induced spatial metrics are conformally compatible. A scale-free generalized-eigenvalue defect provides a direct falsifier. The corresponding clock– cone–matter gate is also corrected by conformal weight: frequencies and dimensionful spectral scales have lapse weight one under a pure lapse deformation, whereas spectral ratios, localiza- tion fractions, and dimensionless stability-window coordinates have weight zero. A Tolman– thermal-time comparison is retained only as a relative lapse-profile gate; absolute time units remain open. Version 4.1 introduced a controlled common-substrate realization. Version 4.1.1 corrects its scope: parity alone excludes only an odd or linear mass/source identification with the same signed coordinate; an even law such as 𝑀 ∝ 𝑑 2 is not excluded by parity. On the declared graph Klein–Gordon sector, charge conjugation reverses Noether/gauge-current orientation while leaving mode energy and localization intensity unchanged. A grounded-graph Green- kernel theorem fixes the spatial uniformity of the cross-term sign, while the Coulomb sign itself is conditional on realizing a non-dynamical 𝐴0-type constraint sector; the same kernel in a dynamical scalar sector gives the opposite sign. A separate no-go proves that matter Dirichlet energy alone cannot select a nontrivial interior geometry. A state-selected positive geometry Hessian yields the conditional linear response 𝑦 = 𝐾 −1 𝐸 𝜏 , so weak 𝐶-even stress sources add while 𝐶-odd currents can cancel. The principal new bridge is a conditional stationary common causal–transport–matter con- struction. If one protected center supplies a common base, the transport branch supplies a positive spatial metric ℎ, and several modular/physical clocks agree on one relative lapse 𝑁, then 𝑔CTM = −𝑐 2 *𝑁2𝑑𝑇2 + ℎ has one timelike sign, predicts the same null front for all canonically normalized matter sectors, and fixes its stationary volume element without an additional scalar measure. Different masses and opposite 𝑈(1) representation weights remain lower-order data and do not alter the characteristic cone. The independently reconstructed HSMI conformal class remains a held-out test rather than an input to this construction. A second independent Version 4.1 result supplies a conditional physical law selecting com- plex rank two. A nonzero-Chern line cannot be closed under conjugation at rank one on 𝑆 2 , whereas 𝐿 ⊕ 𝐿¯ is the minimal conjugation-closed carrier; independently, ClC 2 ≃ 𝑀2(C) has minimal irreducible complex module dimension two. The existing odd-Chern defect-link con struction realizes this pair. If its Clifford algebra is physically admissible, the local carrier has 𝑀2(C) qubit kinematics. This is not an assertion that opposite electric charges form a coherent qubit, nor that every particle is a qubit. The resulting Version 4.1.1 is a constrained foundational proposal with a frozen primitive core, stronger positive and negative bridge results, a first common stationary geometry can- didate, an independently motivated minimal rank-two carrier, and a reproducibility-oriented ledger for every step from ontological determinacy toward physics. It also makes the external spin-sign, soft-graviton, equivalence-principle, and mass-budget inputs explicit without treat- ing them as evidence for the ontology.
A recurring interpretive move in quantum physics treats the loss of observational distinguishability as equivalent to the loss of ontological structure. In this paper, I show that the formal structure of the theory does not support that move. I prove the Structural Persistence Theorem, which identifies precisely which algebraic invariants survive arbitrary completely positive trace-preserving (CPTP) maps. The invariants form a natural and complete set: the C*-algebra of observables A = B(H), its norm, commutation relations, and positivity structure. No CPTP process removes any observable from the algebra. State-space distinguishability contracts; algebraic structure does not. This partition — preserved structure versus contracted epistemic access — is the core formal result of the paper. I identify and formally diagnose a specific class of ontological overclaiming in the decoherence literature: instances where pointer-basis selection and suppression of off-diagonal density matrix elements are treated as eliminative of superposition. I show exactly where these inferences overreach the formalism and provide corrected formulations. I then demonstrate that this criterion places formal constraints on how the major quantum interpretations can consistently attribute ontological change. Many-Worlds and pilot-wave theory are fully consistent with the criterion. Copenhagen's physical-collapse reading carries an unspecified mechanism burden. GRW and CSL objective collapse models are PC-violating by deliberate design — which the framework clarifies rather than criticizes. Any empirical confirmation of GRW/CSL predictions would constitute direct evidence for PC-violation in nature. Two practical applications are discussed. In quantum error correction, the success of the fault-tolerance threshold theorem is indirect empirical evidence for the Persistence Criterion: decoherence degrades distinguishability but leaves the algebraic structure intact, which is precisely what makes error recovery possible. In effective field theory, the persistence of UV degrees of freedom under coarse-graining is consistent with the same structural partition. This work proposes no new experimental predictions. It clarifies what the existing formalism entails and does not entail — drawing a sharp, formal boundary between what the mathematics licenses and what must be supplied by interpretation.
Abstract Modern physics contains celebrated foundational problems whose empirical foundations are exceptionally strong while some ontological narratives attached to them are less tightly constrained. This paper develops a local logic audit of individual inferential transitions from established empirical facts O and accepted formal constraints F to stronger physical or ontological conclusions P. Core Unit: A single inferential arrow: given O and F, does P follow? If (O AND F) does not entail P, P is not declared false; it is returned to the status of an additional premise. Methodology: Subtractive and prior to solution-building—before asking how a proposed process X occurs, the audit asks whether the declared O and F establish that X occurs at all. Adjudication: Once inputs are declared, adjudication is logical rather than interpretive. Factual primacy is epistemic rather than metaphysical: a formal derivation cannot supply its own empirical warrant, and a prediction must return to an independently acquired record before it can function as evidence. Domain-Specific Audits The method is applied through three domain-specific audits, with a transversal question-level audit operating within them rather than constituting a fourth domain: 1. The Double-Slit Experiment: Physical which-path interactions alter the relevant state without requiring any special causal role for conscious observation; sequential localized detections nevertheless accumulate into an interference distribution, while quantum-eraser protocols display conditioned correlations without retroactively changing an earlier local record. 2. Reflexive Born-Rule & Entanglement: Separates empirical success, formal derivation, and ontological explanation. The familiar question "what physically collapses the wavefunction?" is audited before it is answered: a formal state update does not by itself establish an ontic wavefunction undergoing a literal physical collapse. In entanglement, operational differentiation, spatial separation, and dynamical decoupling do not by themselves establish physical severance or exhaustive ontological decomposition; the same audit is applied to the EPR Reality Criterion and to narratives of nonlocal recoordination. Relativistic Physics & Quantum Gravity 3. Background Ontology: The third audit asks what background ontology quantum foundations actually require from relativistic physics. Clock relations and Lorentzian structure do not by itself entail time as an independently fundamental substance or four-dimensional spacetime as the uniquely fundamental ontology. Gravitational phenomena and the tested structure of general relativity likewise constrain any deeper account without uniquely fixing its ontology. The GPS Example: The distinction among ontology, physics, and engineering is made explicit through the GPS example: technological dependence on relativistic timing validates the physical relations required for operation while fundamental ontology remains a further question. Quantum-Gravity Audit: Asks what observation, prediction, or formal structure of established quantum theory presently fails in an empirically demonstrated way because gravity has not been made a fundamental quantum interaction, separating cross-framework consistency from prior commitment to one ontology of the deeper theory.
Reconstruction programmes ask whether familiar physical structures—for example time, factorization, quantum theory, or spacetime—can be derived from more modest premises. A derivation may be mathematically correct yet support a stronger headline than those premises warrant. Four recurring failures are that the target is an artifact of representation, is already present in an uncredited law or auxiliary input, follows from a construction too vacuous to discriminate it, or is never connected to the advertised observables and physical regime. This article develops a claim-relative audit that keeps exact mathematics separate from evidence-dependent scientific judgment. It freezes the claim and the experimentally protected interface, tests reversible re-encodings, records a provenance bill of materials, checks law–state noncircularity and anti-tuning, and requires an explicit physical-recovery bridge. Missing required evidence blocks a pass. In the finite class studied here, the same operational interface can be reversibly repackaged from many displayed factors into one: raw declared factor counts are therefore not representation invariants, and the corresponding minimum over admitted presentations is one, while an indecomposable role count requires additional justified factorization structure. Further bounded examples treat naturality, fixed points, hidden time, interventions, and quantum recovery. A worked audit of the Chiribella–D’Ariano–Perinotti reconstruction accepts its exact finite-dimensional conditional theorem while separating that result from claims of unique ontology, empirical inevitability, quantum field theory, spacetime, or gravity. The paper is neither a Theory of Everything nor a universal decision procedure; it specifies what a reconstruction must expose before receiving the inferential credit it claims.