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.
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.
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.
Abstract A “law of laws” is often imagined as a higher-order equation, optimization principle, or universal selector that mechanically generates lower-level laws. The theory developed here reaches a narrower and more falsifiable conclusion. Across heterogeneous mathematical and physical hosts, distinct scientific burdens repeatedly fail when collapsed: composition does not determine valuation; law or type does not select one actual token; local recovery need not survive a claim-complete host; equivalence depends on query-relevant consequences and context; and a complete forward description need not provide inverse identifiability. The surviving law-formation compression separates a specified question and host, generated law-structuring content, and law-form licensure or refusal. The claim is functional rather than graphical: any adequate meta-architecture covering the adopted evidence must preserve these burdens, although another formalism may package them differently. Internal evidence includes exact non-collapse results, a controlled multifield-gravity case, and artifact-frozen prospective calibrations containing both successful structural predictions and a retained hostile failure. The theory is also compared with native results in three external domains without using PLGP as a mathematical premise: causal-set quantum gravity, a PBR/extended-Wigner’s-friend construction, and complex phase retrieval. The first two are retrospective structural instantiations of distinctions already present in the frozen theory; the phase-retrieval demonstration is a prospectively preregistered external theory test. The resulting evidence broadens heterogeneous cross-domain support while leaving universality across science explicitly conjectural and falsifiable. Description This record contains the v1.0 public submission of Toward a Law of Laws, its supplementary evidence and audit record, and three companion external demonstrations. Demonstrations I and II are retrospective structural instances in causal-set quantum gravity and PBR/extended-Wigner’s-friend foundations. Demonstration III is a prospectively preregistered external test in complex phase retrieval. The record also contains source files, claim boundaries, provenance material, a structural corroboration matrix, and exact verification material for the phase-retrieval deletion result. The submission does not claim a universal sufficient criterion for scientific lawhood, independent replication, or proof that the PLGP functions are universally necessary. Universality remains a conjecture beyond the tested host classes.
The Admissibility of Natural Physics, Part I begins where an admissibility-first reconstruction of single-system quantum mechanics ends. Its central question is not whether the familiar tensor-product formalism can be assumed, but whether any physical composition law can be derived without importing composite systems, global state spaces, entanglement, locality, or signalling as primitives. The book develops a disciplined reconstruction of binary quantum composition from operational and structural requirements. It first records the exact content and limitations of the inherited single-system closure, establishes dependency and non-circularity statutes, and introduces the possible object of natural physics only as a provisional target ledger rather than as an assumed ontology. It then examines joint preparation, product states and effects, marginal consistency, operational no-signalling, minimal and maximal probabilistic composites, local tomography, and the classification of admissible tensor-product representations. Particular attention is given to the distinction between a mathematical representation theorem and the uniqueness of a physical composition rule. Real, complex, quaternionic, Jordan-algebraic, minimal, maximal, restricted, and non-tomographic alternatives are compared under explicitly declared admissibility conditions. The complex Hilbert-space tensor product is recovered only on branches satisfying the required factorization, coherence, scalar, and operational closure conditions. Where several inequivalent composites survive, the result is a classified family rather than a falsely asserted uniqueness theorem. Entanglement is introduced only after composition has been commissioned. It is defined as the failure of an admitted joint state to belong to the convex closure of admitted product preparations. The analysis proves, within the resulting predictive grammar, that entanglement is a property of composite-state geometry, not an additional force, substance, interaction mechanism, or signalling channel. Throughout, the argument enforces quotient primacy, refinement stability, finite diagnostic closure, regeneration stability, explicit dependency receipts, local termination, and the possibility of Undefined as a legitimate scientific outcome. Part I therefore supplies neither a speculative ontology nor a presupposed many-world formalism. It provides a conditional classification theorem for binary physical composition and identifies precisely what remains to be established before interaction, repeated composition, particle identity, locality, fields, symmetries, and particle content may be addressed.
A projection-first viewpoint asks which physical structures belong to an effective description and which belong to a richer source from which that description descends. This paper develops the viewpoint as a conceptual tool, not an inevitability theorem. A many-to-one map can identify microscopic states, but it does not by itself define lower dynamics, probabilities, entropy, locality, an arrow of time, quantum theory, or gravity. Those conclusions require additional structures: an intertwining dynamics, a state or measure, observable algebras, stability estimates, and sector-specific source maps. Modal Triplet Theory provides exact examples of finite projectors, a shared phase line, fixed-point constructions, and selected free field and finite Standard-Model carriers at declared tiers. Its broader physical reconstructions remain conditional where the required maps are incomplete. The projection-first framework is therefore most useful as a discipline for typing levels of description and exposing missing bridges.
From one requirement — that existence is mutual validation, and validation is transmitted in finite time — the classical sector is recovered: the Lorentz factor from interception geometry, gravitational time dilation without fitting, the full light deflection as a sum of two contributions rather than a fitted coefficient, and Mercury's perihelion by a composition law the data selected over its rival. Novelty lies in the grounding, not the numbers. The quantum sector is then developed from named premises rather than offered as an interpretation. Time is the counted distinction between a lock's two states, so the correlation entering any Bell test is a count, E = 1 − 2D − s; the Born value follows as D = sin²(θ/2), its square the half-angle of the projection that makes the correlation a cosine; and the indivisibility of the act yields complementarity, the Zeno effect, and the ineliminability — not the value — of single-shot randomness. The Tsirelson bound follows from one axiom we name and do not derive: the settings of a single undivided act are unconstrained unit vectors of a real inner-product space, not pointwise ±1 records carried apart. The parallelogram law is not the load, since a local hidden-variable model satisfies it too. The same axiom excludes Popescu–Rohrlich boxes, which no-signalling alone does not. Spin and statistics follow from the twist a closed mode's held ties can trap. A massless excitation, whose links are renewed at every step, holds none: the picture supplies no fermionic option for it, and forbids what standard theory permits. Undischarged and named: the vector axiom; the isomorphism on which the general Born rule depends; the three-dimensional soliton Finkelstein–Rubinstein requires. The predictions are given with their weakness stated — the picture fixes the form of its residuals and not their scale, so a null result tightens a bound rather than breaking the theory. All simulation code, including four withdrawn arguments, is openly available; the state accompanying this paper is archived at 10.5281/zenodo.21266573.
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.