The Non-Separable Fiber Program — A Propensity Model of Quantum Correlations, the Three Screens, and the Case for Decomposition-Independence: Deposit v1
This record deposits, as one versioned set, three companion documents of the Non-Separable Fiber Program. 1. A Non-Separable Propensity Model of Quantum Correlations (v5.2). A constructive stochastic hidden-structure model of two-photon polarization correlations. The model distinguishes kinematic locality (no superluminal signaling) from statistical separability, and discards only the second: each entangled pair bears one token fiber state with two bearers — a definite point on the Poincaré sphere, an affine (Malus) propensity coupling, a measurement-triggered update rule, and, at the pair level, a presentation structure identifying how the point stamped at one wing is consulted at the other. The model reproduces the full quantum joint distribution for every two-qubit pure state exactly, in both actualization orders, with no-signaling resolved into two named, contingent conditions (the complementarity identity of the coupling; matched fiber equilibrium). Two theorems locate the quantum/super-quantum boundary — the same architecture reaches the Popescu–Rohrlich maximum under a threshold coupling, and the update dynamics identifies the quantum correlations with the harmonic purity of the local coupling — and the cos² coupling itself is derived from stated premises by non-contextual normalization, with Busch- and Wright–Weigert-type completions and a named residue. The presentation structure is identified explicitly as the quantum steering identity realized as token structure, and the paper states, in Bell/Jarrett vocabulary, exactly which locality conditions the model concedes at the hidden level and which it preserves operationally. 2. Three Screens: Why the Foliation Is Hidden (v1.4). The companion synthesis. On the paper's preferred (conditional) reading, the actualization order is supplied by a real foliation; this document explains that structure's empirical concealment as the joint consequence of three contingent, parameterized identities — exact Lorentz invariance (the Mansouri–Sexl α̂ bound), the complementarity identity (derived within the model), and matched fiber equilibrium — each with a named breaking parameter that experiment constrains, addressing the Balashov–Janssen "unexplained conspiracy" objection. 3. Why Decomposition-Independence: The Dispositional Case for P4-mix (v1.3). The companion essay on the derivation's load-bearing premise: its exact statement, the positive dispositional case, a stress-test against the strongest objections, and an analysis showing the premise is experimentally enforced for all realized devices within the model's propensity ontology, with the residual scope stated exactly. The three documents cross-reference by section and are deposited together as one record; this is version 1. The framework was developed with AI assistance under the disclosed-provenance practice described in the paper's Author's Note and Acknowledgments; its mathematics has been verified independently by multiple methods, including hostile cross-model review, as documented there. Full development transcripts, referenced in the Acknowledgments as the authoritative attribution record, are available from the author on request; archival deposit of the transcripts is planned to follow.Each document is provided as PDF and as its Markdown source.
This record deposits, as one versioned set, three companion documents of the Non-Separable Fiber Program. 1. A Non-Separable Propensity Model of Quantum Correlations (v5.2). A constructive stochastic hidden-structure model of two-photon polarization correlations. The model distinguishes kinematic locality (no superluminal signaling) from statistical separability, and discards only the second: each entangled pair bears one token fiber state with two bearers — a definite point on the Poincaré sphere, an affine (Malus) propensity coupling, a measurement-triggered update rule, and, at the pair level, a presentation structure identifying how the point stamped at one wing is consulted at the other. The model reproduces the full quantum joint distribution for every two-qubit pure state exactly, in both actualization orders, with no-signaling resolved into two named, contingent conditions (the complementarity identity of the coupling; matched fiber equilibrium). Two theorems locate the quantum/super-quantum boundary — the same architecture reaches the Popescu–Rohrlich maximum under a threshold coupling, and the update dynamics identifies the quantum correlations with the harmonic purity of the local coupling — and the cos² coupling itself is derived from stated premises by non-contextual normalization, with Busch- and Wright–Weigert-type completions and a named residue. The presentation structure is identified explicitly as the quantum steering identity realized as token structure, and the paper states, in Bell/Jarrett vocabulary, exactly which locality conditions the model concedes at the hidden level and which it preserves operationally. 2. Three Screens: Why the Foliation Is Hidden (v1.4). The companion synthesis. On the paper's preferred (conditional) reading, the actualization order is supplied by a real foliation; this document explains that structure's empirical concealment as the joint consequence of three contingent, parameterized identities — exact Lorentz invariance (the Mansouri–Sexl α̂ bound), the complementarity identity (derived within the model), and matched fiber equilibrium — each with a named breaking parameter that experiment constrains, addressing the Balashov–Janssen "unexplained conspiracy" objection. 3. Why Decomposition-Independence: The Dispositional Case for P4-mix (v1.3). The companion essay on the derivation's load-bearing premise: its exact statement, the positive dispositional case, a stress-test against the strongest objections, and an analysis showing the premise is experimentally enforced for all realized devices within the model's propensity ontology, with the residual scope stated exactly. The three documents cross-reference by section and are deposited together as one record; this is version 1. The framework was developed with AI assistance under the disclosed-provenance practice described in the paper's Author's Note and Acknowledgments; its mathematics has been verified independently by multiple methods, including hostile cross-model review, as documented there. Full development transcripts, referenced in the Acknowledgments as the authoritative attribution record, are available from the author on request; archival deposit of the transcripts is planned to follow.Each document is provided as PDF and as its Markdown source.
A supplementary calculational note to the interpretational program "Spacetime as Register, Not Stage". The note reconstructs the full structure of spin-1/2 singlet correlations — the joint distribution P = 1/4(1−αβ·a·b), the correlation E(a,b) = −a·b, and CHSH S = 2√2 — from the program's picture of the "entangled" pair as one indivisible complement unit read out locally at two sites by independently oriented detector settings. The note proves sufficiency, not derivation, and keeps an explicit ledger of its epistemic status: two rules are added and underived (a half-angle spinor readout structure, and the square law for amplitudes), two are derived conditionally (antisymmetry, relative to an explicit phase bridge; normalization, fixed by completeness with no free parameter), and every remaining gap is recorded in a debt register. The model exits the factorizable (Bell) class exactly where quantum mechanics does: conditioned on the full preparation state, local marginals remain 1/2 (parameter independence holds per preparation state), while outcome independence fails — with no superluminal transport claim derived from statistics, no superdeterminism (the preparation state carries no free parameter that could co-vary with later settings), and operational no-signaling verified numerically. A deterministic hidden-orientation contrast model is included, reproducing the linear correlation −1+2θ/π and S ≤ 2, to show that the cosine requires a genuine exit from the factorizable class rather than a change of vocabulary. The English text is a full translation of the author's Polish source version (both files included; frozen 28.07.2026, changes tracked in the program's correction register, Series 33).
Complementarity-First Foundational Release III develops reciprocal phase architecture, conditional gauge and incidence geometry, finite Lorentzian connection selection, and relational quantum-information tasks. This paper synthesizes the eight research preprints and one reproducibility dataset in Waves A–C without transferring theorem ownership or treating their separately admitted carriers as a single derived physical system. The release is organized by four distinctions: structural admission versus conditional selection; geometric covariance versus operational implementation; restricted agreement versus complete identification; and mathematical existence versus a resource-accounted realization. The reciprocal quantum construction separates local inclusion, coherent completion, entanglement, finite projective valuation, and individual outcomes. Its synthetic biphoton companion distinguishes image intensity from phase-sensitive entanglement evidence. The geometric papers distinguish a derived compact phase-frame type from electromagnetic gauge interpretation and constitutive dynamics, anti-linear opposite-weight pairing from same-bundle reversal, an indefinite incidence form from positive records, and geometric-section agreement from independent connection variation. The Wave C papers supply finite addressing classifications, task- and record-relative recovery, encoded-preparation advantages, and exact exchange constructions with trajectory and timing bounds. Cross-wave comparisons locate genuine imported interfaces and identify bridges that remain absent, including the passage from finite Born-form valuation to general instruments and from a recorded group-error model to a physical timing-error model. Analytic proofs, finite calculations, numerical certificates, recorded replays, and scoped Lean verification are assigned distinct evidentiary roles. The contribution is a source-attributed scientific synthesis and an explicit dependency and residual-premise map, not a new primitive derivation of quantum theory, electromagnetism, or gravity.
This is Paper 142 in the Anaxiomatic Mechanics / pq-Spacetime stack. It develops a finite mechanical account of quantum entanglement within pq-spacetime. Entanglement is identified with the persistence of a non-factorable family of admissible future histories. Two measurement regions can therefore appear as separate local systems in emergent spacetime while still remaining projections of one joint finite closure problem. Bell inequality violation follows because the joint outcomes are not generated by two independent local completion families. No-signalling is nevertheless preserved because complete changes to a distant measurement boundary do not alter the local marginal outcome weights. The paper establishes the Entanglement Closure Theorem and distinguishes microscopic non-factorability from observable entanglement after coarse-graining into stable measurement records. It also gives an explicit minimal singlet construction using two opposed history fibers carrying the relevant four-phase weights. The resulting finite ledger is antisymmetric, nonseparable, and exactly balanced at each local wing. Complete changes of basis on the distant side preserve those local marginals. Using the previously derived Hilbert-space and beta-Dirac bridges of pq-spacetime, the paper recovers the familiar spinor overlap law, the quantum singlet correlation, the maximal Bell-CHSH value, monogamy of maximal entanglement, and decoherence through environmental boundary enlargement. The analysis also explains why no preferred measurement ordering is required and why entanglement remains compatible with relativistic causality. The resulting picture is direct. Entangled systems do not exchange superluminal messages, carry classical answer sheets, or require a force acting across space. Their local outcomes arise from one shared finite admissibility structure whose joint correlations are nonlocal while its controllable local statistics remain causal. Entanglement is therefore physically real, nonclassical, and nonlocal in correlation, but not a signalling mechanism.
A Kernel-Role Determinacy Theorem for Bell-Witness Fixation, No-Signaling, and Tensor-Level Compatibility This manuscript develops a fixed-domain AASC analysis of Bell-nonlocal quantum entanglement as a theorem of reusable witness determinacy. It does not introduce hidden variables, modify quantum mechanics, derive Hilbert-space formalism from below, or propose a new signaling mechanism. Instead, it asks a prior structural question: once a Bell-type operational family is used as the same non-degenerate witness across settings, lawful transformations, retained records, comparison, and later classification, what admissible same-domain standing form is forced? The governing claim is that AASC is not an optional interpretive overlay on physics. Once an operational Bell family is asserted as a determinate reusable witness, admissibility, standing, reference, and irreversibility are already active as minimal necessity conditions of same-witness objecthood. Target instantiation therefore carries governance occupancy: an alleged determinate Bell witness with no admissible governance realization is not an empty alternative, but a refusal or retyping of the target. The manuscript defines finite operational Bell objects with explicit setting carriers, outcome families, channel/interface data, standing-token valuations, continuation and report/reuse structure, comparison profiles, and act-time status. It then defines object-indexed query sorts, dependent response families, exactly recoverable operational simulations, lawful Bell groupoids, six governance-effect functors, and target-active extensional governance equivalence. The result is a typed interface in which arbitrary native formalisms can be compared by their target-bearing governance effects rather than by their internal syntax. The central Bell-specific theorem states that every same-target candidate-admissible Bell-governance construction is forced component by component into the certified boundary-compatible standing form on the complete target-active practice. Candidate admissibility does not assume the canonical form at the outset. Instead, target occupancy, lawful transport, standing-flow exclusion, compatibility certification, coordinate-deviation exhaustion, and componentwise closure force exact target-bearing realization and governance equivalence to the canonical representative CP∗C^{*}_{P}CP∗. The target-induced governance quotient therefore has exactly one element. The Bell carrier is treated as a compatible empirical model on a finite measurement cover. Bell-local completion is identified with the existence of a global section, and Bell nonlocality is the obstruction to such a section. The manuscript separates operational marginal invariance, absence of controllable communication, and exclusion of same-domain standing transport. No-signaling is therefore preserved without retyping Bell nonlocality as superluminal communication, metric transport, distant repair, or hidden standing transfer. The finite-dimensional quantum specialization uses the standard bipartite tensor-product and local-POVM carrier. Every separable realization in that carrier is Bell-local; therefore, if the fixed Bell-nonlocal empirical model has such a finite-dimensional quantum realization, every realizing state in that carrier is entangled. Post-quantum Bell-nonlocal no-signaling models remain within the general witness theorem but outside the quantum-entanglement corollary. The accompanying Lean 4 development, release v0.8.0, directly verifies the finite Bell-side witness carrier: denominator-32 vector/Born weights, structural no-signaling, CHSH numerator 808080, all sixteen deterministic local extrema, finite denominator-32 Bell-local-envelope exclusion, and conditional endpoint routing. Its direct witness certificate is vectorBorn_flagship_spine, and its deepest released endpoint is reasonableDeepestFiniteEntanglement_spine. The manuscript-level typed governance interface, empirical lawful groupoid, compatibility equivalence, coordinate-deviation exhaustion, completed role collapse, candidate-to-canonical derivation, and finite-dimensional quantum specialization are not attributed to the released Lean layer. This paper is the Bell-witness member of the paired AASC quantum determinacy arc. The record-side manuscript, Admissible Record Construction in Physically Non-Selective Quantum Regimes, fixes when local physical record occurrences stand as the same evidential record objects. The present manuscript fixes when the Bell operational family sampled by such records stands as the same reusable witness. The paired endpoint is therefore: record-role fixation+Bell-witness compatibility.\text{record-role fixation} + \text{Bell-witness compatibility}.record-role fixation+Bell-witness compatibility. The manuscript is classificatory and eliminative rather than mechanistic. It does not claim that AASC generates the Bell probabilities or supplies a hidden physical influence. Its claim is that reusable Bell-witness determinacy strongly constrains how Bell-nonlocal correlations may be coherently classified on a fixed domain: not as independently complete local states later connected by a mechanism, not as Bell-local hidden-variable value assignments, not as superluminal signaling, and not as same-act repair, but as boundary-level compatibility carried by one standing-preserving Bell witness.
CT 4.0.2 is the foundational bundle for Complementarity Theory (CT): physical updating modeled as finite committed record crossing an interface aperture under a least-incoherence selection rule, with mathematical setting in synthetic differential geometry (SDG). The paper presents five contributions: (1) A conditional derivation of the local Minkowski interval at a stable aperture in the first-order single-aperture regime, from CT primitives together with named structural inputs (a smooth aperture model, an adapted-frame choice, a posited seam-budget axiom, and a saturating-history existence hypothesis). Every non-theorem input is stated where it enters. (2) A complex-amplitude structure for the soft-commit regime: composition and superposition as operational axioms; the Born probability map definitional, with a named, independently testable interference-order axiom (after Sorkin) as the stated route to its quadratic form; a finite-dimensional Hilbert structure following from the axioms. (3) A multi-subject geometric proposal: intersection-network gluing with subjects anchored at the primitive substrate. The transported Lorentz triangle product is classified as connection loop holonomy — identity marks a flat face — distinct from Čech patch consistency; the U(1) face holonomy is conditionally realized as the normalized third-order Bargmann invariant. (4) A research program for deriving the residue role H from τ₀-substrate structure in complexified SDG, with the Residue-to-Phase problem restated precisely (the in-paper result is narrowed to a valid minimal-compact-factor theorem) and a conjectural horizon-phase quantization ansatz. (5) A conditional phase-to-spin and two-spinor bridge: three orthogonal noncommuting phase flows on a distinguished C² amplitude sector generate SU(2) ≅ Spin(3), with the exact 3-2-3 correspondence and the standard Penrose two-spinor route to Lorentzian geometry — established mathematics whose CT premises are recorded as named open problems. Version note: 4.0.2 is a status-correction erratum revision of the 15 May 2026 deposit (that record carries the Zenodo version label v4.0.1; there is no intermediate content revision). Claims are re-labeled to match what is proved, in nearly every case restoring the labels the supporting notes themselves use. A new supporting note, Identity as History, proves the record/history recurrence dichotomy behind the paper's arrow-of-time remark; the P-bound diagnostic is added with a reflexive audit caveat. The full changelog is Appendix A of the paper. The bundle contains the paper, twelve supporting notes (LaTeX and PDF), two H-program notes, the standalone SDG note, the Malus note, and a navigation README. An AI-assistance disclosure is included in the paper's acknowledgments.
Q Quantum Theory is formulated here at the foundational and quantum-mechanical level. Its basic postulate is that the physical quantum entity, denoted by Q, is the whole quantum state rather than an independently real material point whose unknown position is described by a secondary probability cloud. In a one-Q sector admitting a local amplitude representation,\begin{equation} Q(x)=\sqrt{\rho(x)}\,e^{i\theta(x)}Z(x),\end{equation}where x is a spacetime point, ρ is the Born response weight, θ is the phase, and Z is a normalized internal structural direction. A dagger denotes the Hermitian adjoint and ∂μ differentiates with respect to xμ. The decomposition has a local rephasing redundancy. This is a redundancy of the local factorization of the complete Q amplitude, not the physical electromagnetic U(1) gauge symmetry. The associated decomposition-invariant phase-orientation one-form is\begin{equation} \kappa_\mu=\partial_\mu\theta-iZ^\dagger\partial_\mu Z =\frac{\operatorname{Im}\langle Q,\partial_\mu Q\rangle}{\rho}, \qquad \rho>0.\end{equation}In Schr\"odinger correspondence sectors this structure yields exact probability-current and momentum identities, including the standard Abelian gauge-covariant current. In that audit the electromagnetic connection is a correspondence variable; its Q-level interpretation as a local representation of inter-Q relational comparison geometry is developed in the companion manuscript Paper II-A. Klein-Gordon and Dirac audits show that relativistic currents and stress-energy depend on the Lorentz representation: κμ carries phase-orientation translation structure, while amplitude gradients and internal orientation can contribute independently to energy and stress. The standard Hilbert-space probability calculus is retained. Interference, tunnelling, entanglement, localized detection and cloud-chamber tracks are interpreted as properties or records of whole-Q states rather than as evidence for hidden point trajectories. Entanglement is represented by a nonfactorizable joint Q state; standard Bell correlations and no-signalling are retained without identifying correlation with a superluminal physical signal. Boundaryless state support is distinguished from the propagation of a newly generated disturbance, which is required to obey retarded relativistic causality. For stable relativistic sectors, invariant mass is treated as a derived characterization of the translation spectrum: timelike Q states possess a rest frame and rest energy, whereas null Q states do not. The foundational structure does not specify a unique interaction action or establish ultraviolet finiteness. Finite-response dynamics requires a separate construction.