An Executable Record Grammar for Quantum Correlations: A finite compression certificate for stabilizer records, Wilson holonomy, magic, detector readout, and bounded residuals
An Executable Record Grammar for Quantum Correlations: A finite compression certificate for stabilizer records, Wilson holonomy, magic, detector readout, and bounded residuals. A finite, executable demonstration of a 'record grammar': a disciplined separation of the full Hilbert-space state from the smaller algebra of detector-readable, stable, reusable records, in which every correlation left outside the grammar must be exactly zero by a selection rule, bounded by a certified trace-norm residual, or promoted to a named collective record. The central result is a four-qubit compression certificate: Bell/stabilizer endpoint records, a closed-loop T-holonomy (magic) record, and a finite detector branch are preserved exactly under the conditional expectation E(rho) = sum_i P_i rho P_i, while incompatible off-record witnesses are bounded by the trace norm and a sign witness saturates that bound. The paper is explicit that this is not a proof of polynomial scalability: a maximal abelian record basis still has 2^n sectors, and the scalable target is a generator-form ledger built from stabilizer/QEC generators, sparse magic resources, and bounded-correlation tensor-network data. Companion scripts demonstrate Wilson dressing of gauge readouts, magic retained as a named holonomy resource, noisy-detector channel laws, plaquette-chain correlation-length triage, and byte-level results on the eight-bit [8,4,4] record cell, including single-error syndrome detection and U(1) and SU(2) closed-loop flux readouts. All scripts are self-checking and reproduce to machine precision. This record is part of the finite-QEC substrate / It-from-Bit publication refresh.
An Executable Record Grammar for Quantum Correlations: A finite compression certificate for stabilizer records, Wilson holonomy, magic, detector readout, and bounded residuals. A finite, executable demonstration of a 'record grammar': a disciplined separation of the full Hilbert-space state from the smaller algebra of detector-readable, stable, reusable records, in which every correlation left outside the grammar must be exactly zero by a selection rule, bounded by a certified trace-norm residual, or promoted to a named collective record. The central result is a four-qubit compression certificate: Bell/stabilizer endpoint records, a closed-loop T-holonomy (magic) record, and a finite detector branch are preserved exactly under the conditional expectation E(rho) = sum_i P_i rho P_i, while incompatible off-record witnesses are bounded by the trace norm and a sign witness saturates that bound. The paper is explicit that this is not a proof of polynomial scalability: a maximal abelian record basis still has 2^n sectors, and the scalable target is a generator-form ledger built from stabilizer/QEC generators, sparse magic resources, and bounded-correlation tensor-network data. Companion scripts demonstrate Wilson dressing of gauge readouts, magic retained as a named holonomy resource, noisy-detector channel laws, plaquette-chain correlation-length triage, and byte-level results on the eight-bit [8,4,4] record cell, including single-error syndrome detection and U(1) and SU(2) closed-loop flux readouts. All scripts are self-checking and reproduce to machine precision. This record is part of the finite-QEC substrate / It-from-Bit publication refresh.
From a finite event record to Bell correlations and their loss under recording A pair is prepared together, read at two separated instruments, and allowed to leave a material record. This paper builds the correlation law from a real source geometry in Artian's Quantum Traction Theory. Its source-to-access equation is pK(r,s∣a,b)=C(KΩ)C[(Πr(a)⊗Πs(b)⊗I)KΩ] Here C is an additive, basis-invariant event capacity, Omega is the normalized orientation-neutral two-channel source, K is a specified record contact, and the projectors select the two instrument outputs. A real quarter-turn and a qualified shared-reference composition generate the readout algebra. Capacity symmetry fixes its quadratic weight. A separately stated capacity-to-frequency condition connects that weight to laboratory counts. The correlation follows before the Bell comparison For a phase-compensated record contact with overlap g between its two normalized record profiles, the construction gives EK(a,b)=−azbz−g(axbx+ayby),0≤g≤1. The intact-source limit is E = -a dot b. The same calculation yields the fixed-setting and optimized Bell responses: S45=2(1+g),Sopt=21+g2. Fresh independent record contacts multiply their overlaps. The paper derives the repeated-contact law, a capacity-based overlap calibration, uncertainty bounds, and a protocol that separates calibration from the Bell observations being judged. A source-first account with an explicit dependency map A1 supplies event-time labels and the clock-angle correspondence; A4 supplies the real dial; A5-X supplies completed-event support, with its inherited A6/A7 conditions. The two-channel preparation, balanced composition, capacity symmetry, frequency bridge, and record coupling are printed separately. Each theorem states exactly which conditions it uses. The Access uncertainty commutator is treated as a distinct inherited algebraic premise, rather than inferred from Bell correlations. When a receiver follows the source Version 2.0 constructs a matched receiver rather than assigning its transformation by name. Preserving every probability of the stated bilinear contact forces its transport to be the conjugate of the source transport, up to an overall phase: ∣rTVTUs∣2=∣rTs∣2for all r,s⟹V=eiαU. A finite set of basis and sum probes certifies this relation. A robust extension converts imperfect probe probabilities into an operator-error bound. Finite clock and shift operations then produce the comparison loop L=M+ω(I−M),ω=e2πi/d. The matched sector cancels the comparison phase while the unmatched sector retains it. This is a joint comparison law; each local readout can remain incompatible. The paper identifies the binary loop's ambiguity, provides additional probes that distinguish it, and transfers the Bell correlations into a complete detector record when the original carrier is consumed. One contact, two observable roles A specified marker contact supplies both the Bell record overlap and a resolved weak-measurement instrument: γK0K1=sinθ,=diag(cos(θ/2),sin(θ/2)),=diag(sin(θ/2),cos(θ/2)). An independent replay executes this instrument on all 40,032 tree records in the public Feng and colleagues archive, reproducing every stored decoder success/failure score. The main five-setting batch contains 32,000 records; the complete archive has six settings. The reproduced job-cluster residual probabilities are p = 0.0188753 and p = 0.0442603, respectively. These diagnose modest tension with the ideal instrument under the stated retrospective covariance. The matched QTT and quantum representations make the same archival predictions, so this replay is not a significance test between them. The package preserves the complete source-first Bell construction and adds finite receiver certificates, physical transport-error bounds, a common-contact derivation, five vector figures, a twelve-item achievements ledger, and offline reproducibility materials. The next operational question is precise: which independently qualified physical contact fixes both the record overlap and the receiver comparison response? Dependencies: QTT Main Book; finite address-capacity counting; real source histories and composition; A1-CHSH spinor character; Observation as Access.
Physical Sources, Finite Detectors, Persistent Records, and Actual Events This paper develops a unified account of quantum measurement under the Admissibility and Standing Constraint (AASC) framework, connecting constructed physical sources, quantum instruments, material amplification, finite record retention, event probabilities, and the actuality of measurement outcomes. The paper distinguishes three separate objects: a complete quantum instrument containing all outcome operations, including unresolved and failed outcomes; a material record carried by a physical system whose acquisition and retention can be analyzed; an actual history describing which occurrences belong to one original experimental run. A complete instrument and a persistent material record can be constructed without assuming that linear quantum dynamics alone selects one globally definite original-run history. Conversely, the admission of an actual event does not by itself determine its probability law or conditional quantum state. The physical construction contains two complementary measurement targets: a regulated interacting gauge–Higgs–fermion source with its full source Hamiltonian retained during finite receiver pulses; an explicitly parameterized six-mode cosine circuit with source and pump interfaces, losses, distinguishable outputs, a two-polarization intrinsic-spin receiver, and a finite energy-resolving thermal amplifier. The material-registration chain includes source-code loading, driven conversion, output registration, pump-displacement removal, transfer to an intrinsic material spin, finite Gibbs-collision amplification, endpoint reading, and quiet record retention. Electronic display labels, material flags, missed counts, dark displays, blanks, and unreadable outcomes remain distinct and are retained in the joint error ledger. The paper establishes: informative bounded receivers on an interacting quantum source; finite-pulse calibration with the complete source Hamiltonian retained; a complete monitored detector model; finite preparation and amplification bounds; coherent composition of instruments and records; adaptive record composition; local-instrument compatibility; calibrated affine probability uniqueness; sharp coherent calibration limits; sequential probability laws and compatible conditional states; explicit actual-history requirements. A finite Fourier residual certificate bounds the complete monitored detector instrument over its full 35.587ms interval by 0.063241 in restricted diamond norm. Exact interval arithmetic gives seeded amplifier endpoint fidelity greater than 0.9999235242 after 1,024 finite collisions, together with an explicit conditional survival bound for a subsequent 100ms quiet hold. The probability analysis shows that positivity, density-operator dependence, affinity under classical mixtures, and calibration fix the trace probability rule for the declared readout. Approximate sector calibration alone permits coherent deviations of order the square root of the calibration error; stronger linear bounds require additional structure. The paper’s central measurement-theoretic conclusion is deliberately separated from its successful detector construction. A complete instrument admits an exclusive-history completion, but linear quantum dynamics alone does not select one such history. Source-specific preparation, reader analysis, and a bounded counting-law completion supply the additional physical input required to select an actual history. The resulting framework substantially develops the material and probabilistic parts of quantum measurement while isolating apparatus errors, actual-history law, and event-selection assumptions as explicit obligations. The work does not claim to solve every interpretation of the measurement problem, derive a universal collapse law, establish unrestricted detector accuracy, or identify a finite calibration certificate with an experimental calibration. Principal contributions A unified source-to-detector account of quantum measurement. Constructed interacting quantum sources with finite receivers. Six-mode cosine-circuit detector realization. Material registration and finite amplification chain. Two-polarization intrinsic-spin receiver. Finite thermal collision and endpoint-reading model. Full-duration restricted diamond-norm detector bound. Interval-certified amplifier fidelity. Conditional quiet-hold survival bound. Retention of blanks, wrong, unreadable, and missed outcomes. Calibrated affine probability uniqueness. Sequential instruments and compatible conditional states. Explicit separation of complete instruments, material records, and actual histories. Source-specific conditions for actual-event selection. Complete physical error and assumption ledger.
Technical Supplement to Paper 5 of the Admissibility Physics Framework (APF), Quantum Structure as Least-Cost Admissible Bookkeeping. v5.97 (April 2026), 157pp, 36 sections, 235 theorem-class environments, 59 bibitems. The supplement gives a finite-regime reconstruction of the Hilbert–Born formalism from APF's enforcement-substance primitives: complex Hilbert space, the Born trace rule, tensor products, CPTP dynamics, and measurement as record-locking, all derived rather than postulated. Headline result. The Hilbert–Born endpoint is licensed by a chain of finite, certifiable gates traceable to a single APF primitive — closed-world ledger conservation paired with no-phantom-records. The framework derives what canonical quantum-reconstruction programs (Hardy 2001; Chiribella–D'Ariano–Perinotti 2011; Masanes–Müller 2011; Barnum–Wilce 2014) postulate. Core spine (sections in order): Quantum Admissibility Condition (QAC) — produced at branch-(IJC) record-complete coherent interfaces; coherent continuations whose Boolean record-locking incurs strictly positive preservation distortion. Branch taxonomy Sepstr / Sepadm / IJCstr / IJCadm / IJCpres / Seppres with forced inclusions Sepadm ⇒ Sepstr, IJCstr ⇒ IJCadm, and explicit anti-conflation: capacity-only failure (Sepstr + IJCadm) is structurally classical and does NOT trigger QAC. Operational radical via no-phantom-record quotient — every element of the operational radical does no record-distinguishing work and is quotient-eliminable; a Wedderburn bridge identifies ϱop = Jac(𝒜) under stable-simple completeness. Finite matrix-sector representation — the faithful semisimple quotient enters a finite ⊕-of-matrix-blocks structure via Artin–Wedderburn applied to the closed-world quotient. Field selection by SPLIT closed-world composite gates — APF-complete composite closure decomposes into two independently-derivable conditions: (i) finite tensor closure (rules out ℍ structurally because Mn(ℍ) ⊗ℝ Mm(ℍ) ≅ M2nm(ℝ), not quaternionic), and (ii) finite tomographic locality (rules out ℝ via Wootters–Hardy local-marginal parameter count: 2×2 joint dimension 10 < locally-reconstructible 15). ℂ is the unique field passing both legs; the selection is a conjunction of independently-derivable conditions, not a single black-box axiom. Born trace rule ⟨E, ρ⟩ = Tr(ρE) — every positive linear functional on Mn(ℂ) is a density-matrix-and-effect pairing; trace-rule positivity is licensed by upstream cone-preservation. Gate-certified Hilbert–Born pipeline — composite meta-theorem: four gates (positivity preservation under quotient + closed-ledger reciprocity + operational-radical-equals-Jacobson + split closed-world complex selection) jointly license the H–B endpoint. Each gate is independently necessary; no single gate is redundant. If any gate fails, the framework stops at the corresponding fallback rather than silently importing quantum formalism. The derivation chain. The standard "regime gates" — reciprocal calibration → self-duality + adjoint, stable simple-record completeness, APF-complete finite composite closure → ℂ selection — are not independent postulates. They are joint consequences of closed-world ledger conservation + no-phantom-records: Tclosed-ledger reciprocity derives reciprocal calibration → adjoint from no-hidden-debt symmetric pairing B(p, m) = ∑ pi mi on a finite ledger; the adjoint is the swap partner under B, not a postulated involution. Tno-phantom-record quotient + Toperational-radical-equals-Jacobson derive stable simple-record completeness on 𝒜 = ℝ[x]/(x3), giving a quotient 𝒜/(x) ≅ ℝ that is semisimple and eligible for matrix-sector classification. Tsplit-closed-world-complex-selection derives ℂ-selection through the explicit split into tensor closure + tomographic locality. Six countermodels and red-team. Explicit countermodels for Weinberg non-linear quantum mechanics, real-amplitude QM, Bohmian mechanics, Kochen–Specker hidden variables, GRW/CSL collapse, quaternionic QM. Red-team analyses for the three paper-specific hypotheses (H1 coherent-distinction closure, H2 tensor-product admissibility, H3 spectral-action compatibility). Theorem index, dependency diagram, regime-gate certification audit table, and changelog close the document. Readable without prior exposure to the APF series. Code and reproducibility. GitHub repository Colab walkthrough notebook (one-click) Interactive dependency DAG Codebase backing (v7.5). 23 bank-registered checks span the supplement's quantum-derivation chain across three modules: apf/aps.py (Admissible Possibility Space primitive + continuation preorder, 3 checks); apf/quantum_admissibility.py (branch-taxonomy inclusions, κBool minimum, capacity lower-bound certificate, QAC, ℂ-selection uniform-defect form, Born trace rule — 6 checks); apf/closed_world_completeness.py (the closed-world derivation chain itself, 14 checks: closed-ledger reciprocity, no-phantom-record quotient, operational-radical-equals-Jacobson, positive-cone quotient compatibility, split tensor closure, split tomographic locality, split closed-world ℂ-selection, preservation-IJC obstruction, constructive commuting realization, closed read/write self-duality, capacity-only-distinct-from-structural-IJC, gate-certified Hilbert–Born pipeline, closed-world-completeness-derives-three-gates, adjoint closure of stable simple sectors). All 471 verify_all checks load cleanly; 467 PASS. About the APF series. The Admissibility Physics Framework derives Standard Model and cosmological structure from a single primitive — finite enforcement capacity — through a chain of papers plus a machine-verifiable engine. Each paper has a main text and, where applicable, a Technical Supplement, deposited on Zenodo and collected in the admissibility_physics community; the canonical engine (APF-Engine v24.3.427, 3,918 bank-registered checks) backs every quantitative claim. The full series index is at admissibilityphysics.com. DOIs below are concept DOIs (they always resolve to the latest version). Paper 0 — What Physics Permits: A Constraint-First Framework for Physics — 10.5281/zenodo.18439523 Paper 1 — The Enforceability of Distinction — 10.5281/zenodo.18439200 · supplement Paper 2 — Finite Admissibility and the Failure of Global Description — 10.5281/zenodo.18439274 · supplement Paper 3 — Entropy, Time, and Accumulated Cost — 10.5281/zenodo.18439363 · supplement Paper 4 — Admissibility Constraints and Structural Saturation — 10.5281/zenodo.18439397 · supplement Paper 5 — Quantum Structure from Finite Enforceability — 10.5281/zenodo.18439433 · supplement Paper 6 — Dynamics and Geometry as Optimal Admissible Reallocation — 10.5281/zenodo.18439445 · supplement Paper 7 — A Minimal Quantum of Action from Finite Admissibility — 10.5281/zenodo.18439513 · supplement Paper 8 — The Admissibility-Capacity Ledger — 10.5281/zenodo.19721384 · supplement Paper 9 — The Geometric Substrate as Cost Structure of Comparison Continuations — 10.5281/zenodo.20041675 · supplement Paper 10 — The Calculus of Finite Continuability — 10.5281/zenodo.20041680 · supplement Paper 11 — Forced Universality from Capacity-Bounded Admissibility — 10.5281/zenodo.20684198 · supplement Paper 12 — The Gauge Sector of Admissibility Physics — 10.5281/zenodo.21212521 · supplement Paper 13 — The Minimal Admissibility Core — 10.5281/zenodo.18361446 Paper 14 — The Quantum Story — 10.5281/zenodo.21212188 · supplement Paper 16 — Markov Breakdown and the Hard Problems — 10.5281/zenodo.20684207 Paper 18 — The Electroweak Sector as a Capacity Equilibrium — 10.5281/zenodo.20684209 Paper 19 — Large-Angle CMB Suppression as a Finite-Continuability Constraint — 10.5281/zenodo.21199218 Paper 20 — The Enforcement Crystal — 10.5281/zenodo.18531732 · supplement Engine (Paper 21) — Admissibility Physics: An Executable Constraint Framework and Constants Map — 10.5281/zenodo.18529115 Paper 23 — Magnetically Dark Winding-Class Quantum Processors — 10.5281/zenodo.21199220 Paper 24 — The Recruitment-Radius Extension — Foundations — 10.5281/zenodo.20684211 · supplement Paper 25 — The Recruitment-Radius Extension: Applications — 10.5281/zenodo.21199222 · supplement Paper 28 — Absolute Mass Scales from Electroweak Capacity Saturation — 10.5281/zenodo.20684215 Paper 29 — Plaquette Representation Dominance and Confinement — 10.5281/zenodo.20684218 Paper 30 — A Tube Mechanism for the Lattice Mass Gap — 10.5281/zenodo.20684220 Paper 31 — Osterwalder–Schrader Structure of Lattice Yang–Mills — 10.5281/zenodo.20684222 Paper 32 — Quark Anchors as APF Trace Masses — 10.5281/zenodo.21199226 Paper 33 — Trace-to-Scheme Export Architecture — 10.5281/zenodo.20684224 · supplement Paper 35 — The Dark Sector as a Two-Role Capacity Decomposition — 10.5281/zenodo.20684228 · supplement Paper 36 — The Missing Floor — 10.5281/zenodo.21199228 Paper 37 — Collapse as Realignment — 10.5281/zenodo.21199231 · supplement Paper 38 — Unification as Ledger — 10.5281/zenodo.21199233 · supplement Paper 39 — Coherent Phase Regimes in the APF Interface Engine — 10.5281/zenodo.21199235 · supplement Paper 40 — The Thermodynamics of Finite Distinction (Between Symmetry and the Void) — 10.5281/zenodo.20684235 · supplement Paper 41 — The Horizon as a Continuation Ledger — 10.5281/zenodo.20684241 · supplement Paper 42 — The Weak Mixing Angle Is Not Free — 10.5281/zenodo.20684245 Paper 43 — The Neutrino Sector — 10.5281/zenodo.21194191 Paper 44 — What a Finite Theory Owes the Continuum — 10.5281/zenodo.21195874 · supplement Paper 45 — What the Vacuum Can Keep — 10.5281/zenodo.21194195 · supplement Paper 46 — The Strong CP Angle Is Not Free — 10.5281/zenodo.21194197 · supplement Paper 47 — The Confinement Antecedent Is Not Forced — 10.5281/zenodo.21194199 · supplement Paper 48 — The Light-Bending Weight Is Not Free — 10.5281/zenodo.21199627 · supplement Technical Supplements cross-link to their main paper via isSupplementTo and to the companion GitHub reposito
Files of this version are restricted (18 October 2026) because it was released under earlier licence terms: the source code was under the MIT License. All current versions use one clear licensing: paper, figures and data under CC BY 4.0, source code under the Apache License, Version 2.0. Please use the latest version: https://doi.org/10.5281/zenodo.21134454 Standard correlation witnesses — spatial Bell/CHSH inequalities, temporal Leggett–Garg K₃, and KCBS contextuality — are known to detect nonstabilizerness ("magic") in some settings. We report a worked example, a k-resolved nonstabilizerness map of the SU(2)_k anyon braid-representation family, in which a standard temporal witness is instead systematically blind: at k=4 the three-time Leggett–Garg witness saturates its macrorealistic bound exactly (K₃=1.000000 over every state, braid element, and measurement axis, in the equal-time-step protocol of Table 1 with V₁=V₂) while the single-qubit fusion channel carries near-maximal nonstabilizerness (M₂=0.5585, 95% of the finite-dimensional ceiling log₂(3/2)). We prove this blindness as a structural theorem: the witness depends only on the Bloch-sphere Gram geometry of the braid orbit, not on nonstabilizerness, and k=4 happens to align the fixed measurement axis with a threefold orbit symmetry (Bloch dot products all −1/3) that caps the witness at 1; a finite, Clifford-generating group — the chiral octahedral group, the k=2 braid image — with a misaligned axis reaches K₃=3/2 under a two-propagator protocol. Neither finiteness of the braid image nor the Clifford property is by itself the mechanism. We complement this temporal certificate with three independent certificates of genuine nonstabilizerness — two of them long-range (a doubled-Fibonacci mutual-information witness, H=1.700979, and a gauge-invariant minimum ground-space stabilizer Rényi entropy, ≥6.5 against an exact-zero toric-code control), the third a complementary gate-based non-Cliffordness measure — an honest negative control confirming that leakage-free constructions remain strictly additive, and a hardware-oriented single-qubit signal-to-noise prediction. We further probe the k=4 dissociation at its shared d=3 interface with Kochen–Specker–Klyachko contextuality, where the KCBS witness shows only a weak, nongeneric correlation with magic. Two reconciliations with the literature are made explicit: the present result contradicts neither the equivalence of maximal nonlocality and maximal magic established for optimized magic states in a different game, nor the contextuality-supplies-magic theorem; both concern a different object than the fixed, per-k braid generator studied here. About this series: This record is part of a series of related works from my independent research on Fibonacci anyons, with Ising anyons as their natural counterpart. I started in April 2026, and it has been a long and insightful journey in which I learned a lot; the work uses different methods and stays within verifiable, nonspeculative physics. The common thread of the series is a split: Ising anyons are limited to Clifford operations, while Fibonacci anyons are computationally universal, and across the series I map what standard witnesses of nonclassicality can and cannot certify on such systems. I consider Fibonacci anyons a serious candidate for topological quantum computing, given their universality and their topological protection against local noise. A hybrid approach with Ising is conceivable, but problems such as instability and certification would have to be solved first, and each needs research of its own.Correction notice (2026-10-10). In the summary above and in the section on the certificates of the paper, item (2) is described as a second long-range certificate: “a gauge-invariant minimum ground-space stabilizer Rényi entropy, ≥6.5”. This description is too strong. The values reported for item (2) are Monte Carlo estimates of the total stabilizer Rényi entropy of individual sampled ground-space vectors on small lattices; they are neither a minimum over the ground space nor a lower bound. They show that these states are not stabilizer states. A value of the total magic at one fixed system size does not certify long-range magic, which is a property of families of states of growing size, defined by robustness under shallow local circuits (F. Wei and Z.-W. Liu, arXiv:2503.04566; D. A. Korbany et al., arXiv:2605.22424; Y. Zhang et al., arXiv:2605.15150). The long-range certificate of this work is item (1); that non-Abelian string-net ground states carry long-range magic is shown by Zhang et al. In the same section, the fraction of Pauli expectation values in {0, ±1}, measured for one ground-space state, is a nonstabilizerness indicator only; it is not a diagnostic proposed by Wei and Liu. No computed value changes. The paper text will be corrected in the next version. This paper asks whether the inert blind spot at k=4, where the temporal Leggett-Garg witness stays exactly at the classical bound, means that the quantum resource is absent or only invisible to that witness, and it finds the nonstabilizerness nearly maximal, confirmed by three independent certificates, while proving the blindness to be geometric: the witness depends on the geometry of the braid orbit rather than on the resource, and a finite Clifford-generating group with a misaligned axis reaches the quantum bound, so neither finiteness nor the Clifford property is the mechanism; within the series it is the resource explanation, where blindness is a matter of alignment, not absence. Use of AI tools: In the research, processing, and writing of this paper and its results I worked together with generative AI tools, in practice a system of multiple coordinated AI instances that I set up and orchestrate (large language models, mainly Claude, by Anthropic, inside Claude Code). At their current context sizes I found it far more effective to work with several specialized instances, each with its own role and its own harness of rules and parameters that I designed and refined through feedback, than to load a single instance with all of the material; for my workflow that would have been inefficient, though this depends on the individual implementation. I lead this collaboration: I choose the research directions, set the goals, and make the final decisions in open exchange with the AI, learning actively as the work proceeds. The AI carries out the drafting, including the mathematical and technical parts, the numerical computation, and the literature search, under my direction. The AI works autonomously only task by task, within the structure I develop through feedback: it completes a task, and at open questions that need me it stops until the point is settled before the next step. Along the way I witness and take many of the decisions that shape the path, and it is common for me to spot things that need improvement. The work spans many separate runs, and a single simulation or build task alone can take up to an hour, so it could not happen all together in one autonomous run; and had I let the AI do all of it together alone, even if it is possible, it would no longer be my work but the AI's. I run multiple verifications at the different stages of the work and one before release, including cross-checks with an unrelated AI model from a different company, and all references are checked against the original sources. In the end what matters are human eyes, a principle that is itself written into the parameters of my system: I reach out to experts after publishing for review and feedback, so I learn what is solid and what must be corrected or falsified. My scripts for reproduction and review are released with this record. These tools are not authors; I am the author, and I take full responsibility for all scientific content and decisions leading to these results and their publication.
A finitist, relational axiomatization of physics: quantum theory and a relativity sector derived from four axioms about group-valued relations and closure. Contributions to the foundations of quantum mechanics (Born rule derivation, quantum reconstruction, local tomography, complex field selection), the emergence of time and causal structure in discrete networks, discrete Noether theorems, lattice gauge structure, and the Schrödinger equation derived by two independent routes. Every claim is graded in a Claim Ledger; every numerical claim is machine-verified with archived scripts; negative results are reported at full strength. What this paper does The universe is taken to be constituted by relations rather than objects. Stable relations form closures (self-consistent cycles) whose holonomies carry the physical content. Four axioms — primacy of relations (group-valued, edge-borne), closure stability, chirality from order, and observation as bidirectional group exchange — yield, at explicitly graded and conditional levels: Quantum sector Exchange-completeness theorems for finite label groups: abelian at all cycle ranks; non-abelian on the single cycle (Wilson readouts plus class-sum convolutions generate the full matrix algebra); the multi-cycle non-abelian case on the operational-equivalence quotient, with the obstruction completely characterized via class-preserving outer automorphisms — and the quotient's necessity now stratified by the source of word blindness (see New in Version 24.0). The Born rule, proved for finite abelian networks from a strictly weaker relational readout premise (statistics of realizable effects depend only on relational content); non-contextuality has this single source; additivity is basis-relative and declared as such. The Schrödinger equation by two routes of unequal premise grade, maintained side by side: a spectral route — the action operator is a weighted Cayley-graph Laplacian in the Pontryagin dual basis, the derived Gibbs state's unique canonical (modular) flow yields the Schrödinger equation with Hamiltonian equal to the action operator, no continuum limit, zero conjectures consumed, the single non-theorem step one flagged identification; and a Madelung route — physical and mechanism-rich (probability density derived from constraint gaps), valid exactly on the domain of the pseudo-continuity conjecture, with its full premise bill stated (continuity equation, Wallstrom circulation condition, m, V). A dedicated comparison subsection gives the line-by-line premise accounting and the machine-measured agreement region. Complex field selection: ℂ selected over ℝ and ℍ within the GPT comparison class in the covered sectors, with a second independent route from chirality (Frobenius–Schur dichotomy, quaternionic double exclusion); "uniquely selected" expressly not claimed. Positivity as pairing: all five in-text positive-semidefiniteness theorems traced to one mechanism (M = B†B with native factor); the Kraus form and complete positivity derived rather than assumed. The Noether sector on Noether's two theorems exactly: Noether I recovered on the holonomy action (compact Lie realization); Noether II identified as present (Bianchi as horn-filling, Schläfli as its Regge form); selection rules recovered for finite groups; the GNS bridge proved non-vacuously on the full exchange algebra; the sole potential extension — conservation as the kernel of exchange — isolated as a registered conjecture, consumed nowhere. A local–global representation theorem: six generative quantities (closure invariant, flux quantization, Weyl phase, non-abelian Stokes, orientation visibility, terminal normalization) are evaluations of cohomology classes against closed chains — one syntax, six exact machine probes. The gatekeeper no-go theorems registered and discharged: Kochen–Specker (the framework posits no global valuation — outcomes are resolutions of constraint gaps, and basis-relative additivity blocks state-independent variants), Pusey–Barrett–Rudolph (the statistical envelope is over resolutions yet to happen, not values already held; machine witness: identical configuration ensembles with opposite relative phase have opposite statistics), Wallstrom (registered as an explicit input, structurally discharged in the finite-abelian sector), Hegerfeldt (the Lieb–Robinson exponential tail identified as the only claimable front form for the continuum limit), Frauchiger–Renner (cross-agent certainty transfer presupposes kernel-free record transport, exactly what exchange-incompleteness excludes), and no-cloning (inherited in the covered sectors); Conway–Kochen and Colbeck–Renner noted as concordant. Relativity sector Time from finite capacity plus genuine randomness: the staging theorem (Θ(d) dependency depth, unbounded chains via the Moore bound; the quantitative failure law conditionalized on measure-level independence with exact minimal witnesses); the temporal quantum defined combinatorially, no Hamiltonian input. The speed of light grounded in an exact discrete dependency cone (combinatorial, no quantum input), the Lieb–Robinson bound consumed at cross-check grade only; a boost no-go theorem reducing Lorentz invariance to named statistical conditions, with the Collins fine-tuning objection recorded as a gate. The trace-descent theorem group: the growth-history measure forced onto the Mazurkiewicz trace quotient; chain reflection positivity at every depth with completely explicit spectrum. An equation sector of nine verification families (Schrödinger, Dirac, Maxwell/U(1), canonical commutator, Yang–Mills SU(2), Regge calculus, Klein–Gordon, Noether loop, Cartan curvature), where every machine-precision claim is the shadow of a proved backbone lemma — including the factor ½ of H = ½L + V, identified as the Wilson Fourier coefficient fixed by the action theorem. Four experimentally testable predictions, including a discriminating flat-versus-sigmoid visibility protocol. The Standard Model gauge group, ħ, and G remain open, with attack routes registered. How to read Three entry paths are marked in the document. Path A (derivational core): axioms → group structure → Noether sector → least action → Born rule → positivity. Path B (physical mechanisms): constraint propagation → time as determination → wave function as gap envelope → fields. Path C (scope and limits): the Claim Ledger, then Discussion and Open Problems — for the reader who wants to know what is claimed and what is not before reading anything else. The Claim Ledger is the single authoritative register of claim status; wherever body text sounds stronger, the Ledger governs. New in Version 24.0 (Version 23.0 is the immediately preceding public release; this version supersedes the internal V12–V15 and V17–V19 series, whose numbers are not used externally.) Version 24.0 resolves the structure of the multi-cycle non-abelian obstruction — the sector's longest-standing open front — following an external research exchange with three rounds of independent re-verification (fourteen core figures, three commutant instruments implemented independently, exact integer arithmetic on the obstruction side) and two rounds of counter-review that corrected one quantifier on each side: A dichotomy of the multi-cycle obstruction (new remark). Word blindness on multi-cycle networks has two identified sources, jointly covering every tested case, with opposite behaviour as cycle rank grows. Type I (global; graded): a class-preserving outer automorphism yields a commutant element by an argument free of cycle-rank reference; its non-triviality holds at theorem grade for b₁ ≥ d(G) via generating tuples, is monotone in b₁, and the threshold is measured at b_σ = 2 on the tested Wall group (at b₁ = 1 the permutation is the identity — no universal claim is made, and the existence of groups with threshold above 2 is registered open). Type II (local; measured): Out_c trivial but fusion fails on a proper subgroup, the blind pairs sitting in non-generating sectors — the same mechanism that defeats Wilson generation; this blindness heals: on every verified group (A₄, SL(2,3), A₄×ℤ₂) the full commutant collapses to trivial at b₁ = 3 by exact computation on two independently implemented instruments, although word readouts remain blind — the shift primitives separate, above a threshold, and the natural explanation (tuples becoming generating) is refuted by the persistence of blind blocks. Three boundaries at full strength: no exhaustiveness proof (a third source is not excluded); no general healing theorem (the verified groups all heal at 3, cause unidentified); the verified Type II sample is narrow. The quotient proposition restated in stratified form. The operational-equivalence quotient's necessity is now part of the proposition's own statement, in three strata: necessary where Out_c ≠ 1 at every b₁ ≥ b_σ(G), with b_σ ≤ d(G) at theorem grade; one-dimensional at b₁ = 2 on the fusion-type groups (verified cases); trivial at b₁ ≥ 3 on every verified fusion-type group and at every tested b₁ for word-separation-complete groups (a fourteen-group scan of orders ≤ 31 found no third source). Pre-registered validation preceded the restatement: a stratification-exhaustiveness scan (pass), a new-witness search (no new witness in range, downgrade clause applied as pre-registered), and a zero-conflict audit of the three strata against all archived data. The residual open problem is now precisely located. What remains of multi-cycle completeness: the rare Out_c ≠ 1 groups (54 in the exhaustive range through order 96) above their measured thresholds, the low-b₁ fusion stratum, a general healing theorem, and whether a threshold above 2 occurs. The multiplicity-freeness conjecture's mechanism sentence is corrected with the two regimes stated separately (at b₁ = 2 the shifts do not separate — the blind-pair transposition commutes with every primitive, integer-exact — and reduce the commutant to
We construct a source-matched reference calibration for distinguishing the coherent law h = 0 from the specified added generator h = J/25 in a finite quantum-record model. A complete-carrier transfer bound connects an accessible reference contrast to a delayed target contrast while retaining the original drift and actual law. On reference coverage and measured admission, restricting both hypotheses by the same observed reference band yields a directed target-set separation of at least 0.0071230619 whenever both compatible classes are nonempty. Rival worlds may have different admitted nuisance parameters. The constants are uniform over independently known finite lengths m >= 65, with tag 65, access prefix 1:32 and target deadline 25.02/J. Finite reference preparation and work/source reset satisfy the declared response budgets. Reset acts on the actual joint input and consumed supply, with the retained reference R exactly inert. It does not assign a universal reduced channel to correlated supplies. Under almost-sure conditional resource and supply bounds, the comparison extends to history-dependent acquisition. A prespecified rule, including abstention below the calibration threshold, has each-law unconditional wrong-declaration probability at most 2 exp(-6) + exp(-85/16) < 0.01. This is neither a posterior probability nor an error bound conditional on admission. The statistical step uses standard bounded-martingale concentration. Global target states and specified auxiliary supplies remain resources. Reset requires additional globally conditioned controls and has very large finite costs. The result is a conditional theorem for the two declared laws; it does not establish practical implementation or a unique diagnosis of fundamental collapse. A supporting Lean 4 companion contains 85 theorem declarations and 30 supporting definitions across Calibration, Operations and Risk. It provides checked scalar, sufficient-bound, resource-arithmetic and finite-history risk consequences under explicit premises. The companion has an executed Linux preflight and accepted returned macOS compilation, named-type and transitive-axiom evidence. The quantum constructions and conditional moment, filtration, tower and tail derivations remain written proofs or external premises; this is not an end-to-end formalization of the physical theorem chain. The original checked companion targeted author v0.4 and is carried forward unchanged, with its scope and execution chronology preserved.