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.
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.
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.
ON THE VERSION NUMBER. "v3" is the version of the NOTE, not of this Zenodo deposit. Versions 1 (February 2026) and 2 were circulated privately and never deposited; v1 contained four errors of substance, which are stated with their repairs in the "What changed" section rather than quietly removed. This is the first Zenodo deposit, so if you see a deposit counter it will not match the document version. The document version is the one that matters for citation. Preprint, version 3 (complete rewrite). This note is the synthesis of the contextuality-obstructions program; the proofs live in the companion papers. The proposal is that the Copenhagen viewpoint, stripped of its rhetoric, is a set of structural statements about one geometric object: the transformation groupoid of measurement contexts (maximal abelian subalgebras) with its canonical U(1) 2-cocycle. In that formulation: local validity, the exact classicality of every single context, is a theorem with an explicit witness; complementarity is the nonvanishing holonomy of the cocycle along closed context loops, which detects exactly the all-versus-nothing sector of contextuality; collapse is pinned by statistics, repeatability and covariance to a one-parameter family per degenerate block whose unique efficient member is the Lueders rule, with a classical twin theorem identifying the same axioms' classical solution as Bayesian conditioning; observer-relativity of facts and the movable cut are theorems of an enlarged observer-context category; and the Frauchiger-Renner argument localizes to an ordinary state-dependent violation, with contextual fraction exactly 1/6, carried by a single CHSH facet, the loop holonomy of the observer switch being provably trivial. ATTRIBUTION. The classification of achievable state-independent values, the even/odd dichotomy and the fixed value d/2, is due to Abramsky, Cercelescu and Constantin (FSCD 2024). It is recast here in certificate language; the priority is theirs and is stated in the text. HARDWARE CAVEAT, STATED UP FRONT. Two signatures were measured on superconducting hardware. The quoted significances, about 56 sigma for the triangle holonomy and 35.4 sigma for the Peres-Mermin witness above the deterministic bound 4, are shot-noise statistical only, computed under the implemented model. They are not systematics-aware, and neither experiment is loophole-free. Read them as consistency checks on real hardware, not as precision measurements. ERRATA. Version 1 of this note contained four errors of substance. Section "What changed" states each of them and its repair. They are recorded rather than quietly removed. STATUS AND SCOPE. This is a preprint, not a peer-reviewed article. Each tenet is either a theorem of the companion papers, a machine-verified certificate in the public suite, or is explicitly labeled a conjecture. The paper offers structural characterizations within its stated axioms; it is not an interpretation-free derivation of Copenhagen and it does not claim to resolve the measurement problem. AI-ASSISTANCE DISCLOSURE. This work was carried out with substantial AI assistance. Every load-bearing claim is machine-verified by scripts that ship with the papers, and the author takes full responsibility for the contents. COMPANIONS. Paper A: https://doi.org/10.5281/zenodo.21630431 . Paper B: https://doi.org/10.5281/zenodo.21630630 . Paper D: https://doi.org/10.5281/zenodo.21630697 . Paper C: https://doi.org/10.5281/zenodo.21633744 (posted 2026-07-28, after three adversarial review passes; it carries a labelled retraction of an earlier sqrt(2) reading). VERIFICATION CODE. https://github.com/manuflog/contextuality-obstructions
From Distinction to Quantum Structure Compiling Physical Geometry from the Change Axiom Chain Driven by Dean Kulik July 2026 Abstract We present a foundational axiom chain that compiles physical geometry from a single primitive: distinction exists. Beginning with C0 (distinction) and C1 (every distinction admits lawful continuation), we derive — without importing spatial geometry, coordinates, time, or quantum mechanics as primitives — the necessity of a linear state space, a complex inner product, Hilbert completion, self-adjoint observables, and the structure of a probability measure on observable subspaces. We further derive the unique free-field Lagrangian consistent with the axiom constraints, the gauge principle as a structural consequence of independent classification, and the quantization bridge connecting the classical field to operator algebras. The central result is the Division Algebra Theorem (candidate): among the three finite-dimensional division algebras admitted by Frobenius’s theorem, only the complex numbers simultaneously satisfy the continuation independence requirement (C1a) and the dual-encoding requirement of C5. The paper maintains a strict five-category epistemic discipline — primitive, definition, compiled theorem, candidate theorem, empirical calibration — throughout, ensuring every claim carries its exact epistemic status. 1. Introduction: The Foundational Inversion Standard physical theory begins with space. Objects occupy locations in a pre-existing spatial manifold; motion is defined relative to that manifold; forces act within it. Newton’s mechanics, Einstein’s general relativity, and the Standard Model of particle physics all share this architecture at the foundational level: a stage is assumed, and the physics plays out on it. The program presented here inverts this order. We propose that space, time, geometry, and quantum structure are not primitives but derived objects — outputs of a more fundamental algebraic structure built from the minimal concept of distinguishable change. The chain begins: rather than: This is not merely a philosophical reordering. It is a concrete research program with specific mathematical obligations at each step: each layer must be derived from the previous layers without importing external structure, and every claim must be categorized by its epistemic status. The framework is falsifiable — if any compiled theorem fails its formal derivation, either the derivation or one of the primitives must be revised. 1.1 Motivation: SHA-256 as Physical Evidence The SHA-256 hash function provides an unexpected but precise illustration of the C1-first claim. SHA-256 is field-balanced in both axes: • Horizontal (input → output): Bit content redistributes across the compression function. The total information content of the input is preserved in the digest — different shape, identical content. The mapping is a redistribution, not a creation. • Vertical (round → round): The carry palindrome property holds: KL divergence between forward and backward carry distributions equals zero. The AHRC (Algebraic Hash Round Consistency) result shows to machine epsilon across all 64 rounds. The geometry is self-balancing at every step. Neither property was engineered into SHA-256. The designers specified diffusion targets; the field obeyed the redistribution constraint underneath and the two-axis conservation emerged. This is the claim of the axiom chain in concrete form: the transition algebra runs without an observer, and we arrive afterward to read what it did. SHA-256 does not choose to balance. It cannot not balance. Law 3 — redistribution conserves total — runs underneath every hash computation invisibly, and we measure it as a mathematical law about SHA-256. The chain argues this is the universal situation: what we call physical law is the transition algebra’s self-accounting, read from inside by instruments that are themselves running the same algebra. 1.2 Program Overview This paper establishes: 1. The primitive constraint set (Section 2) 2. Definitions required for precision (Section 3) 3. Compiled theorems through the free-field Lagrangian (Sections 4–6) 4. The internal symmetry and gauge principle (Section 7) 5. The quantization bridge — six elements of the Quantum Kinematics Theorem (Section 8) 6. The Division Algebra Theorem — the central new argument of this paper (Section 9) 7. Candidate theorems and open problems with proof strategies (Section 10) 8. Full dependency graph (Section 11) 1.3 Epistemic Categories Throughout this paper, every claim is labeled with one of five categories: Label Meaning [P] Primitive — assumed, irreducible [D] Definition — terminology, requires no proof [C] Compiled theorem — formally derived from prior P/D/C entries [T] Candidate theorem — strong evidence, formal proof incomplete [E] Empirical calibration — requires measurement, not deduction This discipline has a structural consequence: if a [C] theorem fails, either the derivation contains an error or one of the primitives must be revised. If a [T] theorem fails, the program survives intact — that conjecture was incorrect, and the framework needs refinement at that node only. If an [E] calibration disagrees with experiment, the structural theory may remain correct while the mapping to physical units requires revision. 2. The Primitive Constraints We assume the following as irreducible primitives. They are not derived from anything else in the framework. Their justification is that each is genuinely minimal — no proper subset generates the others. [P] C0 — Distinction Exists At least two states exist that are not identical. This is the logical precondition for any other constraint. C1 cannot operate on a single undifferentiated object. C0 is the one irreducible prior: something must be distinguishable from something else. Without C0, the entire chain has no content. [P] C1 — Every Distinction Admits Lawful Continuation Every state in the system must admit at least one transition to a successor state. This is the change axiom. No state is a dead end. No distinction terminates. The system cannot freeze, because freezing would require a state with no admissible successor — and that state would constitute a privileged terminal configuration, which is ruled out by C1 itself. Every local rule must be well-defined on every admissible state: this immediately excludes absorbing dead states from the dynamics. [P] C1a — Independence Preservation Independent distinctions remain independently continuable. This is stronger than C1. It says not only that every state continues, but that the continuation of one distinction cannot be blocked or modified by the simultaneous continuation of an independent distinction. Two systems that are independent at time must continue to be independently continuable. This axiom is what forces linearity (see Section 4) and what later eliminates quaternionic algebras (see Section 9). [P] C2 — Continuation Preserves Reachable History Every continuation preserves the set of states reachable from any prior state in the history. Nothing in the past is erased. The execution history — the accumulated record of all prior transitions — remains reachable. This is not a claim about memory in any computational sense; it is a structural requirement that the transition graph not delete nodes from the accessible state space. C2 forces completeness of the state space (Section 4) and the one-directionality of the ordering relation (Section 5). [P] L3 — Redistribution Conserves Total Every lawful continuation redistributes the total content of the field without changing that total. The field never gains content; it never loses content. Every transformation is a redistribution — a shift in the configuration of a fixed total. This is the deepest form of the conservation principle. It does not assume conservation of energy, momentum, or charge; it says something more primitive: the field’s total is an invariant of continuation. Those physical conservation laws are derived from L3 operating in specific geometric contexts. [P] L4 — Redistribution Is Local Redistribution propagates through local adjacency. Content cannot shift from location A to location B without occupying every intermediate location. This is the locality axiom. It follows from C2 applied to intermediate locations: if content jumps from A to B without passing through the intervening field, every intermediate location is denied its C2-guaranteed reachable history. The inheritance constraint — every new location must inherit all primitives — makes this inadmissible. L4 is therefore arguably compilable from C2, but we list it as a primitive for clarity because it plays an independent role throughout the chain. [P] C5 — The Observable Event Primitive An observable event is the minimum continuation that simultaneously propagates (extends through at least one L4 step) and leaves a distinguishable residue. C5 defines the minimum unit of observation. Three constraints are built into it: • Propagation (C1 minimum): the event must extend. A continuation that fails to propagate is not a continuation. • Residue (C0 requirement): the event must leave a mark distinguishable from prior state. Without residue, C0 is not satisfied at the event level — nothing registered. • Simultaneity: propagation and residue are not sequential. They coexist in the same elementary event. This simultaneity requirement is the key structural feature of C5. It will force complex amplitudes (Section 9) and the uncertainty principle (Section 8). 3. Definitions Definitions introduce terminology. They do not require proof; they establish the language
STATUS (18 October 2026). The physics programme that motivated this work was concluded in October 2026 and its claim of a unified derivation withdrawn. The results in this paper do not depend on that programme and stand as stated. NOTE ON SCOPE (18 October 2026). Where this paper says that the Standard Model's matter content, charges or gauge structure are derived from, forced by or emerge from the eight-bit error-correcting cell, read encoded in or assigned to. The finite results themselves stand: the code, its constraints and the anomaly arithmetic are exact. But two things are premises of the framework, not consequences: the identification of codewords with particles, and the choice of the eight-bit [8,4,4] cell. In particular, the step from read/write balance to a single CSS code is not derived [R22]. The author's October 2026 review of the programme concluded that the framework's Standard-Model content is assigned rather than derived. No observation currently distinguishes the framework's account from the Standard Model itself. This revised note argues that, within the accepted complex quantum-error-correcting record substrate, the quadratic Born form arises from linear record writing, orthogonality of record sectors, and isometric normalization before any probability measure is introduced. Conditional uniqueness is treated separately through Gleason-type and refinement-stable record-sector routes. The 30 August 2026 additivity-audit revision cites Jiaxuan Zhang's analysis of five Born-rule derivations (arXiv:2603.06211) and makes the premise accounting explicit: a Gleason frame function includes orthogonal additivity, while Marko Lela's route begins with a non-negative extensive valuation on disjoint continuation bundles. The closed-record-pair route assumes neither measure-level object, but establishes the quadratic form rather than a standalone uniqueness theorem. The resulting open frontier is to obtain both form and uniqueness without importing measure-level additivity. The paper also records the minimal [8,4,4] record cell and the bare monitored service rate alpha_0 = 1/137, while retaining the deeper reconstruction question as open.
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
Complementarity-First Foundational Release I is a ten-record research release consisting of nine technical papers and this overview. The technical corpus comprises 246 date-neutral public-manuscript pages and spans a conceptual-formal primitive, four quantum-foundations studies, a paired-incidence and transport architecture for finite/local gravity, two distinct local Regge descendants, and a source-controlled Unified Dynamics synthesis. This article supplies the release- wide paper map, dependency graph, claim/evidence classification, artifact register, and open-problem ledger. Its organizing principle is anti-flattening: conceptual proposals, conditional theorems, exact countermodels, finite computations, prospective tests, negative results, and source-controlled syntheses are not treated as interchangeable evidence. The foundational paper defines a completed relation with internal role distinction and shows by elementary independence models that the primitive does not itself determine probability, continuity, geometry, dynamics, or complex quantum theory. The quantum branch separates a conditional reconstruction audit from three focused problems: readout of the two-rebit tomographic defect, certificate-relative operational objectivity underanoninjectivepublicinterface, andtheresourcerequirementsforrecordsandfiniteautonomous maintenance without a free thermodynamic arrow. The gravity branch begins only after a rank-two paired-chiral carrier, Lorentzian real structure, orientation, affine displacement sector, and transport law are selected; common-coframe data then arise only conditionally through the admitted simplicity, gluing, and nondegeneracy chain, after which the branch reaches conditional Palatini–Regge structure and exact finite periodic endpoints but not arbitrary-mesh or continuum closure. Two later gravity papers address different questions: descriptor-local H2/H2R transfer and a conditional curved-Regge identity, versus an intrinsic six-sector Reynolds cancellation mechanism for local zero germs. Unified Dynamics organizes controlled quantum and gravity descendants around a finite dual-pair carrier and a common BF-type kernel while retaining a variation-space obstruction, open complement-operation coherence, no absolute scale, and no Level-4 prediction. The strongest defensible conclusion is therefore a disciplined finite/local reconstruction architecture with exact technical advances, explicit failures, and auditable selectors. Release I is not a completed theory of physics, a continuum unification, a derivation of the Born rule or complex scalars from primitive complementarity, a quantized-gravity result, or an externally peer-reviewed and independently replicated corpus.