This paper develops finite temporal observability in two parts, with a third in a companion[1]. Part I isolates the structure of a single finite-observability conjugate pair (u, v) andpushes it as far as it goes with no specific physical identification assumed. A finite observerresolves real registers whose entire content is a dimensionless ledger of distinctions, capped atλmax and carrying a total λ+ and a split λ−; positing the symplectic pairing dresses these asthe cell area K = δu δv and the slope Luv = δv/δu. A single shared distinguishability ledgerthen makes the reciprocal cell a consequence — split-invariance forces exponential resolutionmaps, the cell boundary is the full-budget locus, and the saturated cell carries the compatiblecomplex structure supplying the bracket’s imaginary unit. From this alone follow noncommutativityat scale K, the complex unit, an implied wave with a Born rule read as a Fubini–Studytransition probability, a causal bound with one unconditional theorem (the causal slope equivalentto non-negative mass-squared), a reversible generator, the forced first-order (Clifford) form,the non-fixability of the scale, and composite objects as differentiated cell bundles. The singleresidue of the wave construction — the Wallstrom single-valuedness condition — is reduced tothe cell’s prequantum integrality, leaving the integral period 2πK as the one named quantuminput rather than a free-standing posit. Part II supplies the physical reading — the conjugatepairexploration. Validated on the regular pairs the wave is Schr¨odinger’s, the bound is therelativistic mass-shell with L = c, and the first-order form is Dirac’s; extended to exotic pairs(horizon angle and area, holonomy and flux, modular flow and entangling area, the cosmologicalconstant and four-volume) a single per-pair criterion — whether the exchange rate Luv vanishes— sorts discrete from continuous spectra, consistent with the careful literature each time; and asurvey of laboratory prospects finds the frontier mapped but no forced, allowed, novel signature.The architectural extensions to gauge fields and gravity — fermionic statistics from stability,the gauge coupling from comparing cells, and the metric with the Lovelock field equations —are developed in the companion [1]. Every claim is graded — theorem, conditional construction,or candidate route. The whole is offered as a constraint grammar of possible universes, not aderivation of ours.
This paper develops finite temporal observability in two parts, with a third in a companion[1]. Part I isolates the structure of a single finite-observability conjugate pair (u, v) andpushes it as far as it goes with no specific physical identification assumed. A finite observerresolves real registers whose entire content is a dimensionless ledger of distinctions, capped atλmax and carrying a total λ+ and a split λ−; positing the symplectic pairing dresses these asthe cell area K = δu δv and the slope Luv = δv/δu. A single shared distinguishability ledgerthen makes the reciprocal cell a consequence — split-invariance forces exponential resolutionmaps, the cell boundary is the full-budget locus, and the saturated cell carries the compatiblecomplex structure supplying the bracket’s imaginary unit. From this alone follow noncommutativityat scale K, the complex unit, an implied wave with a Born rule read as a Fubini–Studytransition probability, a causal bound with one unconditional theorem (the causal slope equivalentto non-negative mass-squared), a reversible generator, the forced first-order (Clifford) form,the non-fixability of the scale, and composite objects as differentiated cell bundles. The singleresidue of the wave construction — the Wallstrom single-valuedness condition — is reduced tothe cell’s prequantum integrality, leaving the integral period 2πK as the one named quantuminput rather than a free-standing posit. Part II supplies the physical reading — the conjugatepairexploration. Validated on the regular pairs the wave is Schr¨odinger’s, the bound is therelativistic mass-shell with L = c, and the first-order form is Dirac’s; extended to exotic pairs(horizon angle and area, holonomy and flux, modular flow and entangling area, the cosmologicalconstant and four-volume) a single per-pair criterion — whether the exchange rate Luv vanishes— sorts discrete from continuous spectra, consistent with the careful literature each time; and asurvey of laboratory prospects finds the frontier mapped but no forced, allowed, novel signature.The architectural extensions to gauge fields and gravity — fermionic statistics from stability,the gauge coupling from comparing cells, and the metric with the Lovelock field equations —are developed in the companion [1]. Every claim is graded — theorem, conditional construction,or candidate route. The whole is offered as a constraint grammar of possible universes, not aderivation of ours.
Finite observability is built in two stages. First, abstractly: a finite observer resolving realvaluedregisters carries a dimensionless ledger of distinctions, capped in total at λmax, withtwo coordinates — the capped total λ+ = λu + λv and the free split λ− = λv − λu. Second,the registers are reformulated as a conjugate pair (u, v) by positing the symplectic pairing,which dresses the capped total as a resolution cell of minimum area K = δu δv; a second,per-pair finiteness Luv ceilings the rate at which distinguishable change is exchanged betweenthe members, and marks the distinguished (null-diagonal) cell on the saturation locus. Theshared ledger makes the reciprocal cell a consequence, not a postulate: split-invariance forcesexponential resolution maps, and δu δv = K is the full-budget locus. From this we derive:noncommutativity at scale K; the imaginary unit as the saturated cell’s complex structure; aconstructed wave with Schr¨odinger-form evolution and a Born rule as Fubini–Study transitionprobability; one unconditional causal theorem (subluminal propagation equivalent to a nonnegativedispersion invariant); a forced first-order (Clifford) form; measurement decomposedinto the cell’s own motions, with one testable consequence — collapse of massive superpositionsabove a derived ceiling (∼ 1012–1014 amu) on the Di´osi–Penrose timescale via a conservative,non-radiating mechanism; the non-fixability of the scale; and composites as differentiated cellbundles. The physical reading — position and momentum, c, Dirac, gauge fields and gravity— is deferred entirely to a companion paper. The claim here is structural: the grammar of onefinite-observability conjugate pair, with no particular physical pair assumed.
Finite Determinacy (FD) was developed from a representational question: whether theuse of real numbers for physical quantities should be read as implying arbitrarily precisephysical determination. Replacing that idealisation by objectively finite determinationleads to bounded shared resolution depth for related records. Close finite-informationand relational antecedents in quantum foundations were identified subsequently and areacknowledged here; they were not the route by which the present framework was developed,and no historical priority is claimed for those principles. This companion paper asks whatdynamical restrictions follow once the resulting finite-record geometry is combined withexplicit finite-rate premises.For self-containment the paper first reproduces the common foundation: bounded jointdepth and split-invariant refinement give exponential resolution and a non-zero two-registerwidth-product floor; a homogeneous, finitely additive area regularity promotes that scalarconstraint to a local area measure; and a primitive tick/readout role asymmetry suppliesorientation, after which the two-member sector is symplectic. The positive symmetric formused for compatible complex structure remains an independent structural input. Dynamicsthen adds a universal pace ceiling rmax, a saturated intra-pair exchange ceiling |dv/du| ≤ L,and an inter-pair causal conversion c∗. In the quantum branch, explicit coherent-recordand record-faithfulness assumptions lead through Weyl–Heisenberg representation theoryto finite-step unitary evolution and the Schrödinger law-form. In the gauge branch, recordgeneratedtransport and holonomy lead, under a minimal local reversible continuum closure,to Yang–Mills curvature-square dynamics. In gravity, locality, reversibility and isotropy givea minimal hyperbolic principal part, while an explicit spatially relational continuum closureleaves two transverse-traceless modes.The proposed contribution is therefore not a new finiteness or relationality principle,nor an exclusive derivation of familiar terminal equations. It is an independently developedfinite-geometric route from the physical interpretation of real-number representation to acommon pre-Hilbert, pre-gauge and pre-metric substrate, followed by sector-specific dynamicalconsistency conditions.
For stationary, stable linear systems, quantum form (symplectic form, complex structure, Hilbert inner product) is not a set of external postulates but geometric architecture already carried by the classical action and its flow; read through a local projection, for which decoherence is the explicit candidate, only one postulate remains: that states are sections. The Born measure is not derived here. This is a foundations paper. It adds no new dynamics, and most of its mathematics is known; its contribution is to arrange known results inside one ontology and to check what that ontology can and cannot carry. The ontology has a static space of consistent configurations, a single actualized history, a many-to-one projection Π and a selection operator A, and was proposed to account for quantum structure, the arrow of time and the Born rule. Taking each claim to the smallest system on which it can be computed, we find that the natural explicit candidate for Π, a projection onto locally accessible degrees of freedom, is standard decoherence theory; we do not show that Π must take this form. For linear systems with stable dynamics the quantum structure the ontology presupposes is reconstructed from the classical action: the symplectic form from the boundary term, the complex structure from the flow, and the Hilbert inner product from their combination. Stability of the linearized dynamics, rather than positivity of the action's Hessian, is the condition for quantum form to exist. Given the section postulate, the topological invariants of the ontology become the integrality conditions of geometric quantization; under the preservation assumption of Proposition 1, a dynamics that couples subsystems admits a single value of ħ; and if topology fixes dimensionless constants at all, it can do so only at a boundary, the measured values being images under renormalization-group flow (an illustrated pattern, not a derivation). The hidden sector splits into a gauge part and a temporally accessible part, which exposes a dilemma for structural accounts of irreversibility. A global selection cannot signal under three stated conditions, the central one being that its criterion reads only unconditioned reduced states in the causal past; we conjecture that selection is triggered by redundant environmental records. A hypothesis that the history begins at a regular horizon is tested against the Einstein equations in homogeneous models. Each result is labelled as known, synthesis or conjecture. The code-backed checks are listed in Tables 2–4 and reproduced by the attached scripts (run_all.py, with assertions on the quoted values; tested on Python 3.11/Linux and Python 3.14/Windows). Of the original framework's three predictions, one coincides with standard quantum mechanics in its safe form, one is withdrawn, and one lacks a mechanism and is bounded by binary-pulsar timing. How to check this paper: every result carries a status tag (known / synthesis / conjecture / withdrawn / scoped numerical evidence) collected in the ledger (Table 1). Code-backed claims are listed with their IDs in Tables 2–4. Unzip scripts_v15.zip and run python run_all.py (a few minutes; --rederive also redoes the symbolic Bianchi IX derivation); it asserts the numbers quoted in the text and exits non-zero on any mismatch. Corrections are welcome.
We develop the quantum layer of the finite ring cosmology framework: observation as the interaction of a Subject and an Object, phase-coherent cyclic subsystems of a common finite Carrier shell. Four identifications carry the construction, each a derivation rather than an interpretation. The wave function is phase: pure states are windings of the Object's cycle, selected by stationarity under the global drive, with E=hf an identity. The probability amplitude is Object-to-Subject projection onto a forced orthogonal basis, so that completeness, the selection rules, and the Lüders update are finite character theory rather than postulates. Probability is a coincidence count in the Subject's ledger - the group ring Z[i] of the shared quarter-turn core - which derives the Born rule below the coherence horizon and forces complex amplitudes. Composition is conservation: the single drive conserves the relative offset of a pair, synchronised orbits are the Bell states, and the framework saturates the Tsirelson bound exactly, S=2(ζ8+ζ8−1)=22, while reproducing the network behaviour of the real-versus-complex discrimination. The same conservation makes gravity an entangling channel whose distinctive parameter-free signature is equal force but unequal entanglement - a source gravitates by its full mass yet entangles only through its coherent fraction --- with entanglement forming at the Newtonian rate under the complementarity V2+C2=1. Every claim is verified by exact arithmetic in three worked configurations (eleven validation suites, eighty-nine checks), and the experimental confrontation closes in a single falsifiability ledger on one committed carrier scale.
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
This paper tells the quantum-mechanical account of Admissibility Physics in one place, from the first declared fact to the last committed record. From a single finite-capacity axiom (A1) plus one declared occupancy fact, the story runs through the Δ calculus that prices jointness (Δ = ε(J − R), derived, with two fences: Δ is not an information functional, and Δ > 0 is not a quantum criterion); the separable / irreducibly-joint fork, decided by an exact Boole-polytope feasibility test; the Boolean-defender bridge that forces noncommutativity where the global Boolean section fails; the gate pipeline that earns complex Hilbert space and the finite Born trace rule as endpoint theorems rather than postulates; the correlation ladder from product states to Tsirelson, with a native family ceiling 2√2·102/103 carried at honest reading grade with a live falsifier; resolution as a class transition, with the free/spend/permanent triad proved as a composition of banked theorems and measurement, decoherence, the Page curve, and the Diósi–Penrose scale as four worked instances of one mechanism; and the arrow of time as the one-way ratchet of the admissibility floor — confinement, the second law, and the quantum as one axis read at graded strengths. Every load-bearing step is anchored to a named, machine-verified check function in the APF theorem bank; the grade of each step is stated where the step is made; and everything the story does not claim is stated in one place. The Technical Supplement (deposited alongside and linked from this record) is self-contained for this paper: every definition, proof, and grade the story rests on, in one document, with a worked end-to-end instance and a reproducibility appendix pinning the theorem bank to a public repository and an archived release. About the series. Admissibility Physics is a structural realist reconstruction program built on a single commitment: any bounded region of the world can hold only finitely many distinctions. A principle of least enforcement cost then selects, among all the ways those distinctions might be arranged, the configurations a finite world can sustain. From this the content of physics is reconstructed rather than postulated: the Standard Model's gauge group and matter content, the Hilbert-space and Born-rule architecture of quantum mechanics, the geometry and field equations of general relativity, the four laws of thermodynamics, and the large-scale budget of cosmology emerge as different readings of one finite-capacity ledger. The unification is quantitative as well as conceptual: the framework's dimensionless constants appear not as free parameters but as counts read off that ledger — among them the dark-energy fraction ΩΛ = 42/61 and the weak mixing angle sin2θW = 3/13 — fixed, in the strongest cases, to within current measurement. The core derivation runs Papers 0–11; the extension papers carry the individual sectors. Each paper's main text and Technical Supplement is deposited separately; every quantitative claim traces to a named, executable check in the public theorem bank (over 3,800 bank-registered theorems, 48 quantitative predictions); and each result is carried at an explicit, graded level of confidence — from analytically forced to structurally grounded — with the measurements that would refute it named. Admissibility Physics is offered as a candidate, not a finished theory. If the program holds, the laws of physics could not have been otherwise: they are what a finite world permits. Website: admissibilityphysics.com. Engine and theorem bank: https://github.com/Ethan-Brooke/APF-Engine. Full series and latest deposits: Zenodo community admissibility_physics. The Engine — Admissibility Physics: An Executable Constraint Framework and Constants Map — DOI 10.5281/zenodo.18529115. Paper 0 — What Physics Permits: A Constraint-First Framework for Physics — DOI 10.5281/zenodo.18439523 Paper 1 — The Enforceability of Distinction — DOI 10.5281/zenodo.18439200 Paper 2 — Finite Admissibility and the Failure of Global Description — DOI 10.5281/zenodo.18439274 Paper 3 — Entropy, Time, and Accumulated Cost — DOI 10.5281/zenodo.18439363 Paper 4 — Admissibility Constraints and Structural Saturation — DOI 10.5281/zenodo.18439397 Paper 5 — Quantum Structure from Finite Enforceability — DOI 10.5281/zenodo.18439433 Paper 6 — Dynamics and Geometry as Optimal Admissible Reallocation — DOI 10.5281/zenodo.18439445 Paper 7 — A Minimal Quantum of Action from Finite Admissibility — DOI 10.5281/zenodo.18439513 Paper 8 — The Admissibility-Capacity Ledger — DOI 10.5281/zenodo.19721384 Paper 9 — The Geometric Substrate as Cost Structure of Comparison Continuations — DOI 10.5281/zenodo.20041675 Paper 10 — The Calculus of Finite Continuability — DOI 10.5281/zenodo.20041680 Paper 11 — Forced Universality from Capacity-Bounded Admissibility — DOI 10.5281/zenodo.20684198 Paper 12 — The Gauge Sector of Admissibility Physics — DOI 10.5281/zenodo.21212521 Paper 13 — The Minimal Admissibility Core — DOI 10.5281/zenodo.18361446 Paper 14 — The Quantum Story — DOI 10.5281/zenodo.21212188 Paper 16 — Markov Breakdown and the Hard Problems — DOI 10.5281/zenodo.20684207 Paper 18 — The Electroweak Sector as a Capacity Equilibrium — DOI 10.5281/zenodo.20684209 Paper 19 — Large-Angle CMB Suppression as a Finite-Continuability Constraint — DOI 10.5281/zenodo.21199218 Paper 20 — The Enforcement Crystal — DOI 10.5281/zenodo.18531732 Paper 23 — Magnetically Dark Winding-Class Quantum Processors — DOI 10.5281/zenodo.21199220 Paper 24 — The Recruitment-Radius Extension — Foundations — DOI 10.5281/zenodo.20684211 Paper 25 — The Recruitment-Radius Extension: Applications — DOI 10.5281/zenodo.21199222 Paper 28 — Absolute Mass Scales from Electroweak Capacity Saturation — DOI 10.5281/zenodo.20684215 Paper 29 — Plaquette Representation Dominance and Confinement — DOI 10.5281/zenodo.20684218 Paper 30 — A Tube Mechanism for the Lattice Mass Gap — DOI 10.5281/zenodo.20684220 Paper 31 — Osterwalder–Schrader Structure of Lattice Yang–Mills — DOI 10.5281/zenodo.20684222 Paper 32 — Quark Anchors as APF Trace Masses — DOI 10.5281/zenodo.21199226 Paper 33 — Trace-to-Scheme Export Architecture — DOI 10.5281/zenodo.20684224 Paper 35 — The Dark Sector as a Two-Role Capacity Decomposition — DOI 10.5281/zenodo.20684228 Paper 36 — The Missing Floor — DOI 10.5281/zenodo.21199228 Paper 37 — Collapse as Realignment — DOI 10.5281/zenodo.21199231 Paper 38 — Unification as Ledger — DOI 10.5281/zenodo.21199233 Paper 39 — Coherent Phase Regimes in the APF Interface Engine — DOI 10.5281/zenodo.21199235 Paper 40 — The Thermodynamics of Finite Distinction (Between Symmetry and the Void) — DOI 10.5281/zenodo.20684235 Paper 41 — The Horizon as a Continuation Ledger — DOI 10.5281/zenodo.20684241 Paper 42 — The Weak Mixing Angle Is Not Free — DOI 10.5281/zenodo.20684245 Paper 43 — The Neutrino Sector — DOI 10.5281/zenodo.21194191 Paper 44 — What a Finite Theory Owes the Continuum — DOI 10.5281/zenodo.21195874 Paper 45 — What the Vacuum Can Keep — DOI 10.5281/zenodo.21194195 Paper 46 — The Strong CP Angle Is Not Free — DOI 10.5281/zenodo.21194197 Paper 47 — The Confinement Antecedent Is Not Forced — DOI 10.5281/zenodo.21194199 Paper 48 — The Light-Bending Weight Is Not Free — DOI 10.5281/zenodo.21199627 Technical Supplements cross-link to their main paper via isSupplementTo and to the engine via isDocumentedBy. 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