This paper is the mathematical core of a three-paper programme around the Ontological Totality Functional (OTF). Its claim is not that physics needs one more totalizing action, but that it lacks a rigorous language for physical admissibility: the conditions under which a configuration can count as physically stable rather than merely mathematically specifiable. The paper recasts the OTF accordingly. The backbone is a local-to-global construction on a finite 2-complex of contexts. Local states, pointer subalgebras, and quantum channels are assigned to vertices and edges. Two defect terms measure admissibility: the gluing defect, defined from failures of triangular composition of channels in the diamond norm, and the noetic defect, defined from distance to a pointer subalgebra via conditional expectations. Together with a sector-dependent effective action, they define an admissibility functional whose minimizers form the admissible set at cutoff Lambda. Four controlled results are proved in finite-dimensional truncations: existence of minimizers, a zero-defect criterion for the noetic sector, an observable bound implying approximate classicality when the noetic defect is small, and a global path-consistency theorem showing that local triangle defects bound route dependence across any filled disk in the context complex. A continuum scalar surrogate for coarse-grained coherence defects is also introduced, and its effective stress tensor is shown to be conserved on shell. Finally, the paper defines the central target of the programme: mixed category-algebra-scale fixed points, namely compatible families of admissible minimizers across cutoffs. This record is part of the Ontological Totality Functional (OTF) series. Companion works include OTF II, OTF III, OTF IV, and the OTF Master Edition. Companion records in the OTF series:OTF II — DOI: 10.5281/zenodo.19075284OTF IV — DOI: 10.5281/zenodo.19076867OTF Master Edition — DOI: 10.5281/zenodo.19077303
This paper is the mathematical core of a three-paper programme around the Ontological Totality Functional (OTF). Its claim is not that physics needs one more totalizing action, but that it lacks a rigorous language for physical admissibility: the conditions under which a configuration can count as physically stable rather than merely mathematically specifiable. The paper recasts the OTF accordingly. The backbone is a local-to-global construction on a finite 2-complex of contexts. Local states, pointer subalgebras, and quantum channels are assigned to vertices and edges. Two defect terms measure admissibility: the gluing defect, defined from failures of triangular composition of channels in the diamond norm, and the noetic defect, defined from distance to a pointer subalgebra via conditional expectations. Together with a sector-dependent effective action, they define an admissibility functional whose minimizers form the admissible set at cutoff Lambda. Four controlled results are proved in finite-dimensional truncations: existence of minimizers, a zero-defect criterion for the noetic sector, an observable bound implying approximate classicality when the noetic defect is small, and a global path-consistency theorem showing that local triangle defects bound route dependence across any filled disk in the context complex. A continuum scalar surrogate for coarse-grained coherence defects is also introduced, and its effective stress tensor is shown to be conserved on shell. Finally, the paper defines the central target of the programme: mixed category-algebra-scale fixed points, namely compatible families of admissible minimizers across cutoffs. This record is part of the Ontological Totality Functional (OTF) series. Companion works include OTF II, OTF III, OTF IV, and the OTF Master Edition. Companion records in the OTF series:OTF II — DOI: 10.5281/zenodo.19075284OTF IV — DOI: 10.5281/zenodo.19076867OTF Master Edition — DOI: 10.5281/zenodo.19077303
Paper I argued that the Ontological Totality Functional (OTF) should be read not as a new totalizing theory, but as a theory of physically admissible structures. Paper II provides the first dedicated physical realization of that claim. It focuses on one channel only: the classicalization of primordial tensor modes. The central thesis is that a tensor mode does not become physically real merely by being mathematically definable or dynamically squeezed. It becomes physically admissible when two conditions are met simultaneously: local-to-global closure across effective descriptions and sufficiently small noetic defect relative to a pointer subalgebra. The paper formulates a reduced tensor-sector OTF in quasi-de Sitter space, drawing on the language of open quantum systems and recent work on primordial graviton decoherence and primordial-gravitational-wave phenomenology. A tensor gluing defect G_T(k,a) measures inconsistency between competing coarse-grained propagators or channels across scale windows, while a tensor noetic defect N_T(k,a) measures the trace-norm distance of the reduced state to a preferred pointer algebra. These defects define a mode-wise admissibility rate. Gamma_OTF(k,a) = alpha G_T(k,a) + beta N_T(k,a), which enters a defect-dependent Lindblad evolution for the reduced tensor density matrix. The resulting decoherence factor defines suppression of off-diagonal tensor coherences and a scale-dependent classicalization epoch. Three main results are obtained. First, positivity of the defect rates implies monotonic decay of off-diagonal coherences in the pointer basis. Second, if the integrated admissibility rate crosses a finite threshold, then classicalization occurs at a finite epoch for that mode. Third, the OTF channel induces a clean phenomenological parameterization in the tensor sector: a coherence-suppression window and an effective modification of the primordial tensor signal that can be bounded with future B-mode searches. This record is part of the Ontological Totality Functional (OTF) series. Companion works include OTF I, OTF III, OTF IV, and the OTF Master Edition. Companion records in the OTF series:OTF I — DOI: 10.5281/zenodo.19068375OTF IV — DOI: 10.5281/zenodo.19076867OTF Master Edition — DOI: 10.5281/zenodo.19077303
This paper extends the Ontological Totality Functional (OTF) programme into the domain of quantum causal structure. Its central claim is that physical admissibility cannot be exhausted by state-level consistency or dynamical stability alone. It must also constrain the admissibility of causal organization itself. The paper introduces a causal defect functional for higher-order quantum processes and argues that definite causal order can emerge as a limiting case of admissible structure. Working in a finite-dimensional process-matrix setting, the paper defines the causal defect as the trace-norm distance to the set of valid causally separable processes with fixed normalization. It proves that this defect is non-negative, vanishes exactly on the causally separable set, and is convex. A free class of admissible supermaps is then identified: linear maps on processes that preserve validity, preserve causal separability, and are contractive in trace norm. Under these maps, the causal defect is monotone. An exact dual operational characterization is established: the causal defect equals the maximal bounded-test advantage over the causally separable set for Hermitian tests of bounded operator norm. In this sense, bounded causal witnesses arise as certified lower-bound functionals for admissibility. To connect the formalism to concrete physical scenarios, the paper studies a dephased-switch family W_eta = W_diag + eta X, where W_diag is causally separable and X encodes interference between orders. For this family, the defect is bounded above linearly in |eta|, while a witness with positive overlap on X yields a matching linear lower bound. As eta tends to zero, the process approaches definite-order admissibility. Within the OTF series, this paper functions as a frontier extension. Paper I introduced physical admissibility mathematically, Paper II studied admissibility in a tensor-cosmology channel, and Paper III interpreted admissibility ontologically. Paper IV shows that the same programme can be pushed into higher-order causal structure, where admissibility constrains not only which states and channels are physically stable but also which causal architectures can count as physically realized. Companion records in the OTF series:OTF I — DOI: 10.5281/zenodo.19068375OTF II — DOI: 10.5281/zenodo.19075284OTF Master Edition — DOI: 10.5281/zenodo.19077303
Description This paper develops a formal calculus of admissible correlation, providing the technical backbone for a constraint-first approach to physical description. Building on a conceptual framework in which enforceability and finite correlation capacity are taken as primitive structural requirements, the present work makes these notions explicit, operational, and compositional. Correlations are treated as primitive relational constraints enforced across interfaces endowed with finite capacity. Admissibility is defined as joint enforceability under these capacity limits and is shown to be inherently non-closed under composition. Correlation capacity is formalized as a finite, interface-localized resource whose saturation and redistribution determine which correlation sets can coherently exist. This yields a precise, pre-dynamical criterion for physical feasibility that precedes probability, stability, and dynamical law. Within this calculus, regime transitions arise when admissible correlation sets change due to capacity reallocation rather than dynamical evolution. The ordered loss of descriptive structures—global states, subsystem factorization, metric geometry, and time itself—is characterized as a consequence of finite enforceability rather than as a breakdown of physical law. Geometry emerges as an efficient representation of coordination cost where capacity gradients are smooth, while entropy is identified with interface capacity governing record formation and exclusion. The calculus introduces no new dynamics, modifies no existing physical theories, and commits to no microscopic ontology. Its role is structural: to delineate the kinematic envelope within which any coherent physical dynamics must operate. Quantum mechanics and general relativity are shown to function as admissibility-preserving frameworks within the regimes where their descriptive assumptions remain enforceable. This work is intended to stand alone as a technical contribution while serving, together with its companion foundational paper, to clarify the limits of physical description and the conditions under which familiar physical structures emerge, persist, and fail. About the series. Admissibility Physics derives the Standard Model gauge group, fermion content, quantum formalism, Lorentzian spacetime, the Einstein field equations, the cosmological constant, and the neutrino, strong-CP, and dark sectors from a single assumption — that enforcement is finite at every causally connected region — with zero free parameters. 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, and every quantitative claim traces to a named, executable check in the public theorem bank (over 3,800 bank-registered theorems across roughly 450 modules, 48 quantitative predictions). 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 13 — The Minimal Admissibility Core — DOI 10.5281/zenodo.18361446 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 20 — The Enforcement Crystal — DOI 10.5281/zenodo.18531732 Paper 24 — The Recruitment-Radius Extension — Foundations — DOI 10.5281/zenodo.20684211 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 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 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 Technical Supplements cross-link to their main paper via isSupplementTo and to the engine via isDocumentedBy. Concept DOIs above resolve to the latest version. Author. Ethan Brooke, Independent Researcher, San Anselmo, California, USA. ORCID: 0009-0001-2261-4682 LinkedIn: linkedin.com/in/ethanbrooke GitHub: github.com/Ethan-Brooke Contact: brooke.ethan@gmail.com
The Admissibility of Natural Physics, Part I begins where an admissibility-first reconstruction of single-system quantum mechanics ends. Its central question is not whether the familiar tensor-product formalism can be assumed, but whether any physical composition law can be derived without importing composite systems, global state spaces, entanglement, locality, or signalling as primitives. The book develops a disciplined reconstruction of binary quantum composition from operational and structural requirements. It first records the exact content and limitations of the inherited single-system closure, establishes dependency and non-circularity statutes, and introduces the possible object of natural physics only as a provisional target ledger rather than as an assumed ontology. It then examines joint preparation, product states and effects, marginal consistency, operational no-signalling, minimal and maximal probabilistic composites, local tomography, and the classification of admissible tensor-product representations. Particular attention is given to the distinction between a mathematical representation theorem and the uniqueness of a physical composition rule. Real, complex, quaternionic, Jordan-algebraic, minimal, maximal, restricted, and non-tomographic alternatives are compared under explicitly declared admissibility conditions. The complex Hilbert-space tensor product is recovered only on branches satisfying the required factorization, coherence, scalar, and operational closure conditions. Where several inequivalent composites survive, the result is a classified family rather than a falsely asserted uniqueness theorem. Entanglement is introduced only after composition has been commissioned. It is defined as the failure of an admitted joint state to belong to the convex closure of admitted product preparations. The analysis proves, within the resulting predictive grammar, that entanglement is a property of composite-state geometry, not an additional force, substance, interaction mechanism, or signalling channel. Throughout, the argument enforces quotient primacy, refinement stability, finite diagnostic closure, regeneration stability, explicit dependency receipts, local termination, and the possibility of Undefined as a legitimate scientific outcome. Part I therefore supplies neither a speculative ontology nor a presupposed many-world formalism. It provides a conditional classification theorem for binary physical composition and identifies precisely what remains to be established before interaction, repeated composition, particle identity, locality, fields, symmetries, and particle content may be addressed.
This paper introduces a constraint-first framework for physical law based on a single structural requirement: that distinctions and correlations be enforceable without contradiction under finite capacity. Rather than proposing new dynamics, entities, or microscopic mechanisms, the work reframes foundational questions in physics by asking a prior question—under what conditions is physical description itself possible? Central to the framework is the recognition that correlation enforcement cannot be unlimited. From this finiteness follows a notion of admissibility, separating correlation structures that can be jointly realized from those that are structurally incoherent, independent of probability or dynamics. Geometry, time, entropy, and global state descriptions are treated not as universal primitives, but as regime-dependent representations that emerge when enforcement constraints can be smoothly distributed—and fail when they cannot. Within this perspective, long-standing foundational puzzles—such as the arrow of time, entropy bounds, horizon paradoxes, and the breakdown of global descriptions—are reinterpreted as signals of regime mismatch rather than failures of physical law. Apparent paradoxes arise when descriptive tools are extrapolated beyond the regimes in which their enforcement is possible. The paper is deliberately pre-dynamical. It does not modify quantum mechanics or general relativity, nor does it derive specific equations or predictions. Its contribution is structural: to articulate the minimal conditions that any coherent physical description must satisfy, and to clarify why familiar physical structures appear where they do, persist where they can, and fail where they must. This work serves as the conceptual foundation for a companion technical paper that formalizes admissibility and finite correlation capacity as a calculus. Together, the papers aim to delineate the boundary between meaningful physical description and questions that cannot be consistently posed. About the series. Admissibility Physics derives the Standard Model gauge group, fermion content, quantum formalism, Lorentzian spacetime, the Einstein field equations, the cosmological constant, and the neutrino, strong-CP, and dark sectors from a single assumption — that enforcement is finite at every causally connected region — with zero free parameters. 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, and every quantitative claim traces to a named, executable check in the public theorem bank (over 3,800 bank-registered theorems across roughly 450 modules, 48 quantitative predictions). 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 13 — The Minimal Admissibility Core — DOI 10.5281/zenodo.18361446 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 20 — The Enforcement Crystal — DOI 10.5281/zenodo.18531732 Paper 24 — The Recruitment-Radius Extension — Foundations — DOI 10.5281/zenodo.20684211 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 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 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 Technical Supplements cross-link to their main paper via isSupplementTo and to the engine via isDocumentedBy. Concept DOIs above resolve to the latest version. Author. Ethan Brooke, Independent Researcher, San Anselmo, California, USA. ORCID: 0009-0001-2261-4682 LinkedIn: linkedin.com/in/ethanbrooke GitHub: github.com/Ethan-Brooke Contact: brooke.ethan@gmail.com
A finite interface either admits a single classical assignment consistent across all the records it holds at once — a global Boolean section — or it does not. This paper develops the gauge-sector consequences of that dividing line inside a capacity-denominated cost calculus, and it is built to be verified from this document and one public repository alone. We prove exact, finite theorems: a characterization theorem forcing cost = count from three axioms with no continuity hypothesis; an additivity theorem and a non-monotonicity no-go for the superadditive surplus Δ; the classification of sharp gauge-invariant colour records at every N (the unique meson record is the entangled singlet, the unique N-fundamental record is the entangled baryon, with an abelian control showing both are non-abelian features); and a contextuality census of gauge-invariant interfaces, including an exact Kochen–Specker colouring obstruction in the physical SU(3) octet channel and an exact 1/6 robustness floor for the verdict. The centerpiece is a fully worked model: SU(2) Hamiltonian lattice gauge theory at strong coupling, static sources joined by flux strings, where Δ is computed on a precisely defined cut and set beside the standard diagnostic. The verdict is structured — co-movement on the N-ality partition, under-determination beyond sign within a family, divergence on split flux, and a checked witness that the capacity side never recomputes the Casimir — and the structure is the result. One section, clearly bounded, reads these theorems onto confinement; it declares its imports and conditions its conclusions on a named saturation premise. No energy gap is derived, no line-operator algebra is constructed, and no thermal claim is made; the paper says exactly where those boundaries sit and why. Every theorem carries a named machine-verified certificate in exact arithmetic. The Technical Supplement (deposited alongside and linked from this record) is the proof-dense companion and the canonical formal home of the Δ calculus for the series. 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 repository (github.com/Ethan-Brooke) via isDocumentedBy. Author. Ethan Brooke, Independent Researcher, San Anselmo, California, USA. ORCID: 0009-0001-2261-4682 LinkedIn: linkedin.com/in/ethanbrooke GitHub: github.com/Ethan-Brooke Contact: brooke.ethan@gmail.com