Part I A Structural Closure of Physical Description

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