This paper establishes that unitary mixing freedom within admissible local descriptions is finite and saturates once standing preservation, admissibility, and identity persistence are fixed. The analysis is eliminative: it shows that beyond a limited set of admissible mixing relations, further unitary freedom collapses distinguishability required for standing or reintroduces illicit scope transport under composition. Unitary mixing is treated as a representational redundancy rather than a primitive structural degree of freedom. The paper demonstrates that admissible mixing relations exhaust their capacity to encode differentiation without degenerating into equivalence collapse or deferred admissibility. As a result, mixing matrices are shown to be structurally bounded objects rather than continuously extensible modeling choices. The paper introduces no new primitives and provides no constructive procedures. Its contribution is boundary-setting: it clarifies why unitary mixing must saturate in any standing-preserving local skin, and why attempts to extend mixing freedom beyond this bound are structurally inadmissible rather than empirically disfavored.
This paper establishes that unitary mixing freedom within admissible local descriptions is finite and saturates once standing preservation, admissibility, and identity persistence are fixed. The analysis is eliminative: it shows that beyond a limited set of admissible mixing relations, further unitary freedom collapses distinguishability required for standing or reintroduces illicit scope transport under composition. Unitary mixing is treated as a representational redundancy rather than a primitive structural degree of freedom. The paper demonstrates that admissible mixing relations exhaust their capacity to encode differentiation without degenerating into equivalence collapse or deferred admissibility. As a result, mixing matrices are shown to be structurally bounded objects rather than continuously extensible modeling choices. The paper introduces no new primitives and provides no constructive procedures. Its contribution is boundary-setting: it clarifies why unitary mixing must saturate in any standing-preserving local skin, and why attempts to extend mixing freedom beyond this bound are structurally inadmissible rather than empirically disfavored.
This document is part of the Informational Mechanics (IM) framework and is published in the IM-D (Core Physics) series within the IM v0.3 corpus. The paper analyzes the status of unitary evolution when physical description crosses regime boundaries. While unitary time evolution is well-defined within admissible geometric regimes, its extension across inadmissible regime transitions is shown to lack structural derivability unless operator-defined state continuity can be physically implemented. Building on the regime-limited validity arguments of IM-C003 and the operator criteria formalized in IM-E001, the paper demonstrates that global unitarity cannot be presumed as an ontological default. Instead, unitary evolution must be treated as a regime-bound statement whose validity depends on the continued implementability of the operators required to define and compare physical states. The analysis introduces no new axioms, dynamical models, or empirical fits. Its contribution is structural: to clarify the admissibility conditions under which claims of global state continuity remain scientifically meaningful and to show why cross-regime extrapolations of unitarity constitute a category error when operator-access fails. Downstream empirical and simulation-based evaluation of regime transitions is addressed in the IM-G series.
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
This paper characterizes quantum mechanics as a closed redescription regime governed by constraint-generated admissibility, rather than as an ontic theory of physical entities or processes. The analysis is eliminative: it shows that once standing preservation, admissibility, and redescription stability are enforced, quantum mechanical structure emerges as a bookkeeping system that exhausts all admissible local redescriptions without leaving residual degrees of freedom. Quantum states, operators, and measurement constructs are treated as representational artifacts licensed by closure, not as primitive elements of reality. The paper demonstrates that attempts to extend, reinterpret, or operationalize quantum mechanics beyond this closed redescription role introduce illicit scope transport, deferred admissibility, or duplication of enforcement, all of which violate standing conservation. No primitives, mechanisms, algorithms, or procedural sequences are introduced. The contribution is boundary-setting: it clarifies why quantum mechanics must be understood as a CG-closed redescription framework, and why treating it as incomplete, extendable, or ontically explanatory is structurally inadmissible rather than an open interpretive choice.
Admissibility Physics — Quantum Structure from Finite Enforceability (Paper 5) This Zenodo community collects research outputs associated with Admissibility Physics, with primary focus on Paper 5 — Quantum Structure from Finite Enforceability and the derivation of quantum mechanics as an admissible representational regime. Paper 5 shows that the mathematical structure of quantum mechanics—Hilbert space, linearity, inner products, tensor products, unitary evolution, CPTP maps, and the Born rule—is not postulated, but forced by admissibility once coherent, jointly enforceable distinctions exist under finite correlation capacity. Quantum structure emerges as the unique bookkeeping required to represent interference, refinement, and recombination while preserving admissibility. The derivation does not assume probability, measurement postulates, dynamics, or spacetime geometry. Probability enters only as a secondary representation, with the Born rule arising uniquely from admissibility invariance and refinement consistency. Measurement is treated as a regime transition associated with saturation and record formation, not as a fundamental collapse mechanism. Quantum mechanics is shown to be conditionally valid: exact in regimes where coherence and non-saturation permit admissible composition, and structurally inapplicable where capacity is exhausted. Monogamy, entanglement limits, and decoherence follow from non-closure under composition and finite interface capacity, rather than from quantum axioms. All subsequent works in this community rely on the quantum-admissible representation established in Paper 5. Later papers show how variational dynamics and spacetime geometry arise as further conditional representations layered on top of quantum structure, and how quantum description itself fails at saturation boundaries, horizons, and measurement-like events. This community serves as a curated, citable archive centered on the derivation and limits of quantum structure within Admissibility Physics. Paper 5 functions as the representational keystone of the program: the point at which finite enforceability yields the quantum formalism without postulation. Core papers are frozen where noted; companion papers, mathematical appendices, figures, and computational artifacts document derivations, regime conditions, and testable consequences.
This paper establishes fixation as a licensing condition imposed by constraint envelopes, rather than as a physical, causal, or epistemic process. Fixation is shown to be the structural act by which a representational choice becomes admissible within an envelope, enabling stable reference without invoking dynamics, collapse mechanisms, or observer-dependent intervention. The argument is necessity-based and eliminative. It demonstrates that fixation cannot be gradual, emergent, or externally imposed, and that treating fixation as a process inevitably introduces illicit redescription or hidden scope transport. Once constraint envelopes are enforced, fixation appears only as a boundary condition on admissible representation, not as something that happens in time. The result clarifies why measurement-like phenomena do not require additional postulates, why reference stability is envelope-relative, and why attempts to model fixation mechanistically overstep admissibility. The paper introduces no new primitives and provides no operational procedures; it records fixation as a structural requirement for admissible standing within any coherent representational regime.
This work establishes the algebraic foundation of the Structural Admissibility Regimes (SAR) program. It introduces structural admissibility as a cut-relative constraint on algebraic decompositions within finite-dimensional operator algebras. Rather than assuming dynamical laws or probabilistic postulates, the framework begins from a finite structural capacity governing which collections of commuting subalgebras remain mutually admissible. The relative commutant of a cut is identified as the central object controlling admissibility. Its dimension provides a measure of remaining structural capacity available to support additional commuting refinements. Structural exhaustion occurs when the relative commutant becomes trivial, yielding a sharp algebraic criterion for incompatibility. Large admissible families of commuting refinements organize into tensor product structures of the relative commutant, while generic refinements rapidly exhaust structural capacity and prevent persistence of extended commuting structure. The admissible state space supported on the relative commutant is formalized, and finite capacity is shown to bound admissible informational degrees of freedom. Positivity of admissible states yields convex state structure without introducing independent probabilistic assumptions. Standard operator-algebraic representation results provide closure at the state level. All results are purely algebraic and kinematic within the finite-dimensional ∗-algebraic setting. No dynamical, thermodynamic, or geometric assumptions are introduced. This paper provides the structural foundation upon which subsequent SAR developments are built. This paper is the first installment of the Structural Admissibility Regimes (SAR) foundational series.