APF Paper 8 — The Admissibility-Capacity Ledger

Abstract

Paper 8 of the Admissibility Physics Framework (APF), The Admissibility-Capacity Ledger. The paper presents the unifying scalar record (K, deff) — capacity K, effective dimension deff — read through six regime projections (πT thermodynamic, πG gauge, πQ quantum, πF fermion, πC cosmological, πA action) and four cross-regime consistency identities I1–I4 (holographic, gauge–cosmological, thermo-quantum, action–thermo). Hierarchy of claims. Three of the four identities are intentionally modest. I1 reduces to a horizon-convention identity under Khorizon = A/(4ℓP2), reproducing SBH = A/(4ℓP2) by construction. I3 is the standard finite-dimensional entropy closure SvN(ρmax) = ln N. I4 is the standard high-temperature limit limβ→0 ln Z(β) = ln N. The paper's only non-trivial structural claim is the gauge–cosmological bridge I2: Theorem 1.1 (Formal Kernel; Gauge–Cosmological Bridge). A unique GSM-invariant 42-dimensional subspace VΛ ⊂ V61 exists under the Standard-Model gauge action GSM = SU(3) × SU(2) × U(1) and satisfies the T12 partition constraint. Proof: Maschke's complete-reducibility theorem (Hall 2015) plus dimension-counting under the partition. The subspace induces the residual partition 3 + 16 + 42 = 61 and the cosmological fraction ΩΛ = 42/61 ≈ 0.6885. What the paper offers. An argument-first main body (35pp) opening with the formal kernel, the argument shape, and a tabulated taster of the derived constants — sin2θW = 3/13, Ngen = 3, ΩΛ = 42/61, ρΛ/MPl4 = 42/10262, H0 = 70.03 km/s/Mpc, (TCMB/MPl)4 = 48/10264. A focal section §O ("The Gauge–Cosmological Bridge: Integrated Nontrivial Content") integrates Theorem 1.1, the forcing chain, two-tier uniqueness, and the brittleness analysis into a single reading. What this paper does not claim. A competitive joint-likelihood fit to Planck/BAO/SN under full nuisance parameters. A derivation of log-A corrections to SBH that microscopic frameworks (LQG, string, SUSY-localisation) supply. A first-principles microscopic derivation of the integer counts (61, 102) beyond APF's internal stack. A resolution of the observer-dependence question (formalised with explicit transformation laws, not resolved). Why this matters for the series. Paper 8 is the formal home of the Admissibility-Capacity Ledger. Paper 3 introduces the ledger; this paper treats it as a first-class object with full proof spine. Papers 0/2/3/5/6/7/13 each project through one or more of the six regime projections. Paper 8 explains why the projections cohere across regimes — and which of the cross-regime identities is the load-bearing one. Companion artifacts. Full proof spine in the Technical Supplement (107pp). A Bridge Visualizer interactive HTML figure in the paper-companion repository. Code and reproducibility. GitHub repository Colab walkthrough notebook (one-click) Interactive dependency DAG Codebase backing. Every theorem traces to a named check function in the canonical apf/ codebase (v7.5; 454 bank-registered theorems, 471 verify_all checks, 39 modules + standalone). Paper 8's I1–I4 consistency identities and Theorem 1.1 (gauge–cosmological bridge) live in apf/unification.py; the three-level integer/scalar/subspace witnesses live in apf/unification_three_levels.py; the I1-bridge construction lives in apf/horizon_joint_bridge.py; the VΛ uniqueness witness lives in apf/formal_kernel.py. 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