APF Paper 7 — A Minimal Quantum of Action from Finite Admissibility

Admissibility Physics — A Minimal Quantum of Action from Finite Admissibility (Paper 7) This Zenodo community collects research outputs associated with Admissibility Physics, with primary focus on Paper 7 — A Minimal Quantum of Action from Finite Admissibility and the mathematical necessity of a nonzero minimum action. Paper 7 establishes that zero accumulated action is structurally inadmissible for any transition that introduces an independent, irreversible distinction. Working entirely within the admissibility framework, the paper defines an accumulated enforcement cost functional and proves that, under finite admissibility and uniform finite distinguishability, the spectrum of admissible accumulated costs for record-forming paths is bounded away from zero. No assumptions are made about discreteness, spacetime structure, probability, quantum postulates, or dynamics. The result is purely structural: if distinctions must be jointly enforceable under finite capacity, then introducing a new, irreversible distinction necessarily incurs a strictly positive minimum cost. Arbitrarily small but nonzero costs are excluded. When accumulated enforcement cost is identified with action in regimes admitting variational description (as established in Paper 6), this isolated minimum plays the role of a quantum of action. The numerical value of this quantum is not derived and remains empirical; what is established is its structural necessity. Quantization is therefore not imposed as a postulate but emerges from finite enforceability itself. Paper 7 completes the core mathematical backbone of Admissibility Physics by showing that quantization is required wherever irreversible record formation is possible. Together with Papers 1–6, it explains why classical variational mechanics fails at small scales and why quantum structure must intervene. This community serves as a curated, citable archive centered on the structural origin of quantization. Paper 7 functions as the mathematical keystone linking finite enforceability, irreversibility, and the existence of a minimum action scale, independent of any specific physical realization. Core papers are frozen where noted; companion mathematical appendices, figures, and computational artifacts document proofs, assumptions, and regime boundaries.