From Relation to Effective Physics: Theorems, Closure Constants and No-Go Results in the Ω₀/A2 Formal System

Abstract

Ω₀/A2 is developed here as an auditable theorem system for effective physical structure rather than as a descriptive framework. The formal core is quotient descent: a fine-scale operation admits an exact deterministic effective representation if and only if it preserves the fibres of the declared coarse state. This is extended to a role-complete autonomy criterion covering prediction, intervention, recovery, History/lineage, Mapping and cross-scale operations. The unified framework develops conditional theorem branches for phase and cycle closure, action-like factorization, finite causal propagation, recovery, cross-scale inheritance, generative compression and state–law–coupling co-generation, together with explicit no-go results and falsification criteria. A second major component treats fundamental constants as closure interfaces rather than indivisible inputs. Operational roles of \(c\), \(\hbar\), \(G\), \(k_B\), gauge couplings, mass parameters and cosmological quantities are separated before reunification. For \(c\), the framework derives conditional routes connecting causal-front, wave-front and geometric roles. For action conversion, cross-sector universality is separated from absolute scale selection, with scale-orbit symmetry providing an explicit obstruction to determining a unique dimensional scale without an independent scale-breaking mechanism. Mathematical proof, physical correspondence and empirical validation are tracked separately through an M/P/E discipline. Established mathematical structures recovered from the Ω₀/A2 derivation are treated as structural convergence tests when they were not inserted as decisive assumptions. Computational results are retained only as model-level support or falsification evidence and do not substitute for mathematical proof or physical measurement. This Public Preprint v1.0 is the unified master archive of the current Ω₀/A2 theorem programme. It consolidates previously distributed theorem, no-go, recovery, causality, generative-compression, mechanism-diagnostic and Closure-Constants results while preserving explicit open physical mappings. It does not claim that quantum mechanics, relativity, the Standard Model, or the numerical values of fundamental constants have already been derived. The deposited record contains the main manuscript, the Supplementary Master Registry, and a versioned archival package. The repository timestamp and DOI identify this exact public version.