Genesis III — A Complete Mathematical Theory of Institutional Integrity: Formal Architecture, IFF Cross-Walk,Referee Audit

Genesis III — A Complete Mathematical Theory of Institutional Integrity Genesis III is presented as the first complete mathematical theory of institutional integrity, in the sense that twelve formal layers (OP1–OP12) close into a single action functional whose Noether currents are exactly four invariants: governance integrity (Γ), stewardship (Λ), dignity (D×), and extraction (Eₚ). The unique stable extremum of the action sits at Γ* ≈ 0.97 — a measurable, reproducible, falsifiable threshold derived from producing-institution registers (V-Dem, World Bank Worldwide Governance Indicators, Freedom House, GRECO) rather than stipulated as a target. The threshold is reached by four mathematically distinct routes — all projections of one action functional onto established mathematical structures: a cubic-kernel structural fixed point; a Wilson–Fisher infrared fixed point of a five-coupling renormalisation-group flow; a Bohr–Sommerfeld closed orbit on which ℏ is derived rather than free; and a Coleman–Weinberg minimum of a scale-invariant one-loop effective potential. The four routes return the same number to within their stated precision bands. They are not four independent derivations; they are four projections of one object, and projection-consistency is the substantive content of the claim of completeness. Four pre-registered falsifiers (F1–F4) are stated with success and failure criteria: cascade-timescale exponential fit on V-Dem ERT v16 (F1); order-of-magnitude conformal-bootstrap extraction of η, ν against the Chang et al. 2025 baseline (F2, structural conjecture pending); 2026–2030 forward watchlist accuracy (F3); and machine-verified OP5 fixed-point uniqueness (F4). The framework is cross-walked against the G7-led International Financial Framework (IFF) proposal, demonstrating operational embedding as an admission criterion through three concrete textual insertions covering steering-committee admission, asset tiering, and Prosperity Data Network safeguards. A referee-style audit anticipates eight points of contestation; six are addressed by editorial discipline (the v2.3.1 lock) and applied throughout this version, and two — the F2 universality-class instrumentation and the band-dependence of the cascade-length calibration Lc — are flagged as known empirical dependencies with stated closure paths. Genesis III contributes a single instrument to the institutional-design conversation: a measurable threshold, with four invariants, four falsifiers, and a published kernel that applies the same standard to every jurisdiction. Where existing proposals offer plumbing, this framework supplies a pressure gauge.