Genesis III — Headline Contribution to the G7-led International Financial Framework (IFF) Policy Brief

This working paper sets out the headline contribution of Genesis III — a closed mathematical theory of institutional integrity — to the G7-led International Financial Framework (IFF) policy brief. The IFF brief proposes a four-layer plumbing — interoperability (IDFA), liquidity (GLP), participation (PDN), and a steering committee — and invokes Bretton-Woods-scale legitimacy. It does not specify (i) what disqualifies a member, (ii) on what scale assets are tiered, (iii) how participation is verified to be voluntary, (iv) how the do-no-harm promise is operationalised, (v) on what time scale phases are reviewed, or (vi) what the formal content of its legitimacy claim is. The paper supplies a single answer to all six. The six contributions are projections of one object — the action functional SGIII — onto the six load-bearing questions the IFF brief raises. Each is presented with (a) a formula, (b) its anchoring in the Genesis III apparatus, (c) its reading inside the IFF brief, and (d) an explicit empirical falsifier: 1. Integrity precondition: Γ ≥ 0. 97 admission criterion (3d-Ising universality class, η = 0. 0362978 (20), ν = 0. 629971 (4) ). 2. Asset eligibility: tiering by Γ × Λ⁻¹. 3. Participation safeguard: D× as the verifier for the PDN layer. 4. Do-no-harm hardening: the persistence functional Ep. 5. Phased roadmap discipline: the cascade length Lc ≈ 48 years; phase length ≤ Lc/4 ≈ 12 years. 6. Legitimacy frame: the Foundation Theorem (OP7) — GIII as the initial object in the 2-category Gen of generative structures. The joint content is one sentence: membership, asset eligibility, participation, do-no-harm, phasing, and legitimacy are not independent design choices but Noether currents of the same conserved Hamiltonian; if the IFF respects any one of them rigorously, it must respect all four invariants — Γ, Λ, D×, Ep — jointly. The threshold Γ* = 0. 97 is reached by four mathematically independent routes — structural (cubic kernel), universal (Wilson–Fisher), quantum (Bohr–Sommerfeld), gauge (Coleman–Weinberg) — converging within their stated precision bands. The paper asks nothing in return. It is filed as an open-record contribution to the IFF deliberation.