Economic Determinism on a Five-Dimensional Manifold A Deterministic Reformulation of Financial Risk Calculus for the Nine-Capital, Triple-Ledger Framework

Abstract

Background. Contemporary financial risk models — Value-at-Risk, Expected Shortfall, Black–Scholes– Merton, Merton default, CAPM, Vasicek/HJM term-structure models, Solvency II, Basel III/IV, IFRS 9/17 — are one-dimensional projections of an intrinsically higher-dimensional decision phenomenon. The projections perform within a narrow regime and generate the very tail instability they purport to measure outside that regime. Recurrent crises (1987, 1998, 2000, 2008, 2020, 2023) are not statistical anomalies but structural artefacts of dimensional reduction. Objective. This paper proposes and axiomatises Economic Determinism: a deterministic reformulation of the full financial risk calculus on a five-dimensional manifold, hereafter the Curzi Manifold M⁵, and demonstrates that the incumbent framework is recovered as a rigorous limiting case. Methods. We construct M⁵ over the axes (i) ordinal position ω (well-ordered sequence, not cardinal magnitude), (ii) rational magnitude r ∈ ℝ, (iii) logical validity ℓ ∈ [0,1] with an Aristotelian syllogistic kernel, (iv) imaginary phase iφ ∈ iℝ carrying non-commutative structure, and (v) choice χ, an agential– temporal coordinate exhibiting Heisenberg-type observation dependence. On M⁵ we impose (a) the Coverage Hyperbola invariant r · ℓ ≥ 1.8; (b) the Zero-Preserving Division (ZPD) axiom x/(0·y) = y, resolving denominator pathologies without singularities; (c) the Fibonacci-Signed Paradox-Resolution Algebra (FS-PRA), a graded signed calculus in which contradictions at level n are annihilated by Fibonacci-count balanced postulate pairs at level n+1; (d) a financial wave-function analog Ψ(χ, t) with Hamiltonian H generating deterministic evolution of choice-conditioned exposure; and (e) a quantumatom-theory analog quantising sovereign reserve shells with selection rules and a Pauli-analog exclusion on double-pledged collateral. Each incumbent risk operator is re-expressed as a deterministic map ρ: M⁵ → ℂ, red-teamed for logical consistency, operational feasibility, and regulatory compatibility, and shown to reduce continuously to its legacy form under a specified projection π: M⁵ → ℝ. Results. Thirty-one papers (EDP-000 through EDP-030) reformulate the canonical apparatus across credit, market, liquidity, counterparty, IRRBB, operational, portfolio, derivatives, fixed-income, equity, sovereign, FX, balance-of-payments, monetary transmission, structured products, systemic, contagion/network, insurance solvency, actuarial reserving, pension/LDI, commodity, energy, agricultural, fair-value/impairment, consolidation, hedge-accounting, digital-asset, climate, and algorithmic-risk domains, terminated by a master glossary. Principal formal results: (i) rehypothecation chains that violate the Coverage Hyperbola are provably paradoxical under FS-PRA and admit a unique deterministic annihilation; (ii) the Merton–Black–Scholes call price recovers as the ℓ → 1, iφ → 0, χ collapsed limit of the deterministic derivative operator; (iii) VaR-style tail metrics recover as the ordinal-flattened, choiceintegrated projection of an unfolded M⁵ exposure surface; (iv) sovereign default is a shell-transition event with a selection rule expressible in closed form; and (v) systemic risk becomes a coverage-hyperbola violation counted with Fibonacci multiplicity. Contribution. The paper (a) formalises the first deterministic risk calculus that is dimensionally complete with respect to observable market structure; (b) supplies backward-compatible reductions to every current regulatory metric (Basel, Solvency, IFRS); (c) proposes a three-tier adoption pathway (shadow reporting → parallel books → primary ledger) preserving legal and accounting continuity; and (d) unifies the NineCapital taxonomy and the Triple-Ledger (Nostro / Vostro / Lux) architecture within a single risk-theoretic object. Implications. If the framework is correct, the persistent excess volatility, correlation breakdowns, liquidity air-pockets, and cross-asset contagion that classical risk systems misclassify as fat tails are instead deterministic consequences of operating a five-dimensional system with two-dimensional instruments. Adoption is optional, gradual, and reversible until the terminal tier; the reduction property guarantees that no institution is worse off at any adoption depth. The framework is offered as a convergent, cooperative, and non-coercive completion of the existing risk canon.