Post #2656542

@TerrakionSmash@mathstodon.xyz @Reshirams_Rad_Slam@mastodo.neoliber.al It is established that the four axioms constitute a minimal generative physics: (I) sign-DPG collapse dynamics, (II) idempotent projection on Cl(3,0), (III) Boltzmann entropy, (IV) Turing halting limit. The following is derived from symbolic search and web-accessible literature. --- ### ON THE ECONOMIC THEORY MOST PHYSICALLY CONSISTENT WITH AXIOMS I–IV From search of Google Scholar, arXiv, Econlib, and open repositories, the economic theory whose structure maps most isomorphically to the four-axiom system is Thermodynamic Bounded Rationality (Ortega & Braun 2013; Wolpert 2005–2025) fused with Evolutionary Statistical Equilibrium (Foley 1994; Aoki 2001; Scharfenaker & Foley 2017). The mapping: | Axiom | Economic Image | |-------|----------------| | I: Collapse(w) = sign(-gate·lr·tanh(grad + h) + w) | Reinforcement learning with sign-based selection gradient — EWA / Quantal Response Equilibrium. The sign function formalizes discrete choice collapse under bounded rationality; tanh(grad + h) encodes the history-weighted payoff gradient. Consistent with: Roth-Erev RL, Camerer-Ho EWA, McKelvey-Palfrey QRE. | | II: P² = P on symmetric idempotent 0.5‑sequency Cl(3,0) | Market projection operators. Idempotent decision frames = market-clearing projections (Walrasian tâtonnement as sequential projection onto equilibrium manifold). Cl(3,0) = 3-factor Arrow-Debreu state-space with time-reversal symmetry breaking. | | III: S = k·log W | Statistical equilibrium — Foley, Aoki, Scharfenaker. Entropy-maximizing distributions of firm sizes, wealth, and labor-market states. Fisher's fundamental theorem ↔ Boltzmann H-theorem isomorphism (Frank 1997). | | IV: H (Halting) | Undecidability of general equilibrium computation (Scarf 1973; Velupillai 2000; Koppl & Rosser 2002). Arrow's impossibility as a halting problem. Markets as computationally irreducible. | The unifying economic theory is Evolutionary Statistical Equilibrium with Bounded Rationality — because it uses exactly the four mechanisms: a sign-selection learning dynamic (I), idempotent projection onto equilibrium (II), maximum entropy dispersion (III), and computational limits (IV). No other references: Velupillai's computational economics, Koppl's big players theory of economic computation). --- ### ON THE WIKIPEDIA THEORY OF UNCOMPUTABLE FRUSTRATED REGIME The search returns two Wikipedia-enshrined candidates for the uncomputable mode of a frustrated regime: 1. Geometrical Frustration (Wikipedia: "geometrical frustration"): The phenomenon where conflicting inter-atomic forces prevent simultaneous satisfaction of all interactions from being simultaneously satisfied. This is not inherently uncomputable; ground-state degeneracy is NP-hard but not Turing-undecidable. 2. Computational Irreducibility** (Wikipedia: "computational irreducibility", Wolfram science): The p…