We derive a (3, 1) -signature spacetime with emergent gravitational coupling from a single input: three real-valued measurement coordinates on the open interval (0, 1). Cencov's uniqueness theorem forces the Fisher-Rao metric. The Fokker-Planck equation defines a spectral problem with Pade coupling lambda (b) = 1/ (1 + ab²), both coefficients derived from perturbation theory (a=73. 6, 0. 12% match; c=75. 9, 1. 26% match). A similarity transform reveals the FP operator is a U (1) gauge theory with Berry connection A = f/ (2T), verified to 6e-6 via SUSY factorization. SO (4, 2) admits exactly 7 gauge-fixing families (Witt's theorem). Thermodynamic selection picks Minkowski, yielding (3, 1). Eisenhart-Duval lift + Kaluza-Klein reduction produce G₄ = Tₑff/K. Machine-verified: 42 Lean 4 files, 398 theorems, 12 axioms, 0 sorry. Falsifiable prediction: analog gravity BEC test.
Anthony W. Eckert (Sat,) studied this question.