The Observerse Bridge: A Mathematical Correspondence Between Governance Physics and Geometric Unity

We construct an explicit mathematical bridge between the probability simplex Δⁿ⁻¹ (Governance Physics) and Weinstein's observerse (Geometric Unity). Both spaces are 14-dimensional: the observerse as M⁴ × Sym⁺(4) with dim = 4 + 10 = 14, and the simplex tangent space at n = 15. We define bidirectional maps Φ: Probabilities → Metrics (via Fisher information) and Ψ: Metrics → Probabilities (via normalized diagonal), proving in Lean 4 that: (1) Φ produces symmetric, positive-definite matrices; (2) Ψ produces valid probability distributions; (3) the uniform distribution is a fixed point of Ψ∘Φ; (4) the composition Ψ∘Φ is the Fisher dual (Legendre transform). Complete Lean 4 formalization included with zero sorry markers.