Rigorous mathematical foundations of the displacement framework. Defines configuration space M as a Riemannian manifold, ground state S0 as a stable submanifold, displacement D as geodesic distance from S0, and accumulated displacement Phi as the path integral of D. Proves: Ground State Stability Theorem (Lyapunov), Wrong Attractor Existence Theorem (Morse), Accumulated Cost Lower Bound, DC4 Path-Cost Tradeoff Theorem, Matrix Displacement Theorem for coupled systems.
Establishes information-geometric identity D = D_KL/beta and thermodynamic identity D = DeltaF. DC1-DC9 stated as formal propositions with proofs.
Phronesis