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The Mathematical Foundations of Displacement Dynamics: Ground States, Attractor Geometry, and the Formal Structure of Return

Rincón, D. · 2026 · Zenodo

This is the record, not the paper. The work itself is the deposit on Zenodo, under the DOI below. What follows is its abstract, as deposited.

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.

displacement framework · Lyapunov stability · Riemannian geometry · Morse theory · information geometry · attractor dynamics · ground state · mathematical physics

Read the deposit on Zenodo →doi 10.5281/zenodo.20406541

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