This working paper presents the Geodesic Entropy Collapse Engine™ (GECE™), the mathematical architecture of identity resolution under constraint in Human Locomotor Dynamics™ (HLD™) and Combat Engineering™. Filed as Matrix Concepts Claim III, the GECE™ is the computational framework that implements the governing equation of HLD™: Outcome = argmin(Objective | Identity + Constraints + Environment). The GECE™ computes the geodesic path along which a fighter's identity collapses under constraint toward its confirmed elemental rank. The paper presents the formal definition, the structural isomorphism with AlphaFold, the geodesic path properties, and five deployment domains.