Structural Medicine v1.8: Asymmetric Structural Potential and Irreversible Collapse Dynamics in Disease Progression

This work introduces a structural dynamical framework for disease progression based on longitudinal cognitive data. Conventional models typically describe disease progression as monotonic decline. In contrast, we demonstrate that progression is governed by a two-stage structural process: variance instability → directional collapse bias → symmetry breaking. Using ADNI longitudinal data, we define structural persistence F(t) and derive the time-dependent structural decay rate λ(t). We show that: • The distribution and variance of λ(t) broaden with disease progression, indicating increasing dynamical instability • Variance peaks provide a weak but non-random anticipatory signal prior to diagnostic conversion • Directional asymmetry A exhibits a sharp transition at the LMCI stage, indicating a shift toward collapse-biased dynamics To explain these phenomena, we introduce an asymmetric structural potential V(λ), where recovery-like and collapse-like directions have different effective curvature. A stage-dependent flattening factor represents reduction of restoring forces, producing a symmetry-breaking transition. Dynamic simulations governed by:dλ/dt = −dV/dλ + η(t)reproduce the observed drift toward irreversible collapse-like states. These results suggest that disease progression is not governed by decay magnitude alone, but by deformation of an underlying structural potential. This framework provides a minimal, testable, and cross-domain extension of Structural Medicine, consistent with the broader Integrated Structural Generation Theory (IGS). The model is intentionally minimal and directly falsifiable through longitudinal variance and asymmetry measurements.