Structural Medicine v1.7: Variance Instability and Directional Collapse Bias in Time-dependent Structural Dynamics

This work presents Structural Medicine v1.7, an extension of the Integrated Structural Generation (IGS) framework toward predictive modeling of disease progression using time-dependent structural dynamics. The central contribution is the introduction of two complementary concepts derived from the time-dependent structural decay rate λ(t): Variance instability Directional asymmetry of structural fluctuation While previous versions established that structural decay is not constant but fluctuates over time, v1.7 demonstrates that these fluctuations are not random in structure. Instead, disease progression follows a two-stage dynamic process: Emergence of variance instability in λ(t) Transition toward collapse-biased directional asymmetry Using longitudinal ADNI-derived cognitive trajectories, structural persistence F(t) is estimated from normalized MMSE values, and local decay rates λ(t) are computed. The results show that: The variance of λ(t) increases systematically across diagnostic severity Peak variance of λ(t) occurs before diagnostic conversion in approximately 65% of observed cases The average lead time of variance peaks is approximately 12 months (median ≈ 6 months) Directional asymmetry shifts toward collapse-biased values in later diagnostic stages, particularly LMCI and AD Under stricter longitudinal criteria, the LMCI collapse-biased pattern remains robust These findings suggest that structural disease progression is not driven by monotonic decay alone, but by the emergence of instability in fluctuation structure, followed by directional bias toward collapse. Importantly, negative values of λ(t) are interpreted not as contradictions, but as transient recovery-like fluctuations or compensatory dynamics within a stochastic structural system. This work establishes a minimal, testable, and data-driven framework linking: variance instability → directional collapse bias → clinical transition and provides a foundation for early detection and predictive structural medicine. The ADNI dataset is not redistributed and must be obtained independently.