Structural Medicine v3.2: Limitations of Fixed-Frequency Resonant Control in Non-Stationary Neurodegenerative Dynamics

This repository accompanies the preprint: Structural Medicine v3. 2: Limitations of Fixed-Frequency Resonant Control in Non-Stationary Neurodegenerative Dynamics Structural Medicine v3. 2 extends previous versions (v2. 0–v3. 1) by empirically testing the control hypothesis using ADNI-derived longitudinal cognitive trajectories. In earlier work, neurodegenerative instability was interpreted as a structural transition that could potentially be suppressed through resonant intervention tuned to intrinsic system frequencies. In this study, we test this hypothesis directly. Structural decay dynamics λ (t) are reconstructed from longitudinal MMSE trajectories and analyzed using power spectral density (PSD) to extract dominant frequencies (ωₚeak). Resonant control is then applied using these frequencies. The results show that: - Fixed-frequency resonant control does not consistently reduce structural instability- Both global and high-instability-region metrics indicate negligible or negative improvement (ΔR ≤ 0) - The dominant frequency structure of λ (t) is non-stationary and time-varying These findings reveal a fundamental limitation: neurodegenerative dynamics cannot be stabilized using a single global resonance. This establishes a critical distinction between: - Predictable instability (v2. 0–v3. 1) - Controllable instability (requires adaptive dynamics) The study motivates a shift toward time-dependent adaptive control: U (t) = A (t) sin (ω (t) t + φ (t) ) Included in this repository: - Full preprint (PDF) - Python figure generation script- Figure set (Fig1–Fig14) Figures are synthetic or derived for demonstration consistency, while statistical findings are based on ADNI-derived empirical analysis. Data source: Alzheimer’s Disease Neuroimaging Initiative (ADNI) https: //adni. loni. usc. edu This work provides a unified framework connecting early warning signals, structural dynamics, and the limits of control in neurodegenerative systems.