Structural Medicine v3.6: A Minimal Envelope-Mediated Model for Cross-Scale Structural Stabilization

Structural Medicine v3. 6 extends the framework from physical correspondence toward a minimal cross-scale coupling model linking fast neural oscillations and slow structural stabilization. Structural Medicine v3. 5 established a formal correspondence between adaptive control signals and transcranial alternating current stimulation (tACS), while identifying the cross-scale coupling problem — how fast neural oscillations (~40 Hz) influence slow structural instability (~0. 05 yr⁻¹) — as the central unresolved theoretical limitation. This work proposes a minimal envelope-mediated pathway: Fast oscillation→ Envelope-mediated coupling→ Slow structural stabilization The central hypothesis is that fast oscillatory modulation does not directly suppress structural instability. Instead, modulation acts through an envelope-mediated process that gradually alters slow structural dynamics. A Two-Layer Modulation Model (TLMM) is introduced: kₑff (t) = k₀ + α · ⟨E⟩_τ (t) where: kₑff (t) is effective structural stiffness α is the cross-scale coupling coefficient ⟨E⟩_τ (t) is the entrainment envelope averaged across the cross-scale time constant τc The framework formalizes four minimal components: Fast-to-slow envelope coupling Envelope-mediated suppression of R (t) A phase-lock threshold φcrit required for effective stabilization Finite temporal delay Δτ between modulation and structural response Four new falsifiable predictions are derived: τc dependence α proportionality φcrit stratification k–ε separability The model is intentionally minimal and avoids strong mechanistic overclaiming. Biological grounding is discussed through candidate pathways involving gamma-driven glial activation and synaptic long-term potentiation (LTP). Figures 1–4 provide synthetic demonstrations of: coupling emergence instability suppression phase-lock threshold behavior cross-scale temporal delay The framework converts the cross-scale coupling problem from an open conceptual gap into a testable theoretical structure.