Mathematical Appendix G & J
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Appendix G — Boundedness & Non-Oscillation Formal proof that Φ(t) governed by dΦ/dt = r · λ · γ · Φ · (1 − Φ / Φ_max) is: bounded on (0, Φ_max) monotonic toward Φ_max globally stable Explicit statement that oscillations require sign-flipping λ or γ and therefore falsify the emergent regime. Appendix J — Structural Intensity & Jitter-Before-Snap Definition of structural intensity: K(t) = λ · γ · Φ(t) Formal condition for the jitter-before-snap signature: dK/dt > 0 while d²Φ/dt² < 0 Interpretable as early-warning instability prior to phase transition or collapse.
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2026-01-11
