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Flourishing as the Unique Dynamical Regime of Persistent Systems - On the Structural Necessity of Coherent Growth and the Pre-Collapse Signature
La Profílée establishes IR = R/(F·M·K) ≤ 1 as the unique admissible persistence law. This paper proves that Flourishing — the regime dR/dt 1 (collapse). This paper additionally identifies a non-obvious structural prediction: the Pre-Collapse Signature. Systems approaching IR = 1 from below exhibit a specific oscillatory pattern — alternating phases of growth and contraction — before structural collapse. This signature is structural, not contingent: it follows from the absence of reserve at IR near 1 and the fact that growth-induced R increases cannot be absorbed. The Pre-Collapse Signature is observable independently of the cause of collapse and provides a structural early-warning indicator.
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