The Collapse Inevitability Theorem: Below K_crit, Collapse is a Dynamical Necessity

This paper proves the Collapse Inevitability Theorem (CIT): when the coherence metric falls below the critical threshold K_crit ≈ 0.127, the evaluation update operator loses contractivity, coherence error grows under iteration, and collapse is a dynamical necessity — not a probabilistic risk. The distinction matters: a probabilistic framework treats collapse as an event that might happen; the CIT establishes it as a trajectory property. Below K_crit, a system is not at risk of collapse. It is collapsing. Only operator-level restructuring — Recursive Constraint Regulation (RCR) — can restore contractivity and escape the collapse trajectory. Empirically grounded in financial institution collapse data.