What question did this study set out to answer?

The central aim is to establish the Collapse Inevitability Theorem (CIT), which defines collapse as a dynamically required outcome below a certain threshold.

March 7, 2026Open Access

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

Key Points

The central aim is to establish the Collapse Inevitability Theorem (CIT), which defines collapse as a dynamically required outcome below a certain threshold.
Theoretical proof of CIT.
Analysis of financial institution collapse data.
Identification of the critical coherence metric threshold (K_crit).
Demonstration of Recursive Constraint Regulation (RCR) as a potential solution.
Collapse occurs when the coherence metric drops below K_crit ≈ 0.127.
Loss of contractivity leads to increasing coherence error.
Systems below K_crit are inevitably collapsing, not just at risk.

Abstract

This paper proves the Collapse Inevitability Theorem (CIT): when the coherence metric falls below the critical threshold Kcrit ≈ 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 Kcrit, 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.

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

Key Points

Abstract

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