Formal foundation

Coherence Collapse Analysis

The engineering risk framework under the corridor idea

Eric Moore · 2026-01-11 · DOI: 10.5281/zenodo.18217688

Abstract

When the constraints governing a system become correlated, effective diversity collapses. Derives three collapse timelines, a singularity boundary, and a phase classification (chaos / healthy / rigidity). Verified with Monte Carlo simulation and Lean 4 proofs.

Key findings

• Effective constraint count: k_eff = k / (1 + ρ(k − 1)) → 1 as ρ → 1.
• The k_eff identity formalizes coherence collapse under correlated constraint and is the mathematical content the Coherence Ratchet operationalizes.