AbstractSystems regularly fail to recover from disruption even when the perturbation has been removed and conditionsappear favourable for restoration. This paper proposes that recoherence failure is not a unitary phenomenonbut a probability chain with independently identifiable failure points. Drawing on the physics ofheterogeneous nucleation — where phase transitions require a condensation nucleus, not merely favourablethermodynamic conditions — we formalise the Recoherence Probability Chain:α = P(A) × P(D|A) × P(C|A,D) × η(Φ)where P(A) is the accessibility of a viable attractor (formalised via Arrhenius barrier theory), P(D|A) theprobability the system detects that attractor, P(C|A,D) the probability of successful coupling, and η(Φ) thesystem’s coherence velocity — its capacity to coherently deploy regulatory resources toward the transition.We deploy this chain across three empirical domains — cellular and molecular biology, agricultural soilsystems, and forest ecosystem recovery — demonstrating that each α component can fail independently,producing observationally identical outcomes (persistent decoherence) from structurally distinct causes.Counterfactual historical tests (Aral Sea desiccation, coral reef phase shifts) confirm the framework’sretrospective diagnostic power. The framework resolves a persistent confusion in resilience science: theconflation of ‘insufficient support’ with structural inability to recohere. It derives from and extends the ρ/Carchitecture established in SIP-CORE-01. The internal structure of the decohered state — distinguishingprotective, bifurcated, disordered, and terminal decoherence regimes — is developed in the companion paperSIP-EP-04.Keywords: recoherence failure, nucleation theory, multiple stable states, hysteresis, phase transition, ecologicalhomeostasis, coherence-decoherence-recoherence, Arrhenius barrier, reaction-diffusion, Allee effect
Smith et al. (Wed,) studied this question.