Condensation Nuclei and Recoherence Failure Why Systems Fail to Recover When Conditions Appear Favourable

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