Directed Interventions Near Bistable Coordination Boundaries: A Coarse-Grained Potential Model of Basin Loss, Noise-Assisted Escape, and Conditional Structural Deepening

Abstract

A signed intervention can tilt a bistable landscape, while a structural action can change its geometry. This paper separates these effects in a declared quartic stochastic model. Its identifiable quadratic coefficient is κ = aδ; separating a from δ requires external calibration. The adverse deterministic fold threshold is u_fold(δ) = 2(aδ)^(3/2) / (3√(3c)). The quartic barrier and fold scalings are established consequences, not novelty claims. The model is sharpened with an invariant bound for subfold forcing from the negative equilibrium, an exact rectangular-pulse duration boundary, and an outcome-specific structural comparison that orders first-hitting probabilities beyond the Kramers regime. Exact first-passage boundary-value problems replace an unsupported universal stochastic threshold. Physical double-well and microbial experiments supply realizations and measurement alternatives; their units, noise, outcomes and protocols differ from the synthetic illustration. The remaining DFG contribution candidate is an independently calibrated link from Paper I's load transient to joint changes in potential geometry and intervention response. Papers I-II do not imply this link. Four held-out tests specify predictions, rivals and measurable adverse results. Synthetic checks verify equations and implementations, while empirical validity of the coordination mapping remains unestablished. Note on Version 2.0: this version revises the registered v1.0, titled "The Intervention Paradox: Why Direct Governance Near Criticality Fails" (about 5,400 to 8,400 words). The paradox framing is replaced by a declared quartic stochastic model that separates signed tilting interventions from structural geometry changes, established barrier and fold results are marked as such, and a universal stochastic threshold is replaced by exact first-passage problems. The supplement records 13 of 13 conditional mathematical checks passed and 21 of 21 final-page visual checks; no new domain experiment was run. Files: the v2.0 manuscript and a supplement archive with verification material, a manifest and SHA-256 checksums. Series Paper III of the Governance Geometry Theory (GGT) papers within the author's Deficit-Fractal Governance (DFG) framework.