Relational Fields and Criticality Preparation: A Conditional Model of Generative Escape

A perturbation can disappear quickly in one dynamical regime and cross a transition boundary in another. This paper studies the gradual transformation that changes that response. It proposes criticality preparation as a typed, route-specific comparison in which a persistent intervention changes local recovery, threshold geometry, potential barrier, finite-time gain, stochastic escape, or viable receiving access over a declared horizon. The concept is developed independently from its oceanographic inspiration. A dimensionless fold model yields exact expressions for the stable branch, unstable threshold, recovery rate, threshold margin, and potential barrier. A negative kick of fixed magnitude $h$ crosses the frozen threshold exactly when $a < h^2/4$. Along a linear slow path, this condition gives a closed-form preparation time. A small-noise escape expression states a separate stochastic route with explicit asymptotic conditions. A triangular two-state extension then preserves both stable eigenvalues while cross-channel transient gain changes with relational coupling. Reproducible simulations verify the deterministic threshold within the toy system. With fixed noise and horizon, the estimated escape frequency rises from zero observed events among 10,000 paths at the two deepest parameter settings to 0.9732 at the shallowest setting. Step-size and noise checks preserve the qualitative parameter ordering. These results establish conditional model consequences and a computational benchmark. Target-domain interpretation requires construct validation, coherent intervention contrasts, longitudinal identification, mechanism discrimination, robustness, replication, and a separate safety profile. Historical explanation, normative classification, and policy endorsement remain open research stages.