Karimov & Alekberli — Unified Constructibility Field and Survival Theory - Spatial Criticality, Hazard Dynamics, and Lifecycle Stability in Neural Learning Systems

We present a unified theoretical framework combining spatial constructibility field dynamics (OP6b) with survival-based collapse prediction (OP7) into a single field-theoretic lifecycle model for neural learning systems under deployment stress. Previous Constructibility papers established collapse boundaries, early warning dynamics, proxy monitoring, recovery theory, and survival-theoretic hazard estimation; all prior formulations were fundamentally global, representing collapse risk by scalar observables. The present work introduces a spatially resolved constructibility field formalism in which collapse emerges locally and propagates through correlated subsystems. We define a local constructibility stress field derived from localized causal entropy divergence and introduce an emergent order parameter governing constructibility degradation. The resulting dynamics admit a stochastic Landau–Ginzburg formulation with spatial coupling, critical slowing down, and an effective renormalization-scale structure within a phenomenological one-loop framework. We derive a local hazard field whose spatial integral recovers the global survival hazard of OP7, unifying phase-transition dynamics and time-to-failure theory within a common mathematical structure. The framework yields: (i) local collapse nucleation theory, (ii) spatial hazard propagation, (iii) correlation-length-based lifetime prediction, (iv) intervention operators as field perturbations, and (v) scale-dependent constructibility dynamics via renormalization flow. These results transform constructibility monitoring from a global alarm mechanism into a spatial lifecycle field theory for adaptive AI systems.