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This paper articulates an axiomatized structural framework for analyzing irreversible industrial state transitions in capital-intensive systems. While traditional industrial entry models are grounded in optimization under rational expectations and equilibrium adjustment, sectors characterized by high sunk costs and infrastructural rigidity often exhibit threshold effects and asymmetric recovery dynamics that challenge smooth marginal analysis. To formalize these features, the study introduces a Gate-based feasibility operator $G(X_t) \in \{0, 1\}$, defined over a structured state vector incorporating capital intensity, cost structure, infrastructural coupling, and exogenous constraints. Viability holds if and only if predefined structural threshold conditions are satisfied. Rather than modeling continuation as the outcome of continuous maximization, the framework evaluates whether necessary feasibility conditions are met at a given state, generating a discrete partition of the state space into PASS, HOLD, EXIT, and FAIL regions. The model integrates three dynamic components: a feasibility margin $\Phi_t$ measuring structural distance from critical thresholds; a transition dominance parameter $\Lambda_t$ evaluating the sustainability of value-generating dynamics under perturbations; and a hysteresis variable $H_t$ embedding path dependence and irreversible collapse persistence directly into the transition mechanism. By unifying threshold adjudication and hysteresis within an operator-based structure, the framework extends industrial organization theory toward a complexity-consistent representation of entry and exit dynamics. Although motivated by contemporary energy--compute sectors, the formal structure is industry-agnostic and applicable to any regime characterized by large fixed costs, capital indivisibilities, and constrained adaptability. The present version (v1) establishes the complete theoretical architecture; subsequent versions may incorporate empirical extensions within the same structural framework.