Deployment Survivability of Optimization Formalisms under Assumption Invalidation

This paper identifies a structural failure mode affecting optimization formalisms when they are deployed as executable constraints in irreversible systems. In such deployments, optimization outputs are causally binding on system-level state transitions whose effects cannot be fully reversed by further application of the same formalism. The central claim is that internal correctness guarantees—including convergence, robustness, generalization, and empirical performance—are insufficient to certify safe deployment once execution-enabling assumptions invalidate. The analysis distinguishes internal validity from external effect. Optimization procedures may remain mathematically correct relative to their specifications while inducing irreversible operational failure after ordinary assumption invalidation (e.g., distribution shift, precision degradation, coupling drift). This class of failures arises without error, mis-specification, or misalignment and is therefore orthogonal to existing AI safety frameworks. The paper introduces deployment survivability as a necessary external condition on admissible optimization deployment. A deployment is survivable only if, under plausible invalidation of execution-enabling assumptions, externally realized effects remain recoverable without requiring intervention beyond the optimization formalism itself. Survivability is a structural property of execution coupling, not a refinement of objectives or internal guarantees. A minimal descriptive normal form (ψ₀–ψ₃) is provided to classify withdrawal-induced failures, and the analysis demonstrates why robustness, out-of-distribution generalization, and alignment tools cannot certify against this failure axis. The contribution is additive and classificatory: it delineates when mathematically correct optimization systems should not be instantiated as causally binding mechanisms under irreversibility, while preserving their value as advisory or reversible tools.