Continuity Under World Drift: A Law-Complete Theory of Semantic Survivability

This repository contains the paper Continuity Under World Drift: A Law-Complete Theory of Semantic Survivability, which develops a formal, dynamical theory of semantic continuity for task-bearing systems operating under sustained world drift and partial observability . The paper treats semantic survivability not as a question of performance, optimization, alignment, or interpretability, but as a structural constraint on whether task-relevant referential bindings can persist over time as the external world changes. Semantics is defined operationally: a representation is semantically valid to the extent that it continues to support correct task behavior under intervention, independent of inference correctness, reward optimization, or representational richness. A minimal system model is introduced with explicit state variables for: semantic alignment, semantic entropy induced by world drift, and finite repair capacity. Within this model, the paper proves that computational correctness alone cannot stabilize semantics under drift. A first-order semantic decay law is derived, shown to be robust to the choice of entropy proxy, and combined with structural limits imposed by intervention equivalence classes in the world. The central contribution is a necessary and sufficient survivability condition: semantic continuity over time is possible if and only if cumulative repair capacity dominates cumulative semantic entropy, scaled by the amount of intact semantic structure available at the outset. This condition is law-complete within the stated regime and excludes entire classes of systems regardless of architecture, training procedure, or objective function. The theory is explicitly falsifiable under bounded estimation and partial observability, admits a geometric phase-space interpretation, and makes no assumptions about human meaning, cognition, ethics, interpretability, or normative alignment. The result establishes a constraint on what semantic structures can persist under world drift, rather than proposing methods for improving system performance. This artifact is intended as a theoretical reference and constraint analysis, not as an algorithm, framework, or implementation guide.