Finite-Budget Epistemic Search under Bounded Observation

This paper develops a finite-budget framework for action under bounded observation. Rather than requiring full reconstruction of a hidden environment, it asks when limited structural evidence is sufficient to justify a decision. A cumulative structural arsenal maps finite traces to compatible hidden completions and partitions the observable space into an action core, where completions support a common near-optimal action; an action frontier, where covered completions remain operationally incompatible; and an epistemic residual, where the current representation is inadequate. The paper proves non-asymptotic, solver-agnostic guarantees for action without full identification. Calibrated completion coverage and robust action consensus yield explicit regret bounds, while an overlap-times-action-conflict lower bound shows that observational uncertainty becomes an unavoidable decision barrier precisely when observationally overlapping hidden structures prescribe incompatible actions. It also introduces action-sufficient structural skeletons, analyzes the decision value and costs of cumulative memory, and derives an action-critical time, a maximal actionable scale, and robustness conditions under structural drift. The framework extends finite-budget structural identifiability from diagnosis to action. Its central claim is that local structural evidence can justify rational action without uniquely identifying the hidden structure, provided that the remaining uncertainty is operationally coherent.