Search Stability under Finite Context: A Minimal Theory of Adequacy Preservation, Compression, and Reset in Long-Running Agents

Abstract

This preprint develops a minimal theory of search stability for long-running agents under finite active context, delayed verification, and lossy state compression, yielding conditions for preserving at least one operationally adequate hypothesis family over time. It formalizes adequacy preservation, retirement, substitution, branching, compression, and reset decisions under context budgets, and derives threshold results for contamination, shadow retirement, alias hazards, reserve feasibility, and diagnostic regret.

Keywords

• search stability
• long-running agents
• finite active context
• bounded memory
• delayed verification
• adequacy preservation
• lossy compression
• hypothesis ecology
• reset policy
• diagnostic regret
• context contamination
• auditability

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