Verified Heuristic Memory Management for Long-Context Language Models

This manuscript proposes Verified Heuristic Memory Management (VHM), a theoretical framework for governing memory in long-context language models. Candidate token spans receive dynamic eligibility weights based on salience, recurrence, utility, consistency, freshness, and evidence. A bounded multi-step verification protocol then determines whether each span should become candidate, shadow, active, pinned, stale, superseded, or rejected memory. Promoted memories are organized in a parent–child memory tree in which high-level claims and constraints retain evidence paths to raw context. The framework also records supersession relations so that newer decisions can invalidate older memories without deleting their historical evidence. The manuscript formulates the Memory Promotion Problem and establishes structural properties including bounded online verification cost, optimal top-K selection under equal costs, staged reduction of false promotion probability, preservation of evidence-path invariants, supersession-aware retrieval, and convergence of dynamic eligibility weights under stable feedback. This work is a theoretical proposal and does not report empirical benchmark results. Its purpose is to introduce a verifiable memory lifecycle above attention, retrieval, prompt compression, and cache management.