Poincar\'e Meets Bellman: Revisable Memory, Operational Quotients, and Evidence-Supported Learning in Changing Environments

תקציר מקורי באנגליתarXiv:2512.05990v2 Announce Type: replace Abstract: Memory consolidation determines both what a learner can do now and which changes remain implementable later. We develop a finite-model synthesis of operational state abstraction and optimal control under the stability-evidence-revision (SER) framework. ``Poincar\'e meets Bellman'' names two complementary roles: qualitative dynamics identifies reusable action-response structure, and dynamic programming prices acquisition, retention, reuse, merging, and forgetting. Recurrence enters separately through the timing and value of future demands. We distinguish active quotient merging from historical information erasure, characterize exact repair by zero-error functional coding and causal migration, and derive a Bellman recursion over the joint l