Context Codec: Rate-Distortion Optimization for Persistent LLM State

Stateful LLM systems must decide how much prior context to include ineach inference window. We formalize this as a rate-distortion (R-D)problem: minimizing token budget (rate) while maximizing BehavioralConsistency Score (BCS), a probe-based metric measuring how faithfullyencoded state reconstructs target operating behavior. Applying R-D theoryto a longitudinal personal AI assistant deployment, validated withsubject ≠ judge model separation (subject: claude-opus-4-6; judge:claude-sonnet-4-6), we find: (1) an R-D curve knee at ~992 tokens (BCSrising from 0.480 at zero context to 0.954 at the knee), above whichadditional tokens yield diminishing returns; (2) a Scalable VectorContext (SVC) layered encoding scheme at 518 tokens outperforms randomselection at 730 tokens by +0.10 BCS; (3) the structure advantagereplicates across 10 synthetic personas (knee detected in 10/10). Theseresults establish that compression structure rather than token countdetermines reconstruction quality in persistent LLM deployments.