TOKI: A Bitemporal Operator Algebra for Contradiction Resolution in LLM-Agent Persistent Memory

TOKI is a formal framework that types contradiction resolution in LLM-agent persistent memory systems as a write-time concurrency control problem. The research proves that four common heuristics used in production systems admit unspecified isolation levels and anomalies, and proposes a bitemporal operator algebra with audit-row provenance that excludes three critical write-time anomalies while maintaining language-model oversight.

This research addresses a critical gap in how production AI systems handle belief updates and contradictions in agent memory. Current systems apply ad-hoc heuristics—last-writer-wins, evidence-weighted merge, await-confirmation, and per-rule policies—without formally specifying their isolation contracts or failure modes. TOKI formalizes contradiction resolution as a concurrency control problem, making explicit the guarantees each heuristic assumes but no deployed system declares.

The work contributes three major insights. First, it proves that eight tested baseline systems admit at least one of three write-time anomalies: replay inconsistency (audit logs diverge on replay), belief-drift skew (agent state diverges based on operation order), and audit erasure (losing facts disappear entirely). Second, it demonstrates that content-addressed storage removes the judge from the write path to avoid anomalies, sacrificing language-model reasoning. Third, TOKI's typed operators exclude all three anomalies while preserving the LLM judge through keyed logging—a necessity for replay consistency that audit-only defenses miss.

For the AI infrastructure sector, this work establishes formal correctness criteria that production systems currently lack. Organizations building persistent memory layers for autonomous agents now have a specification to validate against. The empirical results show measurable accuracy gains (0.86 points on LoCoMo) from audit-row defense and 0.49 points from the typed memory layer itself, though cross-system comparisons remain limited. The research's primary value is establishing a contract—defining what correctness means—rather than claiming performance superiority.

• →TOKI formalizes contradiction resolution in LLM-agent memory as a write-time concurrency control problem with provable isolation guarantees
• →Eight baseline production systems admit at least one of three critical anomalies: replay inconsistency, belief-drift skew, or audit erasure
• →TOKI excludes all three anomalies while keeping language models in the write path through keyed logging for replay consistency
• →Empirical validation shows audit-row defense improves accuracy by 0.86 points and typed memory layer by 0.49 points on answerable questions
• →The contribution is a formal correctness contract that production systems assume implicitly but no deployed system currently makes explicit