Belief-MVCC: A Coherence and Transaction Layer for Shared Agent Memory

Abstract

We present a coherent, transactional, semantic shared-memory kernel through which specialised AI cores read and write while staying consistent. The design combines belief revision (AGM; Darwiche–Pearl; Konieczny–Pino Pérez), distributed-systems consistency (causal+, RedBlue, BSP) and database transactions with bitemporality and provenance, applied to meaning rather than to bytes. Its residual contribution is a semantic, belief-level MVCC with a free-text merge algebra, specified and machine-checked in TLA⁺ (Semantic Strict-Serializability up to a Merge Algebra; 790,936 states, 7 invariants), together with six empirical bench stages reproducible at zero API cost on local open-source models. Concurrent work approaches neighbouring parts of this space from other directions and is discussed in the related-work section. Version 2 — changes from v1 (2026-07-25). A systematic source-verification pass (all 158 citation sites read against their sources; quotations checked against full texts) led to the following corrections. The only file replaced is the paper PDF; no empirical results or proofs changed. Three quotations that could not be located in the cited works (at four sites) were replaced with verbatim source wording or rewritten as our own inference: Yu et al. 2026 (abstract, section 1, conclusion), ByteRover (section 2), Lin et al. survey (multicore section). Bibliography corrected and completed: the survey arXiv:2604.16548 restored to its published title and full author list; one article re-attributed to its actual venue (Biometrika 105(2), 2018); a truncated subtitle restored (Abadi 2012); one title and its author list completed (Maril et al. 2001); full author lists added where they had been abbreviated; one web-only source now carries URL, publication date and a web-archive locator. The +6.9 reweighting repair now carries an explicit scope note (a two-item margin; direction robust across every basis computed, magnitude not estimable at n=29). Characterisations of neighbouring work tightened to source-verifiable wording (GEM, Semantic Consensus, Token Coherence, the data-processing-inequality result, machine unlearning); one deployment claim not locatable in its source replaced by benchmark-backed wording. Regulatory framing sharpened: GDPR Art. 17 grounds erasure and Art. 5(2) demonstrability; EU AI Act Art. 12 scoped to high-risk systems (Regulation (EU) 2024/1689). Version 3 — changes from v2 (2026-08-07). This version corrects how quotations from arXiv:2603.10062 are attributed, and pins every multi-version arXiv reference. No empirical results, proofs or model-checking figures changed. The cited preprint exists in two versions whose wording differs at the passage this paper relies on. Version 2 of this record quoted wording that appears only in the superseded v1 ("the largest conceptual gap is consistency", "an analogous notion"). This version quotes wording that is identical in both versions ("the most pressing open challenge is multi-agent memory consistency", from the abstract), and additionally quotes the current v2 verbatim ("agent memory systems face an analogous challenge, yet no equivalent formalism exists"). Twelve references to arXiv preprints that exist in more than one version now carry the version they are quoted from (for example arXiv:2603.10062v2, arXiv:2604.16548v2, arXiv:2503.04800v3), so the quotations remain verifiable if those preprints are revised again. One phrase in the introduction that is our own formulation no longer appears in quotation marks, where its position next to an attributed quotation could suggest it was a citation.