MELVcore: A Thermodynamic Governance Kernel for Multi-Agent AI Systems

Version 4.6.0 — D8 Closure + C6 Resolution (July 2026) Major additions relative to v4.5.6: Equation 3 gate hierarchy — C6 resolved (July 2026). Whether ABM V2.2's silent omission of Equation 3's sigmoid quorum gate was intentional supersession or an unflagged oversight was flagged for author determination. Resolved via a dedicated three-arm ABM comparison ("C6 Arm A", 1,377 seed-paired runs), independently adjudicated by a fresh instance (Grok) under the anti-circularity protocol: (1) the canonical gate H(1-Bxi_inf) is statistically indistinguishable from V2.2's actually-committed gate (0 outcome-bucket flips across 243 seed-paired runs); (2) V2.1's apparent gate-active bimodality (Hartigan dip p~0, n=405) is substantially a clip artifact of the [0.05, 3.00] observation bounds - interior-trimmed, the signal is statistically indistinguishable from unimodal (p~0.77-0.78, independently re-verified against the raw dataset). The V2.1 gate is retired; the canonical gate is locked as the framework's sole gate for all forward work. No published dataset requires correction: outcome classifications (COOP/COMP/THRESH) in the V2.1 deposit are unaffected - only the final_i bimodality claim as originally stated is superseded, reflecting an active, evolving research programme rather than a formal erratum. See Section 6.2 for the full summary. T2 threshold surface coefficient - D8 closed-form derivation, closing D6 (July 2026). a(i0,eta) = eta * atanh[(i0-1)/(i0*eta)], derived by inverting the master equation's own i(t)=1 outcome-classification boundary. Matches all three previously-measured constants (0.242 bee-flower, 0.630 human institutional, 0.092 AI multi-agent) to within 0.7% and correctly predicts all five previously-unresolved threshold entries as exceeding the original 1,083-run sweep's ceiling. Independently adjudicated twice (Claude Sonnet + Grok, both July 2026) and confirmed by the receiving instance. See Section 3.6 and Addendum D8. Also this version: C7 opened, then a proposed resolution reviewed and rejected, not yet closed. While preparing this release, a consistency check against the C6 resolution found that the Dungbeetle keystone-node diagnostic (Section 3.6) defines its formal threshold and its "closing the cooperative gate" claim in terms of the now-retired sigmoid gate's tau=0.5 cutoff. A single-instance proposed derivation (Grok) claimed this could be re-anchored because beta_service is "mathematically distinct" from the canonical gate's beta - on review this claim contradicts the framework's own Section 2.3, which defines beta = beta_physical x beta_temporal x beta_service (beta_service is a factor of beta, not a distinct quantity). The proposal was not incorporated. Tau=0.5 is retained as an explicitly labeled theoretical placeholder - kept for continuity with existing implementation and prior ABM results, not derived - pending a dedicated multi-AI (MAIES) investigation rather than a single-instance fix. Both passages inSection 3.6 and a Section 6.1 limitation entry state this plainly; readers should not treat the Dungbeetle threshold's connection to gate closure as a derived or current claim about the canonical gate. Companion file included in this deposit: "The MELV Framework - What Has Changed and Why" (Version 4.9), a plain-language companion document covering the same D8/C6/C7 material for non-mathematical readers. Independently citable on ResearchGate, DOI: 10.13140/RG.2.2.17524.10880. Author: Laurence W. Evans | ORCID 0009-0001-0963-1840 | Cape Town, South Africa Cite as: Evans, L.W. (2026). MELVcore: A Thermodynamic Governance Kernel for Multi-Agent AI Systems (v4.5.6). Zenodo. https://doi.org/10.5281/zenodo.20907725