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

Version 4. 4 — Preprint Update (June 2026) This version constitutes the full post-Blueprint canonical preprint of the MELVcore framework, integrating current mathematical refinements confirmed through the MAIES Assessment Series (May 2026) and editorial improvements for publication readiness. Major additions relative to v2. 9. 0 (Sessions 1–33): Mathematical and conceptual — βₙorm normalisation (β/ (1+β) ∈ (0, 1) ), completing the mutualism theorem proof universally across all domains — φ dynamics equation (Equation 7) with full compound gating, asymmetry confirmation (α = 0. 01 ≪ δ = 0. 10), and D (t) definition — Saturation form (Equation 1a) with η = 0. 9300 recovered via BI-NLS (RSE < 0. 05) across 810 ABM V2. 2 runs — Signed coordinate system (i = r − rc) and double-well potential landscape V (x) with historical bridge to Blueprint for Harmony formulation — Dungbeetle diagnostic clarified as binary gate-closure classification (βₛervice crosses 0. 50 on node removal), distinct from continuous Sᵥ vulnerability ranking — DeepSeek attribution corrected: axiomatic self-consistency validation, not full equation reconstruction Structural additions — Section 1. 3: thermodynamics definition for non-specialist readers; fractal scale-invariance of R across ecological, institutional, and inter-state AI governance domains; architectural guardrail sentence — Section 1. 5 (new): core equations at a glance with plain-language glosses, introduced before ecological grounding — Section 3: Type 1/2/3 attribution on all equation headings; δ and D (t) definitions before Equation 7; Ω₋ᵥ notation explained; V (x) clarified as derived from MELV equations, not independently imposed — Appendix B (new): full symbol glossary, 21 symbols, written for interdisciplinary readers — Stream 2 bridging note clarifying R² = 0. 9248 (service coupling) versus i = 0. 9995 ± 0. 029 (threshold precision) — Abstract corrected: three Type 3 emergent discoveries (previously stated as two) ; min observed i (t) = 0. 2338 and η median = 0. 9300 now present in validation section Unchanged from v2. 9. 0 — Gateway threshold R = 0. 50 ± 0. 003 (p < 10⁻⁵⁰) — Cooperation theorem CI = 1. 0 at convergence — ESS invasion recovery 34/34 = 100% — 931 passing automated tests — Live deployment: web-production-e14d1. up. railway. app Cite as: Evans, L. W. (2026). MELVcore: A Thermodynamic Governance Kernel for Multi-Agent AI Systems (Version 4. 4). Zenodo. https: //doi. org/10. 5281/zenodo. 20577818