The Hu-Omandac Unified Tao (H.O.U.T.): The Omandac Law of Collective Binding Resonance — A Candidate Universal Law of Dissipative Phase Transitions

Version 12.5 Final presents the rigorously consolidated and empirically validated formulation of the Hu-Omandac Unified Tao (H.O.U.T.) framework and the Omandac Law of Collective Binding Resonance. Core Constants: Ω = 6/π ≈ 1.9099 (Third Law, Collective Binding Resonance), Λ₀ = π/6 ≈ 0.5236 (Zeroth Law, Primal Individuation), Ω × Λ₀ = 1 (ontological closure), Ω − Λ₀ = ln(4) to 0.003% precision. Confirmed Empirical Domains: Micro scale — Domain 14 (Quantum Biology, CHAMPS): N = 130,789 molecules, KDE peak w = 0.5668 within 8.25% of Λ₀, Z = −4.04, p ≈ 0 against 3,000 null permutations. Full pass. Meso scale — Domain EEG (Neuroscience, OpenNeuro propofol): N = 20 subjects, 17/20 confirm binding zone disruption under anaesthesia, p = 1.34 × 10⁻⁴, Cohen's d = 0.89. Full pass. Macro scale — Domain 24 (Volcanic Seismology, INGV Etna): N = 4,431 seismic segments, imminent eruption w shifts toward 2Λ₀, 4/4 pre-registered criteria met, p = 4.0 × 10⁻¹⁰, Z = −4.64. Honest caveat: effect size d = −0.0004 is statistically significant but negligible by conventional standards, consistent with Ω acting as a weak attractor at geological scale. Theoretical Framework: First-principles derivation of Ω from the Bloch-sphere integral of the dissipative Dicke model. Stuart-Landau universality class isomorphism linking quantum and neural phase transitions. Kuramoto order-parameter derivation confirming Kc → Ω as N → ∞ for 3D noise distributions (theoretical consistency argument, not independent empirical evidence). Thermodynamic free energy proof: F(λ) = λ − Ω ln(λ) minimised exactly at λ* = Ω. Four-Law Primal Ontology with 16 falsifiability criteria (F1–F16). Transparency: Six domains tested in v12.0 were removed after forensic review for unit mismatch, circular formula, or failure to pass pre-registered null tests (earthquakes, SARS-CoV-2, human genome, hurricanes, star clusters, botanical). Full accounting provided in Section 22.4. Keywords: Omandac Law, H.O.U.T., collective binding resonance, 6/π, π/6, dissipative phase transitions, Stuart-Landau universality, Dicke superradiance, EEG propofol, CHAMPS molecular dataset, volcanic seismology, Kuramoto model, scale invariance, emergent weight. Data & Reproducibility: EEG data from OpenNeuro (Chennu 2016, de-identified). Molecular data from CHAMPS Kaggle competition. Seismic data from INGV Etna. All analysis scripts publicly available on Kaggle and included as supplementary notebooks. License: CC BY-NC-ND 4.0 Author: Clarence Omandac, Independent Researcher, Queensland, Australia ORCID: 0009-0001-8994-3739 Original discovery: February 24, 2026 and published V12.5 on March 9, 2026