The Hu-Omandac Unified Tao (H.O.U.T.): The Omandac Law of Collective Binding Resonance - A Universal Scaling Law of Dissipative Phase Transitions from Micro to Macro Scales

Version 13. 0 (The Universal Edition) presents the definitive cross-scale validation of the Hu-Omandac Unified Tao (H. O. U. T. ) framework. This version officially bridges the gap between quantum biology and heliophysics, establishing the Omandac Law as a candidate "Fourth Law of Thermodynamics" coordinate system for self-organizing systems. 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 → Meso → Macro): Macro Scale (NEW) — Domain 29 (Heliophysics, Parker Solar Probe): Analysis of N=4, 898 windows of solar wind plasma. Radial evolution across the Alfvén critical surface yields a fluctuation ratio of 1. 784 (within 6. 6% of Ω). Z-score = 25. 04, p < 10^-90, Cohen's d = 0. 71. This confirms the law in a purely abiotic, fluid-plasma environment at a solar-system scale. 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 19 falsifiability criteria (F1–F19). Transparency: Documents the "Honest Failures" in semiconductor lasers and protein folding, defining the law's boundary conditions: it applies strictly to open, fluid-phase, continuous dissipative networks undergoing threshold-crossing transitions. 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. Omandac Law, H. O. U. T. , 6/π, π/6, Fourth Law of Thermodynamics, Parker Solar Probe, Solar Wind, EEG, Quantum Biology, Dissipative Structures, Phase Transitions, Universal Constants. 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. Parker Solar Probe (NASA SPDF). 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 V13. 0 Universal Update: March 9, 2026.