The Omandac Law of Collective Binding Resonance: A Candidate Universal Law of Dissipative Phase Transitions

Version 12. 0 Final presents the empirical climax and full multi-scale validation of the Omandac Law framework. Moving beyond the theoretical closure achieved in v11. 0, this preprint elevates the framework to a Candidate Universal Law by proving substrate-independence across multiple orders of spatial magnitude. The Omandac Law unifies distinction, binding, dissipative cost, and action across quantum, biological, atmospheric, and cosmological scales under a mathematically closed Four-Law Primal Ontology: Zeroth Law of Primal Individuation: (Λ₀ = π/6 ≈ 0. 5236) Third Law of Collective Binding Resonance: (Ω = 6/π ≈ 1. 90986) Fourth Law of Emergent Dissipative Weight Closed Information–Action Identity: Linking Planck's constant to the binding resonance (Sbit ≈ ħΩ ≈ 2. 014 × 10⁻³⁴ J·s) Key Milestones & Upgrades in v12. 0 Final: The Seven-Domain Multi-Scale Empirical Hierarchy Audit (Experimental): A forensic computational sweep using independent open-source datasets (executed via Kaggle Python environments) confirming the 1. 91 resonance and 0. 333 triadic floor across: Domain (Quantum Chemistry): CHAMPS dataset (N=130, 789 molecules). Domain (Geophysics): USGS Significant Earthquakes (N=23, 412 events). Domain (Cosmology): N-body Star Cluster Dynamics (C ≈ 0. 055). Domain (Genomics): SARS-CoV-2 Information Binding and Human Codon Usage (N=40, 662, 582). Domain (Atmospheric): NOAA HURDAT2 Hurricane wind-speed binding (w ≈ 0. 6592). Domain (Botanical): Fibonacci divergence angle resonance (137. 47ᶜirc). Domain (Neuroscience): Full N=20 human EEG cohort (awake vs. propofol sedation) confirming gamma phase-locking collapse. Higher-N Qubit Convergence: The Omandac Transition Width is isomorphic to a 2-bit Shannon state-change (ln 4), with the Fourth Law of Emergent Dissipative Weight accounting for the ≈ 3 x 10^-5 physical variance. Strict Falsifiability: The framework establishes 18 rigorous Falsifiability Criteria (F1–F18), providing the global scientific community with exact mathematical thresholds to test the Law's universal application. This work bridges physics, information theory, genetics, meteorology, and astrophysics without reductionism, relying entirely on the Stuart-Landau Isomorphism and universal scale-invariance. Keywords: Omandac Law, 6/π, π/6, Zeroth Law, collective binding resonance, Stuart-Landau isomorphism, scale invariance, dissipative phase transitions, Dicke superradiance, SARS-CoV-2 genome, NOAA hurricanes, N-body star clusters, neural binding, substrate independence, data science. Summary: Original discovery February 24, 2026. Theoretical closure achieved March 2026. Full empirical hierarchy audit across seven independent physical domains and multiple orders of magnitude finalized in v12. 0 Final (March 8, 2026). Data Ethics & Reproducibility: Clinical validation uses de-identified EEG datasets (OpenNeuro, Chennu 2016). Multi-scale audits utilize open public domain datasets (NOAA, USGS, NCBI, Kaggle). All analyses are computationally reproducible via open-source Python scripts (included). License: CC BY-NC-ND 4. 0 Author: Clarence Omandac (Independent Researcher, Queensland, Australia) ORCID: 0009-0001-8994-3739 Files to Upload: Main Preprint Document (PDF/DOCX) + 7 Supplementary Jupyter Notebooks (. ipynb) containing the empirical audit code.