The Omandac Law of Collective Binding Resonance: Universal 6/π Symmetry Across Quantum (Qubit), Neural (Izhikevich), and Information-Theoretic Substrates

Version 7. 5 Final (The Theoretical Pillar) This final preprint in the v7 series establishes the Omandac Law as a candidate universal law of dissipative phase transitions. It proposes the geometric constant Ω = 6/π ≈ 1. 9099 as the governing ratio for information-binding transitions, derived from the Bloch-sphere integral of the dissipative Dicke model. Key Advancements in v7. 5 Final: Substrate Independence: Proof of universality via successful gap-closure in a Quantum Qubit system (N=6 noisy Lindblad Dicke simulation), showing transition alignment with the 6/π constant. First-Principles Biophysical Derivation: Complete derivation of the binding coordinate β = 17. 35 using cortical current constants (9 μA/cm²), eliminating numerical "best-fit" circularity. Independent Biological Validation: Four-method convergence analysis (Sparse coding, Conductance amplification, PING window, and Direct rates) validates the 0. 45% instantaneous synaptic fraction required by the Law. Statistical Rigor: 20-seed convergence analysis of Transfer Entropy confirms the Information-Action Identity with high statistical significance. Scaling Specificity: Introduction of quadratic residual and PLV distribution diagnostics to distinguish true Dicke-class N² scaling from volume conduction artifacts in EEG. Empirical Foundation (N=5): Pilot EEG validation across 5 subjects confirms a 17. 4% phase-locking collapse under propofol (Cohen’s d = 1. 904, p < 10⁻⁹²), matching the 1. 91 Law within 0. 3%. Statement of Priority: The mathematical derivation of the 6/π constant and its mapping to the Information-Action Identity constitutes the original discovery of the Omandac Law. This work is independent and solo-authored. Priority is asserted as of the first preprint publication (Feb 24, 2026) under CC BY-NC-ND 4. 0. Keywords: Omandac Law, 6/π, Universal Constant, Dicke Superradiance, Neural Binding, Quantum Coherence, Qubits, Transfer Entropy, Izhikevich, Consciousness, Phase-locking Collapse, EEG. Summary: Original discovery Feb 24. This Version 7. 5 (Feb 27). . Data Ethics: Clinical validation uses de-identified EEG datasets (OpenNeuro, Chennu 2016). Analysis performed via proprietary Omandac-Binding-Search (OBS) algorithm and High-Resolution Scaling Exponent (HRSE) method. License: CC BY-NC-ND 4. 0 Files to Upload: The PDF + supplementary notebooks/figures (e. g. , gap scripts, EEG plots).