The Omandac Law of Collective Binding Resonance: A Candidate Universal Law with Zeroth Law Foundation (Λ₀ = π/6) — Complete 6/π Symmetry Across Quantum (Qubit), Neural (Izhikevich), and Information-Theoretic Substrates

Version 8. 0 Final Abstract The Omandac Law proposes that the geometric constant Ω = 6/π ≈ 1. 909859 governs collective binding transitions across substrates via shared Stuart-Landau universality class. This v8. 0 update introduces the Zeroth Law of Primal Individuation (Λ₀ = π/6 ≈ 0. 523599), establishing perfect mathematical reciprocity (Ω × Λ₀ = 1) between ontological distinction (separation of "parts") and collective binding (unity into coherent experience). This completes a four-layer ontology of reality: Zeroth Law: Primal distinction / individuation — the precondition for distinguishable degrees of freedom. Pillar 1: Matter — structure and objects. Pillar 2: Energy — change, transformation, and entropy. Pillar 3: Collective Binding Resonance (Ω) — integration into unified, qualia-rich states. Key Advancements Substrate Independence: Universality demonstrated across quantum (N=6 Lindblad Dicke qubits showing superradiant transition), neural (Izhikevich spiking networks), digital (N=96, 000 Nengo simulations with Einstein-inspired time-dilation scaling), and symbolic (WorldTree substrate folding arbitrary data sizes 10⁶ → 10¹⁰⁰ PB while respecting the Λ₀ distinction gate). First-Principles Derivations: Complete biophysical derivation of binding coordinate β = 17. 35 (from cortical current constants, amplification factor, and scale factor — no circularity). Four-method biological validation of 0. 45% instantaneous synaptic fraction. Statistical Rigor: 20-seed transfer entropy convergence confirming the Information-Action Identity (χTE → 1. 531 at N=200). N² scaling specificity diagnostics (residual curvature, PLV shape, finite-size correction) to distinguish true Dicke-class coherence. Empirical Pilot: N=5 EEG propofol dataset showing 17. 4% phase-locking collapse (p < 10⁻⁹², Cohen’s d = 1. 904). Quantum Teleportation Proof-of-Concept: Real Qiskit circuit demonstrating perfect state transfer (fidelity ≈ 1. 0) using Bell pair + measurement + correction, conceptually grounded in binding resonance. Methodological Innovation: Time-dilation throttling enabling N=96, 000 spiking simulations on commodity CPU, preserving coherent sparse firing vs. anesthetized burst collapse. Novelty and Significance This is the first framework to derive a specific geometric constant (Ω = 6/π) from quantum geometry, introduce its exact reciprocal (Λ₀ = π/6) as the Zeroth Law of distinction, and validate the complete two-sided coin (Ω × Λ₀ = 1) across quantum, biological, digital, and symbolic substrates. It provides first-principles derivations, falsifiability criteria, and scalable computational methods, offering a candidate universal law that bridges physics, information, and consciousness without reducing one to another. Priority Statement The mathematical derivation of Ω = 6/π and its mapping to the Information-Action Identity, together with the reciprocal Zeroth Law (Λ₀ = π/6), constitute the original discovery. This work is independent and solo-authored. Priority asserted as of the first preprint (February 24, 2026) under CC BY-NC-ND 4. 0. Keywords: Omandac Law, 6/π, π/6, Zeroth Law, collective binding resonance, Stuart-Landau universality, Dicke superradiance, neural binding, quantum teleportation, transfer entropy, Izhikevich, consciousness, phase-locking collapse, EEG, substrate independence Personal Keywords: Luke 19: 40 (Universal Substrates), Hu Tao / Son of Man (Transition of Life & Death), Proverbs (Wisdom 9: 10-12 & 25: 2), Revelation 20: 4-6 & Isaiah 65: 20 (Golden Age) Summary: Original discovery February 24, 2026. This Version 8. 0 (Feb 2026) adds the Zeroth Law foundation and completes the two-sided coin symmetry on February 28. Data Ethics: Clinical validation uses de-identified EEG datasets (OpenNeuro, Chennu 2016). All 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: Main PDF + supplementary notebooks/figures (Nengo rasters, quantum teleportation circuit, WorldTree substrate, EEG plots, qubit gap results). Note: With the mathematical unification of the Zeroth Law of Individuation (pi/6) and the Third Law of Binding (6/pi), the Impossible Gap is closed. We exit the age of stochastic noise and enter the Era of New Resonance, where Information is Substance, and Unity is a Universal Law