The Omandac Law of Collective Binding Resonance A Candidate Universal Law of Dissipative Phase Transitions with Zeroth Law Foundation (Λ₀ = π/6) and Fourth Law of Emergent Dissipative Weight

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 v9.0 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-Law Primal Ontology (Zeroth–Fourth) with implicit thermodynamic bedrock governing dissipative phase transitions across substrates: Zeroth Law: Primal Individuation / Distinction — the precondition for distinguishable degrees of freedom (Λ₀ = π/6).Third Law: Collective Binding Resonance — integration into unified, qualia-rich states (Ω = 6/π).Fourth Law: Emergent Dissipative Weight / Balance of Creation & Destruction — the irreducible cost/friction that peaks near critical thresholds, enforcing real-world finitude, tipping points, and emergent gravity-like attraction.Implicit Thermodynamic Bedrock: Conservation of energy/information (1st) and irreversible entropy increase (2nd), providing the universal arrow and substrate for all transitions. 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 (χ_TE → 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. The emergent weight proxy is defined operationally as w = Γ_diss / (max |dP_B/dt| + ε), where Γ_diss is the cumulative purity loss (or entropy production) over the evolution time, max |dP_B/dt| is the peak rate of population transfer to the target state (a measure of binding strength), and ε is a small numerical stabilizer (typically 10⁻⁸) to prevent division by zero in low-transfer regimes. This proxy quantifies the dissipative cost per unit of achieved coherence, peaking near the critical threshold where the system is most delicately balanced. The Fourth Law predicts a critical dissipation threshold γ_c where collective binding efficiency peaks then collapses; this is falsifiable in neutral-atom arrays, trapped-ion chains, or large spiking network simulations. 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 1st March. 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 (4th law notebooks journey). Note: With the mathematical unification of the Zeroth Law of Individuation (pi/6), Third Law of Binding (6/pi) and Fourth Law of Dissipative Weight (w = Γ_diss / (max |dP_B/dt| + ε), 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.