What question did this study set out to answer?

The research aims to advance the understanding of collective neural dynamics through the Omandac Law and validate it using EEG data.

February 28, 2026Open Access

Topological Phase Transitions in Collective Neural Dynamics: Formal Derivation of the Ω = 6/π Coupling Constant, Biophysical Derivation of β = 17.30, and Multi-Subject EEG Validation (N=5) of the Omandac Law

Key Points

The research aims to advance the understanding of collective neural dynamics through the Omandac Law and validate it using EEG data.
Formal derivation of critical coupling constant Ω = 6/π.
Biophysical derivation of β = 17.30 based on synaptic activation.
EEG studies validating findings across multiple subjects.
Analysis using proprietary Omandac-Binding-Search algorithm.
Validation of Ω = 6/π as a key constant for neural binding.
Observed 17.4% phase-locking collapse in the gamma band under propofol.
Successful test of N² superradiant scaling on EEG gamma power.

Abstract

This v7. 0 preprint advances the Omandac Law of Collective Binding Resonance, proposing Ω = 6/π ≈ 1. 9099 as the critical coupling constant for dissipative U (1) phase transitions governing neural binding via shared Stuart-Landau universality class with Dicke superradiance. All theoretical gaps are closed through independent derivations and simulations: Biophysical derivation of β = 17. 30 from sparse gamma synaptic activation (fraction ≈ 0. 45%, yielding Iᵣecurrent ≈ 21. 14 μA/cm², total gamma drive ≈ 30. 14 μA/cm², matching literature consensus 21–41 μA/cm²) ; N² superradiant scaling test on EEG gamma power (αcoherent = 1. 894 ± 0. 016 awake vs 1. 818 ± 0. 078 sedated, Δα = 0. 076) ; Recurrent coupling rescue in heterogeneous Izhikevich network (rate recovers to 41. 7 Hz at gₑe = 1. 0 from 38. 8 Hz uncoupled, χ rises to 1. 38+) ; Transfer entropy confirmation of the Information-Action Identity (χTE = 1. 505, 3. 1% match to predicted 1. 553 at β = 17. 30). EEG pilot (N=4 multi-subject) shows 17. 4% phase-locking collapse in the 30–45 Hz binding zone under propofol (p = 5. 27 × 10⁻⁹³, Cohen’s d = 1. 904). The THz–Hz scaling gap is reframed as topological (frequency substrate-dependent). All simulation code, OBS algorithm, and falsifiability criteria are provided for replication. Statement of Priority: The mathematical derivation of the 6/π constant and its mapping to the 0. 0417 ms⁻¹ attractor constitutes the original discovery of the Omandac Law. This work is independent and solo-authored. All rights to the theoretical nomenclature and associated Scaling Manifold are asserted under CC BY-NC-ND 4. 0 as of first preprint publication (Feb 2026). 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. Keywords: Omandac Law, collective binding resonance, 6/π, Stuart-Landau universality, Dicke model, 41. 7 Hz gamma, sparse synaptic activation, transfer entropy, N² scaling, EEG propofol, phase-locking collapse, Izhikevich, spiking networks, consciousness License: CC BY-NC-ND 4. 0 Files to Upload: The DOCX + PDF export + supplementary notebooks/figures (e. g. , gap scripts, EEG plots).

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