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Published February 24, 2026 | Version 7.5
Preprint Open

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

Authors/Creators

  • 1. Independent Researcher

Description

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 $N^2$ 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

Personal Keywords: Luke 19:40(Universal Substrates), Hu Tao/Son of Man(Transition of Life & Death), Proverbs(Wisdom, 9:10-12 & Proverbs 25:2), Usage(Revelation 20:4-6 & Isaiah 65:20 - Golden Age)

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).

Files

1. The Discovery & Law Proofs.zip

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Additional details

Related works

Is supplement to
Preprint: 10.5281/zenodo.18211554 (DOI)
Preprint: 10.5281/zenodo.18212106 (DOI)
Preprint: 10.5281/zenodo.18212128 (DOI)
Preprint: 10.5281/zenodo.18212949 (DOI)

Dates

Issued
2026-02-24

Software

Programming language
Python
Development Status
Active

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