The φ-Organized Brain: Scale-Free Dynamics, Bridge-State Control, and a Seven-State Neural Architecture [Unfinished working draft]

UNFINISHED WORKING DRAFT — Author status notice, 26 October 2026

This manuscript is an unfinished, exploratory working draft. Its analyses and interpretations remain subject to source verification, reproducibility checks and substantive revision. Claims of validation, universality or mechanism in the original manuscript should be treated as provisional rather than established conclusions.

Outstanding work: This draft substantially overlaps the EEG analysis in Zenodo record 18560751 and should not be counted as independent replication. Source outputs, state definitions and the bridge statistic require reconciliation. The proposed seven-state, special-ratio and field-access interpretations remain unestablished.

The original deposited file is retained for provenance. This notice updates the record status; it does not certify completion of a new analysis.

Original description (historical; subject to the notice above)

How do neural systems organize information across frequency bands? This paper reports that EEG spectral states cluster into two macro-regimes with a stable bridge state mediating transitions (bridge_score = 0.820, N = 137 subjects across two datasets). Frequency ratios cluster in a φ-adjacent basin (mean = 1.695): competitor analysis shows 5/3 = 1.667 as best point estimate, yet 83% of subjects show ratios closer to φ than to 2:1 harmonics (p ≪ 0.001). We interpret φ as a basin attractor—a 'container' region in ratio space—not an exact fixed point.

The mathematical foundation connects the golden ratio to integer structure through the Lucas identity φ⁴ + φ⁻⁴ = 7 = L₄. This identity is presented as a compact algebraic encoding of the observed 7-state topology, not a claimed causal mechanism.

Empirical analysis of EEG data (GAMEEMO N=28; PhysioNet EEGMMIDB N=109) reveals a natural 7-state decomposition: two macro-regimes (φ-like and harmonic) with a bridge state showing high betweenness centrality. Model selection: flat clustering optimizes at k=6; hierarchical topology yields 7 interpretable states with superior transition predictability.

Eight robustness tests address reviewer concerns: Ising model control confirms φ does not emerge from generic criticality; the 13/8 Hz alpha-theta boundary ranks in top 0.8% of possible ratios (p < 0.01); pipeline-aware surrogates yield p = 0.006; cross-dataset replication confirms stability.

The framework generates falsifiable predictions (F1-F4, T1-T4) testable through EEG-magnetometer coupling and shielded-room experiments. Speculative extensions (Schumann reference hypothesis, translational applications) are explicitly separated from core empirical findings.

Code and analysis scripts: https://github.com/ExeqTer91/phi-organized-brain