Scale-Free Dynamics, Bridge-State Control, and a Seven-State Neural Architecture: Evidence from Cross-Frequency EEG Analysis [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 manuscript substantially overlaps the earlier draft in Zenodo record 18477273 and should not be counted as independent replication. Source outputs, hierarchical state labels and the bridge statistic require reconciliation; a universal seven-state architecture and causal control mechanism are not established. 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 and transition between spectral configurations? Here we report a hierarchical 7-state architecture in EEG spectral dynamics (N = 137, two independent datasets) governed by alpha-band gating and resonance quality (Q-factor) control. A bridge state with high betweenness centrality (bridge_index = 0.820, 95% CI [0.81, 0.86]) mediates transitions between two macro-regimes—harmonic (2:1 frequency ratios) and non-harmonic (~1.7:1 ratios)—via reversible Q-factor modulation with bidirectional symmetry (entry/exit ratio = 1.02, no hysteresis). Alpha power dominates bridge detection (AUC = 0.758), and Q at lag t−2 predicts subsequent regime membership (AUC = 0.687; Granger χ² = 16.8, p < 0.0001), establishing Q as a candidate control parameter. The non-harmonic regime's frequency ratios cluster near an irrational attractor (mean = 1.695, SD = 0.120); competitor analysis identifies 5/3 = 1.667 as the best point estimate, yet 83% of subjects show ratios closer to φ ≈ 1.618 than to 2:1 harmonics (p ≪ 0.001). Macro-regime separation is large (Cohen's d ≈ 2.90). Non-harmonic states exhibit distinct scale-free signatures: increased multifractal spectrum width (Cohen's d = 1.02) and power-law inter-event timing (α = 2.74), consistent with proximity to neural criticality. Eight robustness tests—including Ising model control and pipeline-aware surrogates (p = 0.006)—confirm that these patterns do not arise from generic criticality or methodological artifacts. Speculative extensions regarding ambient electromagnetic boundary conditions are explicitly separated from core empirical findings using three-level epistemic labeling, with quantitative falsification criteria (F1–F4). Mathematical background (Lucas identity L₄ = 7) is provided in the Appendix as post-hoc interpretation. Keywords: EEG state dynamics, cross-frequency coupling, neural criticality, alpha gating, gamma oscillations, spectral parameterization, bridge state, attractor dynamics, scale-free dynamics, fractal physiology