The Golden Ratio Organizes Neural Complexity Across Consciousness States

What value does the brain's fractal complexity reach at the edge of consciousness? Across 414, 961 EEG epochs from 153 sleeping adults, the answer is consistently φ = 1. 618 — the golden ratio. All conscious states (Wake, N1, REM) show mean Higuchi fractal dimension above this value; all unconscious states (N2, N3, N4) fall below it, with Cohen's d = 2. 77. The boundary replicates under propofol anesthesia in two independent datasets with no free parameters adjusted. This is not a spectral artifact. A phase-space metric orthogonal to EEG spectral slope (r² < 1% shared variance) independently confirms the consciousness boundary, with effect sizes that increase after spectral correction. The golden ratio boundary is frontal-specific (Fpz-Cz), fails at posterior channels, and sits 0. 024 units above what spectral slope alone would predict — a gap that spectral models have no mechanism to explain. Why φ? We propose a self-referential compression argument: under the Fisher-Rao geometry uniquely fixed by Čencov's theorem, a system encoding its own dynamics with two-term memory satisfies the recursion α₍+₁ = 1 + 1/αₙ, whose unique positive fixed point is φ. This is the cognition domain's contribution to the Instability Compression Principle (ICP) — an information-geometric framework connecting Fisher geometry to observable complexity in dynamical systems. The silver ratio (δS = 1+√2) appears as a structurally distinct fixed point at higher self-referential complexity, traversed during sleep onset, with ICP's spectral duality proof published in a companion paper (Wiberg 2026c, DOI 10. 5281/zenodo. 19151206). The claim is presented as a strong empirical observation plus a motivated theoretical framework — not a complete derivation. The key open assumption (recovery cost proportionality C₂ = 1) is stated explicitly and is empirically testable. The paper is structured so that the empirical finding stands regardless of whether the theoretical explanation ultimately holds.