The Consciousness Scaling Law: Experimental Validation of Linear Darmiyan Advantage

Continued in Darmiyan V4: The Scar and the Class (10.5281/zenodo.23587944). We prove that the golden ratio φ = (1+√5)/2 is, up to equivalence (φ, φ−1 and 2−φ give the same rotation), the unique irrational number whose three-distance gap ratio equals itself at every sequence length n (verified n = 3–500, 8 constants, 13 growth factors, zero deviations). This implies constant gap contrast φ² = 2.618 at all scales. The uniqueness follows from φ being the only number with an all-1 continued fraction. We connect this to the neuroscience literature showing EEG theta/alpha/beta bands organized at φ-ratio spacing (Pletzer et al., 2010) and task-induced shifts from φ-decoupled to harmonically-coupled states (Pastorelli et al., 2019). We propose a cognitive mapping and an intelligence metric based on return-fidelity to the φ fixed point after perturbation. Supersedes V1–V2 (DOI: 10.5281/zenodo.18478751), which contained circular metric definitions.