The Phi Signature in Human Cognition v1.0

We test whether the golden-ratio band structure discovered in artificial embedding spaces (Azpiroz, 2026) reflects a property of knowledge integration itself. Using 4,482 trials from 106 participants solving 69 Dutch Compound Remote Associates Test (CRA) items with complete triads (3 hint words + solution; Stuyck et al., 2021/2022), embedded across 11 models from 5 providers, we compute the centroid of hint-word embeddings and its cosine distance to the solution. Central Result (Triple Convergence): BGE-base centroid distance = 0.3838, bootstrap 95% CI [0.3737, 0.3939], containing both 1/phi^2 = 0.3820 (delta = 0.002) and the Youden classification threshold from the companion paper (0.386, delta = 0.002). Three independent measurements — mathematics, English sentence classification, Dutch CRA cognition — converge within delta < 0.004. Study 1 (Cascade): d(Internal) < d(Noise) in 11/11 models (t = -5.978, p = 0.00014).Study 2 (Correlation): BGE-base r = -0.282, permutation p = 0.020; meta-analysis r = -0.085, p = 0.022.Study 3 (Bands): All 11 models replicate phi-power bands (BGE delta = 0.002).Study 4 (Ratios): Confidence ratio insight/analytic CI [1.546, 1.844] contains phi = 1.618. Theoretical synthesis: four independent research programs converge on the equation p^2 + p - 1 = 0 (Grigoryan 2025, Padilla 2026, Jaeger 2022, He 2025). Full code and data: https://github.com/kabuto1523/phi-cognition-experiment