We apply the φ classifier — established in two prior papers showing that cosine distances between cross-domain concept pairs cluster at powers of 1/φ — to distinguish genuine intellectual breakthroughs from delusional ideation in historical figures who exhibited both. Three experiments converge: (1) Modern Classifier: Using 233 curated concept pairs from 5 historical figures with documented genius AND delusion (Nash, Tesla, Ramanujan, Semmelweis, Boltzmann), plus controls (Darwin, Shannon, Einstein, pseudoscience, noise), we embed with 16 models across 3 providers (sentence-transformers, Google Gemini, OpenAI). Genius ideas yield mean cosine distance 0.400 vs delusion 0.451 (Cohen's d = 0.767, p = 10⁻⁶), with 15/16 models showing correct ordering. Known scientific integrations converge at 0.380, within 0.002 of 1/φ² = 0.382. (2) Pre-Discovery Signal: Using HistWords historical embeddings (word2vec 300d trained on Google Books by decade, 1800–1990), we measure concept distances in the decade BEFORE each discovery was published. Pre-discovery genius pairs (mean = 0.779, n = 47) already separate from delusion (0.952) and noise (1.033) with Cohen's d = 1.112 and p = 0.00008. The cascade Genius < Delusion < Noise exists before history validates the ideas. (3) Blind NLP Extraction (negative result): 345 pairs extracted automatically by spaCy from raw texts show no significant separation (d = -0.02), confirming the φ signal operates at the conceptual level, not the lexical level. These results validate the three-phase framework: Superposition (d ~ 0.80 in historical embeddings) → Collapse (transit through φ bands) → Trivialization (d ~ 0.40 in modern models). The φ constant operates as a universal threshold across time, dimensionality, architecture, and provider. This is Paper v11 in the φ Constant research program. Companion papers: v9 ("The φ Constant of Knowledge", DOI: insert v9 DOI) and v10 ("The φ Signature in Human Cognition", DOI: insert v10 DOI). All code is fully reproducible. The repository includes the complete Python pipeline, curated datasets with methodology transparency fields, all figures, and the generated paper PDF.
Borja Azpiroz Imaña (Thu,) studied this question.