Fathom: Coherence Spectrum Analysis - Hallucination as Concentration in Per-Layer Feature Coherence

New finding: The SHAPE of per-layer SAE feature coherence distributions discriminates hallucination better than any scalar summary (K, C, C_delta). Hallucination is not a depth shift — it is a coherence CONCENTRATION. Key results (n=200, Gemma-2-2B, TruthfulQA): Gini coefficient of per-layer coherence: d=+0.36, p=7.6e-7, AUC=0.685 (best single metric) 13/16 spectral shape metrics significant after Holm-Bonferroni correction Layer 11 is the fault epicenter in 63% of hallucinations (p=2.7e-12, t=7.45) 23/26 layers show significantly elevated coherence in hallucinated responses (p<0.05) Scalar depth (K): AUC=0.550, NOT significant — the mean destroys the signal Cognitive Autopsy (first per-layer fault localization): Layers 11+12 jointly account for 41% of all excess coherence in hallucinations Hallucinations concentrate coherence; correct responses distribute it Practical interventions: Best-of-N spectrum sampler: scores candidates by Cognitive Health Score (Gini + spread + early mass), improves on 100% of test prompts vs greedy Cognitive EKG: first real-time visualization of model cognition during generation Contents: 3 analysis scripts, 3 tool implementations (spectrum steerer, spectrum sampler, cognitive EKG), 5 result JSONs, 4 figures, findings document, OSF pre-registration. Related provisional patents: US 64/020,489 and US 64/021,113. Builds on Zenodo v10 (doi:10.5281/zenodo.19464572).