Fathom: Coherence Spectrum Analysis, Cognitive Autopsy, and Spectrum-Guided Generation

New in this version: Coherence Spectrum Analysis: The SHAPE of per-layer SAE coherence distributions discriminates hallucination (Gini AUC=0.685, n=200). 13/16 metrics significant after Holm-Bonferroni. Scalar depth K is at chance. Cognitive Autopsy: First per-layer fault localization. Layer 11 is the fault epicenter in 63%% of hallucinations (p=2.7e-12). Layers 11+12 account for 41%% of all excess coherence. Cognitive EKG: First real-time visualization of model cognition during generation (26-layer coherence waterfall per token). Best-of-N Spectrum Sampler: Scores candidate completions by Cognitive Health Score (Gini + spread + early mass). Improves on 100%% of test prompts vs greedy decoding. Model: Gemma-2-2B. Data: TruthfulQA (n=200 paired correct/hallucinated). All analysis scripts, tools, results, and figures included. Related patents: US 64/020,489, US 64/021,113.