Spectral Fingerprint Analysis: A Detailed Framework

We present a comprehensive, step-by-step framework for detecting “spectral finger‑prints” of new physics via deviations from the universal 1/E^2 suppression law. Our protocol encompasses: (i) a synthetic demonstration of changepoint detection methods; (ii) quantitative comparison of leading detection algorithms; (iii) a standardized cross-domain data‑conversion strategy; (iv) detailed uncertainty propagation and visualization; (v) parameter‑tuning heuristics; and (vi) a fully elaborated research plan for real‑world implementation on LIGO, collider, and optical datasets. This document serves as a turnkey reference for teams aiming to transform residual analyses into a precision discovery engine for BSM thresholds, symmetry‑breaking scales, and quantum‑gravity signatures.