When a Better Fit Does Not Identify New Physics : A Reproducible Case Study with D–T Reaction Data

A smaller least-squares residual does not, by itself, identify an additional physical mechanism. We develop a computational case study using 17 published deuterium–tritium reaction measurements and a fixed Bosch–Hale reference curve. An inverse-speed-shaped multiplier improves the full-sample fit, but its interpretation changes when normalization, reference shape, or the treatment of energy calibration is changed. A standard weighted-projection calculation makes this dependence explicit. Retrospective higher-to-lower energy prediction worsens from 1.66% to 2.99% mean absolute percentage error, while other prediction scores dependon the metric and parameter constraint. Analytic calibration derivatives show why an energy uncertainty applied to a tabulated astrophysical factor differs from one applied to a cross section before conversion. A freely adjustable energy scale and reference-energy stretch can exactly reproduce the multiplier direction locally. Synthetic examples distinguish statistical recovery of a coefficient from identification of its physical origin. The article and its supplementary data, code, and exercises form a self-contained resource for teaching the difference between fit, prediction, and identification. All numerical coefficient estimates are conditional regression diagnostics; the analysis neither measures an additional nuclear-loss channel nor revises an evaluated fusion rate.