The absorptivity formula put to the test: what passes at 95% confidence and what still fails

Version 11 of the approximate absorptivity formula in the flux theory of three bodies writes the eccentricity wall of note FR-TC-13 as a sharp step, which depends on the relative mass of the incoming body and on the energy of the pair. Fitted only to 939,000 planar scatterings with zero total angular momentum, it was subjected to a formal test at 95% confidence in the free falls of three mass sets, with critical values obtained by parametric bootstrap (200 replicas) and Holm correction. In the set 1-2-3, it passes both in the distribution of the final eccentricity (KS 0.020, critical 0.028) and in the escape fractions, the first set approved in full. The mass limit of the wall, fitted freely, is 0.93 times the reduced mass of the pair, in agreement with the direct measurement. In the sets 1-1-3 and 3-3-1, the formula fails in the shape and, in 3-3-1, also in the escape fraction of the heavy body (4.6% predicted against 6.3% measured). A cross-validation shows that these errors do not come from an excess of parameters, and they are of the same size as those obtained with the directly measured absorptivity. Separating measurement error from failure of the theory requires a more precise measurement in the heavy channels.