When the Neutrinos Leave: Decoupling History and the Threshold for Primordial Black Hole Formation

Building on S. McCormick's result that free-streaming neutrinos raise the threshold for primordial black hole formation (doi:10.5281/zenodo.23808375), this paper asks what sets the way the effect fades when the neutrinos decouple gradually. The neutrino collision operator is read exactly as a cut between what is kept and what streams. All of its non-normality, (1/8)||[L,L*]||^2 = kappa^2 k^2/3, lies on the single link between density and flux. With separate rates for flux and shear it is k^2 kappa1^2/3 + (4k^2/15)(kappa2 - kappa1)^2. The weight across the cut equals the radiation sound speed. McCormick's public code is then run on two cases outside his paper, with their predictions and kill lines written down before the runs. A broad profile that collapses near eps = 7-9 keeps the same share of the neutrino effect as a Gaussian that collapses near eps = 4, or less (G = 0.181 and 0.045 against 0.190 and 0.063), so the clock that sets the effect is not the collapse time. A steeper decoupling history, kappa ~ eps^-6, gives G = 0.317 +- 0.004 at eps_dec = 2, against 0.431 for the standard history, so how the neutrinos leave matters, not only when. The memory of the kept sector, with one weight fitted to McCormick's curve, predicted 0.25 for that history before the run (0.071 from the measurement, inside the 0.08 kill line; one point out of sample). The first maximum of linear theory and a sharp exceptional-point wall fail on McCormick's own curve; a diffusive-escape law and a history-blind rule fail on the new runs. Four further tests are stated: the e+e- annihilation control, shear against flux collision rates, independence of R_nu, and which mean of the group rates sets the decoupling temperature. Every claim is graded inline (derived, computed, measured, fit, proposed). Every script is printed with its output in the appendix. Files: the paper as PDF (paper, proofs, scripts and outputs in one file) and HTML; a zip with every script, run log, result file, figure source, the pre-registration and the working reports. Prepared with AI assistance (Claude, Anthropic): the ideas and direction are the author's; the computation, drafting and checking were done with AI tools.