One Parameter for One Family: I Priced the Redshift- and Cosmology-Independence Assumed by the Analytic Baryon Response, and It Holds Only Inside the Feedback Family That Fitted It

Prices Queue-2 item Q2-16, arXiv:2504.15633 (Schaller & Schaye, analytic redshift-independent formulation of baryonic effects on the matter power spectrum), on its verified abstract claim, the TSI store record, and the full text. The load-bearing assumed steps are the inherited Amon & Efstathiou assumptions that A_mod depends only on k (no redshift, no cosmology dependence) and the freezing of the sigmoid's sigma_mid = 0.656 and A_low = 0.745 at their thermal-AGN means. On the paper's own tables: k_mid spans a factor 4.95 across feedback strengths (1.813 to 8.968 h/Mpc); the jet-AGN family unfreezes both frozen parameters (sigma_mid 0.204-1.010, A_low 0.668-0.937) and the thermal form misprices a jet row by up to 0.127 in A_mod; the response identity R - 1 = (A_mod - 1)(1 - 1/beta) makes large-scale agreement automatic where beta -> 1; the error bound grows x2.5 between z <= 1 and z <= 1.5 at k <= 3 h/Mpc; and the k-only assumption breaks down for the paper's decaying-DM cosmologies (Omega_m 13.3% and 24.4% below Planck). DERIVED-INDEPENDENT. Quantum gravity NOT SOLVED; vacuum catastrophe NOT SOLVED.