The Fiducial Density Buys the Shift: I Moved the Assumed Cosmology Behind the Lyα Points in a Background-Level Hubble-Tension Test, and the Higher H₀ Moved With It

Prices Queue-2 item Q2-01, arXiv:2505.24743 (Manoharan, PEDE/GOHDE at background level), on its verified abstract claim and the TSI store record. The load-bearing step is the assumed fiducial cosmology behind the BAO Lyman-alpha H(z) points at z ~ 2.3: at background level the implied H0 is the measured H(2.3) divided by E(2.3; Omega_m), and moving the fiducial density from 0.30 to 0.25 raises the implied H0 by 8.60% (to 0.35 lowers it 6.84%), with sensitivity d ln H0/dOmega_m = -1.5215 at z = 2.3, zero at z = 0; the transverse side agrees at +4.96%. The higher-H0 preference on including the points is fiducial-denominated. INCREMENTAL. Quantum gravity NOT SOLVED; vacuum catastrophe NOT SOLVED.