ERG Across All Energies: The Running Dew-Point a₀(z) and the Cosmic-Time Renormalisation-Group Flow

Paper XIII of the Entropy-Response Gravity (Bipartite KMS Gravity) programme. Derives and tests the running MOND acceleration scale a_0(z) = cH(z)/sqrt(4 pi^2 - 1) as a cosmic-time renormalisation-group flow, operationalising the dew-point analogy: the e-fold span N_total(z) shrinks monotonically from today to zero at the Planck endpoint. Decisive falsifier: a 3-sigma null BTFR evolution in a mass-restricted JWST sample at z=1-2. Version 3 note: the e-fold convention is corrected to the dimensionless N_total(z) = ln[(c^2/a_0(z))/ell_P] = ln[r_*(z)/ell_P] (the earlier ln[(c/a_0(z))/ell_P] carried units s/m and was unit-system dependent), shifting the present-day value from 122.59 to 142.12 and n_s from 0.9653 to 0.9741 (-0.1 sigma ACT DR6, +2.2 sigma Planck, stated openly), consistent with Paper X v2. The full N_total(z) table is recomputed (constant +19.52 shift) and fig3_efolds regenerated. The running dew-point a_0(z) results, the GS23 BTFR z-evolution test, and all falsifiers are unchanged. Pre-registered at OSF 10.17605/OSF.IO/5HCGF.