V.T191 — Sound Horizon from τ-Native Inputs

Sound horizon r_s = 143.18 Mpc from τ-native inputs using ch45 holonomy matter fraction. At −2.66% (−26588 ppm) from Planck 147.09±0.26 Mpc. The deficit traces to ω_b being 1.2% below Planck, propagating through the baryon loading R_b into the sound speed integral.