Abstract The observed baryon-to-photon ratio ηB = (6.12 ± 0.04) × 10−10 (Planck 2018)has remained unexplained within the Standard Model despite satisfying the three Sakharov conditions. Here we derive ηB from first principles within Array Cosmologyusing zero free parameters: ηB =J (6 − 6Kknot + Znoise)/(MW /ΛQCD)^2 = 6.120 × 10−10 (0.002% error)where J, Kknot, Znoise, MW , and ΛQCD are all derived from the five-axiom set {12, π, γ1, ln 2, φ} in companion papers with no free parameters. Every term has a transparent physical interpretation: J encodes CP violation, the factor (6−6Kknot+ Znoise) encodes the six baryon-rendering channels corrected by knot binding cost and vacuum Landauer friction and (MW /ΛQCD)^2 encodes the electroweak-to-QCD scale projection. Independent verification against BBN constraints (6.097 × 10−10) yields 0.38% agreement