Baryogenesis as a Counting Problem: The Baryon Asymmetry Priced Term by Term

The baryon asymmetry of the universe is a single measured number with a precise price. From the Planck baryon density and the present photon density we derive the baryon-to-photon ratio eta_B = 6.12 x 10^-10 and the baryon yield Y_B = 8.69 x 10^-11, in agreement with the concordant cosmic microwave background and Big Bang nucleosynthesis value of about 6.1 x 10^-10. We recast the three Sakharov conditions as factors in a budget: an asymmetry produced per interaction, a fraction surviving washout, and an entropy dilution factor between production and the present day. For the standard electroweak route, the dimensionless charge-parity violating factor constructed from the Jarlskog invariant and the quark mass differences at a temperature of 100 GeV is 1.16 x 10^-19, giving a shortfall of 5.2 x 10^9, or 9.7 orders of magnitude, relative to the required asymmetry; even against an optimistic literature ceiling of 10^-18 the shortfall is 6.1 x 10^8, or 8.8 orders of magnitude. The electroweak route faces a second, independent deficit, because for the measured Higgs mass the electroweak transition is a smooth crossover rather than the strongly first-order transition required for departure from equilibrium. For thermal leptogenesis we evaluate the Davidson-Ibarra bound: the maximum charge-parity asymmetry at a lightest right-handed neutrino mass of 10^9 GeV is 9.9 x 10^-8, which can meet the required yield only with an efficiency factor of about 0.64; with a representative washout efficiency of 0.1 the required mass rises to about 6.4 x 10^9 GeV, and thermal production requires a reheating temperature at least of that order. No new mechanism is claimed. The result is a budget table in which each known mechanism is credited with what it can supply and charged with what the observation costs, so that the size of each gap is explicit.