The baryogenesis problem is usually framed as the problem of explaining why the observable universe contains a nonzero matter excess after an early history in which particle and antiparticle degrees of freedom were both available. This paper reformulates that problem as a completion-locked asymmetry-survival problem. The relevant question is not only whether a microscopic mechanism can produce a charge bias, but whether a CP-odd charge distinction descends from a specified source datum, survives the production–washout–response channel chain, is recognized by the declared observable law, and is protected against post-hoc retuning of one stage of the chain. The paper proves a conditional structural closure theorem for baryogenesis claims formulated on a charge–survivor datum. The theorem sequence has a kernel-theoretic core. A descent theorem identifies when a charge asymmetry is a physical invariant of the specified source identity relation. A CP-invariant channel-erasure theorem shows that a CP-odd source distinction has zero image under any CP-invariant terminal channel. Applied to the completed production–washout–response chain, this gives a composed-channel erasure result. A survivor-quotient theorem then proves that a nonzero observed asymmetry is certified only by a nonzero survivor class of a CP-odd source distinction. A conditional baryogenesis closure theorem gives sufficient conditions for a nonzero normalized abundance, and a completion-locked non-retuning theorem shows that an operation preserving the source quotient, channel chain, survivor quotient, response law, normalization, and branch data cannot tune only one asymmetry reading while remaining inside the same locked datum. The theorem acts on the separated asymmetry ladder consisting of source, produced, survived, and observed asymmetries. These asymmetry levels are distinct unless the specified descent, channel, recognition, and normalization conditions identify them. Under the survivor package, a CP-odd charge distinction with nonzero source bias, nonzero survivor class, terminal recognition, and positive descended normalization yields a nonzero observed abundance. Under the CP-symmetric closure package, the same source-datum structure forces the recognized asymmetry to vanish. Residual or missing matter–antimatter asymmetry is therefore not an undefined failure mode. The closure theorem identifies its structural source: failed descent, CP-symmetric closure, charge-opening failure, washout erasure, response invisibility, incomplete recognition, normalization mismatch, branch misidentification, or source-space extension. Thus baryogenesis closure is formulated as a theorem of source-datum certification, survivor quotients, observable recognition, and normalization descent. As a companion to The Matter–Antimatter Asymmetry as a Charge–Survivor Datum: Survivor Quotients, Washout Channels, and Observable Recognition, this work proves the closure consequences for the charge–survivor datum identified there. The two papers form a source-datum/theorem pair. The companion paper defines the mathematical object underlying matter–antimatter asymmetry claims, separates source, produced, survived, and observed asymmetry levels, and establishes the corresponding descent, survivor, recognition, and verification framework. The present paper proves the conditional closure theorem for that datum, including CP-erasure criteria, survivor-quotient factorization, conditional baryogenesis closure, and completion-locked non-retuning. Together they place baryogenesis claims on explicit source data, production–washout–response structure, survivor quotients, observable recognition, normalization descent, branch certification, and common-source closure conditions. License note: Distributed under CC BY-NC-ND 4.0.
Salimah H. Meghani (Mon,) studied this question.