Baryogenesis as a quantum-error-correction residue The matter–antimatter asymmetry as the undetectable-fault rate of a finite QEC substrate

Why is the observable universe made of matter and not antimatter, when the two are produced

in equal amounts and annihilate to radiation? Sixty years after Sakharov framed the problem,

no mechanism derives the measured baryon-to-photon ratio η ≡nB/nγ ≈6 ×10−10 from first

principles: grand-unified and standard electroweak baryogenesis are excluded or fine-tuned, and

leptogenesis is viable only with free high-scale parameters. We present a derivation of the

magnitude of η from a single, parameter-free assumption: that the early universe is a finite

quantum error-correcting (QEC) code, the self-dual [8,4,4] extended Hamming code, whose

boot-time pruning is the physical origin of the photon bath. In this picture the asymmetry is

not a fine-tuned initial excess but an error rate: almost all matter and antimatter are erased

back into photons, and the surviving baryon number is the residue of logical faults that bypass

the code’s stabilizers undetected. The minimum-weight undetectable fault has weight equal to

the code distance d= 4, giving a suppression α4

0; a colour-singlet selection over the 14 weight-4

logical channels contributes a branching 3/14; against the Planck value 6.12(4) ×10−10 — a 0.9σ match with no free parameters once the fine-

structure constant α0 is fixed. The three Sakharov conditions map onto three intrinsic features

of the substrate. We are explicit about scope: the magnitude is a genuine parameter-free

prediction; the lepton-number-to-baryon conversion reproduces the standard sphaleron factor

28/79 on the substrate’s particle content; and the absolute sign of the asymmetry remains, as in

all of physics, anchored in a discrete convention — here a geometric phase of the code — rather

than a fully derived dynamical quantity. All numerical claims are reproduced by self-asserting

scripts.