The gauge coupling ratios, withdrawn

This post covers an archived paper, and the peculiarity of this one is that its central result was correct. The paper was archived anyway, because the correctness was luck and the method was wrong, and this archive’s rule is that method is what gets judged.

What the paper claimed

The gauge coupling ratios are among the most tempting targets in particle physics: the three Standard Model couplings, if you extrapolate them, run toward each other at high energy, and their ratios at unification are a number that theories claim to predict. The paper derived the ratios from the category’s data: the levels 4, 3 and 6, combined with the Z6 grading, produce relations among the couplings that, at the right scale, match the extrapolated values reasonably well.

Why it was archived

The audit’s finding was a distinction the paper had blurred, and it is the same distinction that shows up throughout the corrections series. A derivation computes a number from inputs that are fixed before the number is known. The paper’s computation of the coupling ratios required a choice of normalisation scale and a choice of how the category’s levels map to the gauge group’s normalisations, and in each case the choice was made to land on the observed ratios. The relations are real: the levels do constrain the couplings. But the framework had several constraint sets available, and the one used was the one that worked.

The technical verdict, from the selection-principles document the audit produced: the category data provides zero independent constraints on the coupling normalisations beyond what the Standard Model itself already encodes. The match was the Standard Model agreeing with itself, transcribed through the category’s notation.

The lesson, which is about no-go’s

There is a subtlety in why this paper is archived rather than corrected: the result it most resembles, the Z6 congruence, survives in Paper 8, and the difference between them is worth stating precisely. The congruence is a necessary condition verified across every field, and its paper claims exactly that. The coupling paper took a necessary-condition-style match and claimed it as a derivation, which is the move that fails. The underlying relations survive in the framework as facts about compatibility. The claim that the category explains the couplings does not survive anywhere.

The archive’s rule, restated: a correct result reached by fitting is not a derivation, and keeping it labelled as one would poison the ledger for every claim that is a derivation. Paper 8’s trace-ratio downgrade, from theorem to standard GUT normalisation, is the same lesson in miniature, and both entries exist so that the next tempting ratio gets classified correctly on the first pass. The next archived paper failed in an even more upstream way: it built on a paper that was already dead.

The archive closes with one more corpse, and its cause of death is a dependency nobody checked: Paper 7a, baryogenesis.