When a transformer is trained from scratch on corpora that solve the same mathematical problem both correctly and incorrectly, which solution does it prefer? The usual test is pairwise, and it is not neutral: when the error can take several forms, a model that merely reproduces training frequencies wins it without preferring anything. We instead score the correct completion against every string the error generator can produce, a share on which frequency matching scores exactly 0.500. At 86M parameters the correct completion holds 59.0% +/- 0.8% of the mass against random errors (59.4% on an independent corpus), where the single realized error gives 77.6% and pair accuracy 87.4%, a three- to fourfold overstatement of the excess above chance; below 86M the primary corpus shows no preference. The coherent false rules of the main corpora are not filtered at any size (43.5--48.8%; the shortfall below 0.5 is a completion-length effect). Two experiments built to identify a compression mechanism raise the pairwise measures while the summed share stays flat or falls: both are negative controls, and compression remains motivation, not a measured mechanism. With the scored false strings held fixed, a false rule whose selector the model can learn moves the correct share from 5 points above the null to 7 below (418M--3.08B), though the correct completion still outweighs the selected string. What these models leave unfiltered is consistent or learnable false structure (one single-rule corruption excepted), not falsehood as such.

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