Mathematical performance depends on how a language model receives information, uses generated text and submits an answer. We study these dependencies through paired comparisons that separate submission requirements, draft reuse and candidate availability. On 65 development problems, an instruction permitting continued derivation produced no valid final answers in 390 short-output calls; a single-line submission instruction produced 390 format-valid outputs, including 389 parseable answers. Under the fixed submission protocol, 198 problems with failed initial submissions were answered correctly in 9.09p of cases with the question alone, 33.84p with its draft, 46.46p with candidates, and 59.60p with both. Drafts added 13.13 percentage points with candidates fixed, and candidates added 25.76 points with drafts fixed; both effects were significant after Holm correction and were subadditive on the accuracy scale. Retaining a trailing excerpt outperformed retaining a leading excerpt of similar average length by 10.10 points Holm-adjusted p 0.027. A second completion model showed the same directions of input effects on the fixed materials. In a cohort with parseable initial submissions, candidates added no correct answers when the previous draft was supplied, but added 27 points when it was absent. These results establish a conditional value of generated text: a failed submission can leave useful material, whose contribution depends on what else is supplied and what is retained.

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