A 256-step certificate for Turán's pure power-sum constant
We give an exact-input certificate for the upper bound C_42 <= 0.6888863712 in the pure power-sum problem. The construction refines the step profiles of Griego, Röhrig and Plata to 256 middle blocks, without changing their coefficient-cancellation mechanism. It improves the strongest public proposal located in our 22 October 2026 audit, 0.688970, by 0.0000836288. An unmodified public interval checker and a separately written Arb checker verify the strict finite inequalities. The asymptotic implication is proved in the note; no explicit finite threshold, optimality, human peer review or…
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