This archive accompanies the corrected revision of "Certified Reductions of the Weight-6 Euler Sum S4, 2 (x) at Dyadic Arguments. " It supersedes the January 12, 2026 version, whose central claim has been withdrawn. The work studies the weight-6 Euler sum S4, 2 (x) = sum₍>=₁ H₍-₁ xⁿ / n⁵ at the dyadic arguments x = 1/2, 1/4, and -1/2. The first version reported exact closed forms at all three arguments in a 21-constant Ω2 basis, certified by residuals near 1e-95. Those relations are not exact: recomputed in an exactly evaluated basis, their residuals do not decrease as precision increases but plateau near 1e-98, the signature of an approximate integer relation rather than an exact identity. The 21-constant basis was both contaminated, by five Clausen constants at pi/3 that do not arise at dyadic arguments, and incomplete, omitting the single irreducible depth-2 generator of the weight-6 level-2 space. The corrected results, certified by the stronger criterion that the residual decreases without plateau as precision increases and the recovered coefficients are stable across precision levels, are: x = 1/2: an exact closed form in a corrected 13-element dyadic basis, with residual below 1e-500 at 500 digits. x = 1/4: a certified exact relation in a weight-6 depth-2 multiple-polylogarithm basis, with denominators dividing 108. This is not a reduction to independently known constants; it is contingent on un-reduced depth-2 dyadic multiple polylogarithms, including S4, 2 (-1/2). x = -1/2: open. No relation satisfying the certification criterion is found in the dyadic field tested at 550 digits; it is pinned only by the certified relation to x = 1/4. The archive provides the corrected basis definitions, certified coefficient vectors, and verification scripts that reproduce the residual-tracking certification, together with the corrected manuscript. The amortized constant-folding analysis and accelerator microbenchmark are retained, since they do not depend on which arguments admit exact reductions. All results are numerically certified to the stated precision and are not claimed as formal symbolic proofs.
Keenan Williams (Wed,) studied this question.