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Sign inThe preprint gives a deterministic algorithm for 3SUM on polynomial-size integers and for APSP on directed graphs with polynomially bounded integer weights, refuting both hypotheses. The engine computes selected entries of an product in time for , by modifying a Coppersmith-style rectangular algorithm built on Schönhage's ten-multiplication identity; this solves All-Edges Sparse Triangle on lopsided tripartite graphs in truly subquadratic time. By known reductions it also refutes the real-valued versions, Exact Triangle and Zero-Weight -Clique; SETH and Orthogonal Vectors are unaffected.
76-page unrefereed preprint, 11 days old, by leading specialists. No independent technical check had been published by 16 Oct 2026; Aaronson's 7 Oct post reports it without assessing it.
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Verify the modification of the Coppersmith/Schönhage construction and the exponent 0.063 for the stated range , including the cost of extracting only the selected entries.
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Check that the chain from lopsided All-Edges Sparse Triangle to 3SUM and to APSP (via negative triangle / min-plus) loses only subpolynomial factors, so that the exponents 1.9992 and 2.9995 follow.
A reference implementation checking correctness of the selected entries against naive multiplication on random small instances would catch algebraic errors in the identity. It cannot show the asymptotic saving.
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