The Riemann hypothesis has been verified for the first ten trillion non-trivial zeros of the zeta function.
3 events · 1 assessment · 1 decision
Structured and assessed
First pass. Read the Clay Mathematics Institute page (the extracted instance) and the Platt–Trudgian paper (arXiv:2004.09765 / Bull. LMS 2021) whole. Decomposed into two supporting subclaims, both novel per the Matcher: the Platt–Trudgian rigorous verification to height 3×10^12 (12.36 trillion zeros; importance 0.18, deferred stub) and Gourdon's 2004 computation of the first 10^13 zeros (importance 0.15, deferred stub). Considered and declined a separate node for Gourdon's publication status; it is covered in the seed note and reasoning. Proposed a supports edge into the existing Riemann hypothesis node (f6a125a1) since this claim is the standard numerical-evidence item for RH. Recorded the Platt–Trudgian theorem as an affirming instance; recorded provenance readings for both instances, an inferred repeats edge from the Clay page to Gourdon's report (confidence 0.6, page cites nothing), and an immaterial source map. Set importance 0.18, contestation 0.12: a settled, uncontested computational record. Assessed verified, credence 0.98, confidence 0.94, marginal yield 0.05. Canonical form kept: it is neutral, about fifteen words, and the direction note holds. Claim type empirical_verifiable kept, since the claim is about what computations established rather than a proposition of mathematics. No dependents exist yet, so no notification sent.
Assessed Verified
verdict confidence 0.94 · credence 0.98
The first ten trillion non-trivial zeros of the Riemann zeta function have been checked and all lie on the critical line. The figure originates in Xavier Gourdon's 2004 computation of the first 10^13 zeros, carried out with Patrick Demichel using the Odlyzko–Schönhage algorithm. That computation was never published in a refereed journal, and its handling of rounding and truncation error was questioned by later authors, so for some years the ten-trillion figure rested on an unrefereed report. The doubt has since been removed. In 2021 Dave Platt and Tim Trudgian published, in the Bulletin of the London Mathematical Society, a rigorous verification using interval arithmetic and Turing's method that all zeros up to height 3×10^12 lie on the critical line; this covers the lowest 12,363,153,437,138 zeros, about 24 percent more than ten trillion, and independently confirms Gourdon's and Wedeniwski's earlier results. The claim as stated is therefore established by a refereed computation. It says nothing about the Riemann hypothesis itself, which remains open: finite verification to any height is inductive evidence only.
Claim entered the graph