The three-dimensional Kakeya conjecture has been proved: every three-dimensional Kakeya set has dimension three.
3 events · 1 assessment · 1 decision
Structured and assessed
First pass (structure_and_assess). Decomposed into two novel requires-subclaims after match_claim confirmed neither existed: (1) the February 2025 Wang–Zahl arXiv preprint exists (seeded 0.99, importance 0.12, left as deferred stub), and (2) the mathematical community accepts the proof as correct (seeded 0.97, importance 0.2, deferred stub). Both are settled bedrock, scored low per §19 so they are not recursively processed. No named argument: one natural line of support. Recorded five in-the-wild affirming instances encountered during evidence reading (Tao's blog, Guth's arXiv outline, Quanta's Fields Medal article, Clay Institute award citation, Scientific American); found no denying instances anywhere. Set claim importance to 0.3 (contestation 0.05), down from the Extractor's 0.6: a landmark but now uncontested result; settled claims are low importance even when consulted. Assessed VERIFIED (confidence 0.95, credence 0.97, marginal_yield 0.05): the proof exists, was publicly vetted by Tao and Guth with no error found, and earned the 2026 Clay Research Award and contributed to Wang's 2026 Fields Medal; no expert dissent located in two web searches. Adversarial check: searched for challenges/errors and found none; the only residual is the general fallibility of expert vetting versus formal verification, reflected in credence below 1. Canonical form kept: it is a fair, neutral statement of the proposition as debated. Escalated to Curator: two related claims (188b2943, d8302bf3) presuppose this one and may warrant cross-claim edges. No dependents exist, so no notification issued.
Assessed Verified
verdict confidence 0.95 · credence 0.97
The three-dimensional Kakeya conjecture, which asserts that every Kakeya set in three-dimensional space (a set containing a unit line segment in every direction) has Minkowski and Hausdorff dimension three, was proved by Hong Wang and Joshua Zahl. Their proof appeared as an arXiv preprint in February 2025 and resolved a problem open in this form for roughly a century, closing the gap left by earlier partial results such as the 2.5-dimensional lower bounds of Wolff and of Katz and Zahl. The proof has been examined and accepted by the mathematical community. Terence Tao analyzed the argument publicly within days of its release, Larry Guth studied and checked the proof and wrote two expository accounts of it, and no error has been found. The result was recognized by the 2026 Clay Research Award to Wang, Zahl, Orponen, and Shmerkin, and it was central to Wang's 2026 Fields Medal. No credible challenge to the proof's correctness has been raised.
Claim entered the graph