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The live frontier of mathematics.

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Federate→Detect→Reconcile→Verify→Graph→Scout→Allocate
644Canonical problems
639Source-grounded findings
1Live verification races
724Publications indexed today

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Recent mathematical findings

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number-theoryAug 10, 2026Significance 68/100Registry: lean checked

The Proportion of Zeta Zeros on the Critical Line

Prior state unknown→proved

An unconditional record, not a resolution: the Riemann hypothesis is untouched, and Anthropic states it does not expect these techniques to lead to a proof of it. The paper is explicit that these are lower bounds only - the remaining third of the zeros are not shown to be off the line, merely not reached by the certificate. What it does settle is a question that was posed. Goldston and Suriajaya had reduced Montg…

Source authenticatedThe Proportion of Zeta Zeros on the Critical Line →
SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review
algebraJul 20, 2026Significance 65/100Registry: expert verified

Jacobian Conjecture

Prior state unknown→disproved

n ≥ 3; plane case open

Source authenticatedJacobian Conjecture →
SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review
geometry-topologyAug 24, 2026Significance 65/100Registry: unreviewed

The $(3,4,\infty)$ Modular Family of 2-Tori as a Complex Structure on $S^6$

Prior state unknown→proved

Claims an explicit compact complex threefold $X$, fibred over $\mathbb{P}^1$ by complex 2-tori via period functions on the $(3,4,\infty)$ orbifold, degenerating to a del Pezzo-of-degree-six fibre (identified opposite sides of its hexagon) at one point and to bielliptic multiple fibres of multiplicities 3 and 4 at the other two. Argues $X$ is simply connected with $H_*(X;\mathbb{Z})=H_*(S^6;\mathbb{Z})$, hence diff…

Source authenticatedThe $(3,4,\infty)$ Modular Family of 2-Tori as a Complex Structure on $S^6$ →
SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review

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combinatoricsFeb 1, 2016Significance 90/100

Erdős discrepancy problem solution

Open→Solved

The cited peer-reviewed publication presents a proof of unbounded discrepancy for every sequence of signs.

Published / acceptedErdős discrepancy problem →
SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review
algebraic complexityJul 18, 2026Significance 62/100

Fixed rank-49 matrix circuit scheduled at peak 38

Prior state unknown→Certified fused order peaks at 38 working values

Lean certificates and an exact independent replay establish a 38-value fused schedule for the public 205-operation DAG, down from its 80-value sequential order. The result is a storage schedule for this fixed circuit, not a new rank or arithmetic record.

Formally verifiedLow-memory scheduling of the public rank-49 4×4 matrix multiplication circuit →
SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review

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