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701Canonical problems
690Source-grounded findings
5Live verification races
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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 Montgom…

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,∞)(3,4,\infty) Modular Family of 2-Tori as a Complex Structure on S6S^6

Prior state unknown→proved

Claims an explicit compact complex threefold XX, fibred over P1\mathbb{P}^1 by complex 2-tori via period functions on the (3,4,∞)(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 XX is simply connected with H∗(X;Z)=H∗(S6;Z)H_*(X;\mathbb{Z})=H_*(S^6;\mathbb{Z}), hence diffeo…

Source authenticatedThe (3,4,∞)(3,4,\infty) Modular Family of 2-Tori as a Complex Structure on S6S^6 →
SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review

Frontier feed

What moved

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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

Verification

Claims become work

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  • 01
    Review HJ(3,3) ≥ 22 and its standing

    Obtain specialist review of the symmetric-coloring reduction and certificate, audit historical priority, and record peer-reviewed or journal status.

    1 open
  • 02
    Review HJ(4,2) ≥ 14 and its standing

    Obtain specialist review of the symmetric-coloring reduction and certificate, audit historical priority, and record peer-reviewed or journal status.

    1 open
  • 03
    Audit WOWII Conjecture 200 source fidelity and priority

    Obtain an independently retrievable primary or archival statement, confirm every definition against the frozen formalization, locate any earlier resolution or document the bounded search, and solicit specialist review of the explicit graph and proof.

    2 open

Frontier Scout / transparent preview

Most wanted

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Current scores are a transparent priority heuristic, not a learned Scout-uplift claim. Prospective baseline evaluation comes first.

Append-only history

Recent corrections

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analysisSep 6, 2026Significance 45/100Registry: lean verified

Smale’s Mean Value Conjecture (K=1K=1)

disproved→disproved

The formal proof constructs a complex polynomial pp such that p(0)=0,p′(0)=1, p(0)=0,\qquad p'(0)=1, and for every critical point cc of pp, ∣p(c)c∣>1. \left|\frac{p(c)}{c}\right|>1. Thus at z=0z=0 there is no critical point satisfying ∣p(0)−p(c)∣∣c∣≤∣p′(0)∣=1, \frac{|p(0)-p(c)|}{|c|}\le |p'(0)|=1, which disproves Smale's conjectured universal constant K=1K=1. The counterexample has very large unspecified degree and violates the bound only by a smal…

Source authenticatedSmale’s Mean Value Conjecture (K=1K=1) →
SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review
number-theorySep 6, 2026Significance 22/100Registry: lean checked

(ξαn)n≥1(\xi\alpha^n)_{n\ge1} is not uniformly distributed modulo one for Pisot α\alpha and ξ\xi in the Cantor set C(α)C(\alpha)

proved→proved

The problem is open, and the repository says so: what is proved are criteria for it and two instances, not the general case. Every compared statement that concludes Problem 10.61 does so for a quadratic setup - a real root α>1\alpha > 1 of X2−aX−bX^2 - aX - b whose conjugate has modulus below one - and both instances are quadratic. The arbitrary-degree material is conditional ingredients: for the family…

Source authenticated(ξαn)n≥1(\xi\alpha^n)_{n\ge1} is not uniformly distributed modulo one for Pisot α\alpha and ξ\xi in the Cantor set C(α)C(\alpha) →
SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review

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