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Mathematical findings

13 source-grounded records. Verification labels remain separate from source authentication and publication status.

All 690unreviewed 432lean verified 144site confirmed 66lean checked 33expert verified 13contested 2

Editorial data from VibeMathed is CC BY 4.0 licensed. Linked papers and authors’ text retain their own rights. Each record links to its registry entry and primary source. Verification labels are attributed to the registry.

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
number-theoryAug 25, 2026Significance 60/100Registry: expert verified

A tilted residue-class construction for long prime-free intervals

Prior state unknown→proved

Claims G(T)≫log⁡Tlog⁡2T/log⁡4TG(T)\gg\log T\log_2 T/\log_4 T against FGKMT's log⁡Tlog⁡2Tlog⁡4T/log⁡3T\log T\log_2 T\log_4 T/\log_3 T, a gain of log⁡3T/(log⁡4T)2\log_3 T/(\log_4 T)^2, together with Y(X)≫Xlog⁡X/log⁡3XY(X)\gg X\log X/\log_3 X for the covering problem behind it. Ben Green resists calling it incremental: "The sieving procedure is different to the Erdos-Rankin one which underpinned all bounds on the problem since 1938, and it wins log⁡3N\log_3 N over that procedure. The [FGKMT] p…

Source authenticatedA tilted residue-class construction for long prime-free intervals →
SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review
geometry-topologyMay 1, 2026Significance 40/100Registry: expert verified

Erdős's Planar Unit Distance Conjecture

Prior state unknown→disproved

VibeMathed recorded: Erdős's Planar Unit Distance Conjecture. Consult the linked registry entry for the original report and scope.

Source authenticatedErdős's Planar Unit Distance Conjecture →
SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review
analysisJul 27, 2026Significance 35/100Registry: expert verified

Crouzeix's Conjecture

Prior state unknown→proved

Two independent proofs within eight days, both with AI in the loop. Jin's (posted 27 July, preprints.org, submitted to Annals) is the first: its decisive theorem came out of an autonomous GPT-5.6 Sol run, and it is the proof Townsend, Greenbaum and Crouzeix have checked. Lorist and Schwenninger's five-page argument (arXiv, 4 August) is a genuinely different route - double-layer potentials plus a perturbation lemma f…

Source authenticatedCrouzeix's Conjecture →
SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review
mathematical-physicsJun 2, 2026Significance 20/100Registry: expert verified

FullRSB Jamming Identity a + b = 1

Prior state unknown→proved

VibeMathed recorded: FullRSB Jamming Identity a + b = 1. Consult the linked registry entry for the original report and scope.

Source authenticatedFullRSB Jamming Identity a + b = 1 →
SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review
algebraJul 29, 2026Significance 20/100Registry: expert verified

Huneke-Wiegand Conjecture

Prior state unknown→disproved

Verified by author of the conjecture

Source authenticatedHuneke-Wiegand Conjecture →
SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review
algebraMar 21, 2026Significance 15/100Registry: expert verified

Simplicity of the Hodge Bundle

Prior state unknown→proved

VibeMathed recorded: Simplicity of the Hodge Bundle. Consult the linked registry entry for the original report and scope.

Source authenticatedSimplicity of the Hodge Bundle →
SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review
combinatoricsAug 4, 2026Significance 12/100Registry: expert verified

The Middle Stair of Parallel Chip-Firing

Prior state unknown→proved

VibeMathed recorded: The Middle Stair of Parallel Chip-Firing. Consult the linked registry entry for the original report and scope.

Source authenticatedThe Middle Stair of Parallel Chip-Firing →
SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review
geometry-topologyFeb 1, 2026Significance 10/100Registry: expert verified

Erdős Problem #654

Prior state unknown→disproved

the strongest form is disproved via configurations where every point sees at most about 3n/4 distinct distances; the weaker improvement remains open

Source authenticatedErdős Problem #654 →
SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review
analysisFeb 1, 2026Significance 10/100Registry: expert verified

Erdős Problem #1040

Prior state unknown→disproved

capacity alone does not determine the invariant; the zero-measure clause is a separate open question

Source authenticatedErdős Problem #1040 →
SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review