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Mathematical findings

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

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.

number-theoryJul 21, 2026Significance 10/100Registry: lean verified

Erdős Problem #469

Prior state unknown→proved

VibeMathed recorded: Erdős Problem #469. Consult the linked registry entry for the original report and scope.

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number-theoryJul 8, 2026Significance 10/100Registry: lean verified

Erdős Problem #866

Prior state unknown→proved

h₄(n) = 4 for every n ≥ 331,777, with improved global bounds; the broader problem remains open

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number-theoryApr 22, 2026Significance 10/100Registry: site confirmed

Erdős Problem #863

Prior state unknown→proved

VibeMathed recorded: Erdős Problem #863. Consult the linked registry entry for the original report and scope.

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number-theoryJun 1, 2026Significance 10/100Registry: unreviewed

Erdős Problem #477

Prior state unknown→proved

VibeMathed recorded: Erdős Problem #477. Consult the linked registry entry for the original report and scope.

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number-theoryApr 30, 2026Significance 10/100Registry: unreviewed

Erdős Problem #1201

Prior state unknown→proved

As Tao notes on the problem page, the claim establishes natural LOWER density at least 1-eta but not that the natural density exists, so the problem as stated remains technically open

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number-theoryJul 24, 2026Significance 10/100Registry: lean verified

Erdős Problem #131

Prior state unknown→proved

The new content is the upper bound; the matching N^(1/5) construction is prior work of Erdős and Csaba. erdosproblems.com has not accepted the claim

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number-theoryJun 5, 2026Significance 10/100Registry: lean verified

Erdős Problem #696

Prior state unknown→proved

VibeMathed recorded: Erdős Problem #696. Consult the linked registry entry for the original report and scope.

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number-theoryApr 6, 2026Significance 10/100Registry: site confirmed

Erdős Problem #26

Prior state unknown→disproved

The question as posed was implicit in Davenport–Erdős (1951); the AI result settles Tenenbaum's open variant negatively

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number-theoryJul 1, 2026Significance 10/100Registry: site confirmed

Erdős Problem #320

Prior state unknown→proved

VibeMathed recorded: Erdős Problem #320. Consult the linked registry entry for the original report and scope.

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number-theoryDec 26, 2025Significance 10/100Registry: lean verified

Erdős Problem #897

Prior state unknown→disproved

VibeMathed recorded: Erdős Problem #897. Consult the linked registry entry for the original report and scope.

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number-theoryJul 1, 2026Significance 10/100Registry: site confirmed

Erdős Problem #793

Prior state unknown→proved

VibeMathed recorded: Erdős Problem #793. Consult the linked registry entry for the original report and scope.

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number-theoryApr 15, 2026Significance 10/100Registry: unreviewed

Erdős Problem #856

Prior state unknown→proved

Identifies the exponent as a variational sunflower-capacity constant, sharpening the Tang-Zhang bounds; the value of that constant itself remains open, as does site acceptance

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number-theoryMar 31, 2026Significance 10/100Registry: site confirmed

Erdős Problem #380

Prior state unknown→proved

VibeMathed recorded: Erdős Problem #380. Consult the linked registry entry for the original report and scope.

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number-theoryJul 13, 2026Significance 10/100Registry: lean verified

Erdős Problem #394

Prior state unknown→proved

VibeMathed recorded: Erdős Problem #394. Consult the linked registry entry for the original report and scope.

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combinatoricsMay 3, 2026Significance 10/100Registry: lean verified

Erdős Problem #750

Prior state unknown→proved

VibeMathed recorded: Erdős Problem #750. Consult the linked registry entry for the original report and scope.

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theoretical-computer-scienceJul 23, 2026Significance 10/100Registry: unreviewed

Dual Sequential Fat-Shattering and Tight Threshold Extraction

Prior state unknown→proved

VibeMathed recorded: Dual Sequential Fat-Shattering and Tight Threshold Extraction. Consult the linked registry entry for the original report and scope.

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number-theoryJan 29, 2026Significance 10/100Registry: lean verified

Erdős Problem #1051

Prior state unknown→proved

VibeMathed recorded: Erdős Problem #1051. Consult the linked registry entry for the original report and scope.

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number-theoryJun 14, 2026Significance 10/100Registry: lean verified

Erdős Problem #942

Prior state unknown→proved

lower bound improved to ≫ log n/(log log n · log log log n) infinitely often; the extremal order remains open

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number-theoryApr 27, 2026Significance 10/100Registry: lean verified

Erdős Problem #42

Prior state unknown→proved

VibeMathed recorded: Erdős Problem #42. Consult the linked registry entry for the original report and scope.

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number-theoryJun 22, 2026Significance 10/100Registry: lean verified

Erdős Problem #865

Prior state unknown→proved

VibeMathed recorded: Erdős Problem #865. Consult the linked registry entry for the original report and scope.

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number-theoryMay 2, 2026Significance 10/100Registry: unreviewed

Erdős Problem #870

Prior state unknown→disproved

A total refutation is claimed for all k>=3, building on the Larsen-Larsen resolution of problem #868; erdosproblems.com still lists the problem open

SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review
number-theoryJun 19, 2026Significance 10/100Registry: lean verified

Erdős Problem #306

Prior state unknown→proved

VibeMathed recorded: Erdős Problem #306. Consult the linked registry entry for the original report and scope.

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number-theoryJul 13, 2026Significance 10/100Registry: lean verified

Erdős Problem #489

Prior state unknown→proved

VibeMathed recorded: Erdős Problem #489. Consult the linked registry entry for the original report and scope.

SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review
number-theoryApr 25, 2026Significance 10/100Registry: site confirmed

Erdős Problem #888

Prior state unknown→proved

VibeMathed recorded: Erdős Problem #888. Consult the linked registry entry for the original report and scope.

SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review
number-theoryMar 16, 2026Significance 10/100Registry: lean verified

Erdős Problem #1148

Prior state unknown→proved

VibeMathed recorded: Erdős Problem #1148. Consult the linked registry entry for the original report and scope.

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number-theoryJan 10, 2026Significance 10/100Registry: lean verified

Erdős Problem #205

Prior state unknown→disproved

VibeMathed recorded: Erdős Problem #205. Consult the linked registry entry for the original report and scope.

SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review
number-theoryJun 24, 2026Significance 10/100Registry: unreviewed

Erdos Problem #1061

Prior state unknown→disproved

VibeMathed recorded: Erdos Problem #1061. Consult the linked registry entry for the original report and scope.

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number-theoryMay 3, 2026Significance 10/100Registry: lean verified

Erdős Problem #283

Prior state unknown→proved

VibeMathed recorded: Erdős Problem #283. Consult the linked registry entry for the original report and scope.

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combinatoricsJun 4, 2026Significance 10/100Registry: unreviewed

Erdős Problem #623

Prior state unknown→proved

Resolved (if correct) by an independence result rather than a proof or disproof in ZFC: consistency of the positive answer is equivalent to a measurable cardinal, of the negative to ZFC alone

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number-theoryApr 26, 2026Significance 10/100Registry: site confirmed

Erdős Problem #896

Prior state unknown→proved

VibeMathed recorded: Erdős Problem #896. Consult the linked registry entry for the original report and scope.

SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review