Source authenticated

Erdős Problem #424

Proves positive lower density. The Formal Conjectures encoding asks for Set.HasPosDensity, a density that exists and is positive; erdosproblems.com says Erdos most likely meant lower density.

Exact FrontierDelta

Prior state unknown→proved

Scope and record

Occurred: Jul 20, 2026

Delta type: SOURCE CLAIM

Assumptions: VibeMathed verification: lean-verified. Publication: announcement. AI contribution: ai-co-developed. Editorial metadata: CC BY 4.0; linked content retains its own rights.

Canonical aliases: Erdős Problem #424 · Erdős #424 · Problem 424

Confidence: Not scored

Registry verification: lean verified · announcement · candidate

Open the source record ↗

Attribution

VibeMathed
registry · event recorded by

Samuel Korsky
human · human collaborator

GPT-5.6 Pro
model · ai model contributor · OpenAI

Evidence vector

SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review

Named evidence

VibeMathed record: Erdős Problem #424

specialist registry · passed

Lean 4.32.0 and Mathlib v4.32.0 formalization by Boris Alexeev, produced with Codex, from the informal argument of Samuel Korsky and GPT-5.6 Pro. Rebuilt independently on 2026-08-02 against Lean 4.32.0 and Mathlib v4.32.0 (the file as published, sha256 ca4a2371918b1a7c66dccfe324305298): all 6,394 lines compile in 1,215 s with no sorry and no admit, and #print axioms reports the top theorem depending on exactly [propext, Classical.choice, Quot.sound], the three standard Lean axioms, with no sorryAx and nothing assumed. The formalized conclusion is positive lower density, stated against the same nextGeneration, sequenceSet and generatedSet definitions the Formal Conjectures statement of #424 uses. Status is candidate rather than resolved because erdosproblems.com has not accepted the claim: its proof-claims page states plainly that appearing there is no guarantee of correctness and does not mean anyone associated with the site examined any part of the proof.

Source ↗

Lean proof (Erdos424.lean)

lean artifact · passed

lean-proof link supplied by the VibeMathed registry.

Source ↗

Manuscript (PDF)

paper · pending

paper link supplied by the VibeMathed registry.

Source ↗

Formal Conjectures statement of #424

formal registration · pending

lean-statement link supplied by the VibeMathed registry.

Source ↗

Problem 63 of Ben Green's 100 Open Problems

specialist registry · pending

problem-record link supplied by the VibeMathed registry.

Source ↗

Proof claim on erdosproblems.com

witness · pending

discussion link supplied by the VibeMathed registry.

Source ↗

Erdős Problem #424

witness · pending

Primary source named by the VibeMathed record. Presence in this import is not an independent mathematical verification.

Source ↗

Artifacts and verifiers

Lean proof (Erdos424.lean)

lean artifact · passed

Artifact ↗

Formal Conjectures statement of #424

formal registration · pending

Artifact ↗

Compute record

No linked compute attempts recorded.

Lineage and corrections

This event attributed to Samuel Korsky

This event attributed to GPT-5.6 Pro

Proves positive lower density. The Formal Conjectures encoding asks for Set.HasPosDensity, a density that exists and is positive; erdosproblems.com says Erdos most likely meant lower density. parent of this event

Erdős Problem #424 parent of this event

Manuscript (PDF) evidence for this event

Formal Conjectures statement of #424 evidence for this event

Problem 63 of Ben Green's 100 Open Problems evidence for this event

Lean proof (Erdos424.lean) evidence for this event

VibeMathed record: Erdős Problem #424 evidence for this event

Proof claim on erdosproblems.com evidence for this event

Erdős Problem #424 evidence for this event

Act on this frontier

Verify, challenge, or extend the result.

Help verify Open canonical problem Explore evidence graph