Source authenticated

Erdős Problem #180: Compactness Conjecture

For every finite family $\mathcal{F}$ of graphs, is there a single $G \in \mathcal{F}$ with $\mathrm{ex}(n;G) \ll_{\mathcal{F}} \mathrm{ex}(n;\mathcal{F})$? A counterexample refutes the Erdős-Simonovits compactness conjecture.

Exact FrontierDelta

Prior state unknown→disproved

Scope and record

Occurred: Aug 1, 2026

Delta type: SOURCE CLAIM

Assumptions: VibeMathed verification: lean-verified. Publication: announcement. AI contribution: ai-discovered. Imported under CC BY 4.0.

Canonical aliases: Erdős Problem #180: Compactness Conjecture · Erdős #180 · Problem 180

Confidence: Not scored

Registry verification: lean verified · announcement · candidate

Open the source record ↗

Attribution

VibeMathed
registry · event recorded by

Astra (internal preview)
model · ai model contributor · OpenAI

Evidence vector

SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review

Named evidence

VibeMathed record: Erdős Problem #180: Compactness Conjecture

specialist registry · passed

Kernel-checked Lean 4 certificate in OpenAI's public ten-proofs repository (Lean 4.32, mathlib, `lake build All`), with an independent Comparator checking route. Statement fidelity and community review of the day-old company announcement remain pending, hence candidate status.

Source ↗

Lean certificate (CompactnessAndDegeneracy.lean)

lean artifact · passed

lean-proof link supplied by the VibeMathed registry.

Source ↗

Quantum Parallel Repetition

witness · pending

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

Source ↗

Manuscripts (ten-proofs paper, PDF)

paper · pending

paper link supplied by the VibeMathed registry.