Source authenticated

Crouzeix's Conjecture

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 for 2-dilations - produced with ChatGPT 5.6 Pro exploring proof strategies. The entry's headline axes record Jin's proof; the earlier version of this entry recorded Lorist-Schwenninger's as primary while Jin's AI provenance was still unknown.

Exact FrontierDelta

Prior state unknown→proved

Scope and record

Occurred: Jul 27, 2026

Delta type: SOURCE CLAIM

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

Canonical aliases: Crouzeix's Conjecture

Confidence: Not scored

Registry verification: expert verified · preprint · resolved

Open the source record ↗

Attribution

VibeMathed
registry · event recorded by

GPT-5.6 Sol
model · ai model contributor · OpenAI

Emiel Lorist
human · human collaborator

ChatGPT 5.6 Pro
model · ai model contributor · OpenAI

Shanmu Jin
human · human collaborator

Felix L. Schwenninger
human · human collaborator

Evidence vector

SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review

Named evidence

VibeMathed record: Crouzeix's Conjecture

specialist registry · passed

Independently expert-verified, publicly on record: Townsend and Greenbaum's essay of 14 August 2026 states that both authors and Michel Crouzeix himself "have checked the proof thoroughly and believe that Dr. Jin's manuscript is correct" - the conjecture's own poser among the verifiers, and Greenbaum co-organized the 2017 AIM workshop on the problem. This site read that essay in full and audited Jin's repository (commit 9df0783): 82 Lean files with zero sorry, zero axiom declarations and zero native_decide with comments stripped, on toolchain v4.28.0, alongside an Annals-formatted manuscript and the complete autonomous-run prompt - though the Lean was not compiled here and its statement-to-conjecture correspondence not audited, so the tier rests on the expert endorsement, not the formalization. The independent second proof by Lorist and Schwenninger (arXiv:2608.03841) has no comparable public endorsement yet and the essay stops short of vouching for it. Neither manuscript is refereed.

Source ↗

Lorist-Schwenninger Remark 2 positivity question

witness · passed

independent link supplied by the VibeMathed registry.

Source ↗

Townsend and Greenbaum, The Neurosurgery Resident Who Proved Crouzeix's Conjecture (14 Aug 2026)

independent reproduction · passed

independent link supplied by the VibeMathed registry.

Source ↗

Wikipedia: Crouzeix's conjecture

witness · pending

wikipedia link supplied by the VibeMathed registry.