Erdos Problems #593 and #1177
Erdős problem #593 · erdosproblems.com/593
Erdos Problem #593 asks which finite triple systems occur in every uncountably chromatic triple system. The answer is exactly the class generated from private-vertex expansions of finite bipartite graphs by finite disjoint unions and one-point amalgamations. Problem #1177 on exact spectra is settled alongside it.
- Result
- Proved(see note)
- Status
- Resolved
- AI contribution
- AI co-developed
- Method
- Argument
- Field
- Infinite combinatorics
- Posed by
- Paul Erdos
- Year posed
- —
- Years open
- —
- Solved
- 2026-06-23
- Model
- ChatGPT, Aristotle
- Vendor
- OpenAI / Harmonic
- Collaborators
- Eric Li
- Verification
- Unreviewed
- Publication
- Preprint
- Significance
- 10 / 100
- Disclosed cost
- —
- Wikipedia
- No dedicated article
What was actually shown
settles two numbered Erdos problems at once
What the AI did
The declaration says large language models, primarily ChatGPT, were used extensively throughout the research, with the author originating the ideas, and that the accompanying Lean formalization was produced with Harmonic's Aristotle under the author's direction and audit.
Verification
A Lean formalization produced with Aristotle accompanies the paper; we have not compiled it. arXiv preprint, not peer-reviewed.