First Proof Question 8: Smoothing Polyhedral Lagrangians
Question 8 of the First Proof experiment (Abouzaid et al.) asks whether a polyhedral Lagrangian surface with exactly four faces meeting at every vertex necessarily admits a Lagrangian smoothing. The research report assembles ChatGPT-suggested constructions into an affirmative argument for orientable surfaces in : smooth the edges, verify the vertex links are unknots with rot 0 and tb -1, and cap off with Lagrangian disks via Chartraine's results.
- Result
- Proved
- Status
- Candidate (review pending)
- AI contribution
- AI co-developed
- Method
- Construction
- Field
- Symplectic topology
- Posed by
- Mohammed Abouzaid et al. (the First Proof experiment)
- Year posed
- 2026
- Years open
- 0y
- Solved
- 2026-02-13
- Model
- ChatGPT 5.2, Gemini Pro
- Vendor
- OpenAI, Google DeepMind
- Collaborators
- Antonio Alfieri, Connor Novak
- Verification
- Unreviewed
- Publication
- Preprint
- Significance
- 10 / 100
- Disclosed cost
- —
- Wikipedia
- No dedicated article
What the AI did
A deliberate two-team methodology: Team A explored solutions with ChatGPT 5.2 and had to defend the generated material; Team B checked correctness with human reasoning plus Gemini Pro. The report even documents ChatGPT's initial wrong idea (a spurious obstruction), and a key citation the model gestured at was pinned down by the humans in review meetings.
Verification
A self-described research report with an unusual format; the argument is assembled but no independent review has appeared, so it enters as a candidate.