First Proof Question 8: Smoothing Polyhedral Lagrangians
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Statement
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.
Context
A numbered question from the First Proof experiment, a curated 2026 problem list by leading symplectic topologists designed precisely to test AI-assisted mathematics.
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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.
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