Discoveries / geometry-topology

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 $(\mathbb{R}^4, \omega)$: 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.