math.MP — Mathematical Physics
Perfect t-embeddings: existence
This note gives an affirmative answer to an open question posed in [Chelkak, Laslier, Russkikh'21]. Namely, it demonstrates the existence of perfect t-embeddings for each sufficiently non-degenerate planar bipartite graph with positive edge weights. The non-degeneracy condition on is formulated in terms of its perfect and almost perfect matchings and does not concern the choice of edge weights. The proof and the main part of the writing were produced by GPT-6 Astra in response to a series of prompts. We manually added Section 1.1 to put this result into a bigger context and slightly edited the introduction in order to improve the readability. We plan to provide a better human-digested version of this result later.