{"paper":{"title":"Tripod in uniform spanning tree and three-sided radial SLE$_2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Hao Wu, Jiacheng Ding, Mingchang Liu","submitted_at":"2025-11-14T10:29:47Z","abstract_excerpt":"Fix a bounded $3$-polygon $(\\Omega; x_1, x_2, x_3)$ with three marked boundary points $x_1, x_2, x_3\\in\\partial\\Omega$ and suppose $(\\Omega^{\\delta}; x_1^{\\delta}, x_2^{\\delta}, x_3^{\\delta})$ is an approximation of $(\\Omega; x_1, x_2, x_3)$ on $\\delta$-scaled hexagonal lattice. We consider uniform spanning tree (UST) in $\\Omega^{\\delta}$ with wired boundary conditions. Conditional on the event that both branches from $x_1^{\\delta}$ and $x_2^{\\delta}$ hit the boundary through $x_3^{\\delta}$, the two branches meet at a point $\\trifurcation^{\\delta}$ which we call trifurcation, and the union of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2511.11151","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2511.11151/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}