{"paper":{"title":"Flip-graphs of non-orientable filling surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.GT","authors_text":"Hugo Parlier, Lionel Pournin, Pallavi Panda","submitted_at":"2025-05-07T02:25:45Z","abstract_excerpt":"Consider a surface $\\Sigma$ with punctures that serve as marked points and at least one marked point on each boundary component. We build a filling surface $\\Sigma_n$ by singling out one of the boundary components and denoting by $n$ the number of marked points it contains. We consider the triangulations of $\\Sigma_n$ whose vertices are the marked points and the associated flip-graph $\\mathcal{F}(\\Sigma_n)$. Quotienting $\\mathcal{F}(\\Sigma_n)$ by the homeomorphisms of $\\Sigma$ that fix the privileged boundary component results in a finite graph $\\mathcal{MF}(\\Sigma_n)$. Bounds on the diameter "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.04074","kind":"arxiv","version":1},"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/2505.04074/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"}