{"paper":{"title":"Taut fillings","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.GT","authors_text":"Matthew Ellison, Peter Doyle, Zili Wang","submitted_at":"2025-05-14T18:54:34Z","abstract_excerpt":"Let $\\sigma$ be a simplicial triangulation of the 2-sphere, $X$ the associated integral 2-cycle. A filling of $X$ is an integral 3-chain $M$ with $\\partial M = X$; a taut filling is one with minimal $L_1$-norm. We show that any taut filling arises from an extension of $\\sigma$ to a simplicial complex homeomorphic to the 3-ball. The filling is clean: it has no repeated tetrahedron, and its support complex is a clean simplicial complex. This support complex is shellable and flag: every clique in its 1-skeleton occurs as a simplex. The key to the proof is the general fact that any taut filling of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.09736","kind":"arxiv","version":3},"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/2505.09736/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"}