{"paper":{"title":"Non-semisimple open-closed 3d TFT","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.GT","math.MP"],"primary_cat":"math.QA","authors_text":"Ingo Runkel, Yilong Wang","submitted_at":"2026-08-08T10:45:42Z","abstract_excerpt":"Given a spherical finite tensor category C, not necessarily semisimple, and a two-sided modified trace on its projective ideal, we define an open-closed three-dimensional topological field theory with values in vector spaces. The bordism category has as morphisms three-dimensional bordisms with corners, whose boundary is partitioned into the gluing boundary, parametrised by source and target surface, and the unparametrised free boundary. The free boundary is equipped with an embedded C-coloured graph satisfying an admissibility condition. Our construction starts from a new three-manifold invar"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.08057","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/2608.08057/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"}