{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:QLCT36ZEAL7GPZUDYLWPRXWMLN","short_pith_number":"pith:QLCT36ZE","schema_version":"1.0","canonical_sha256":"82c53dfb2402fe67e683c2ecf8decc5b4d2712231ed01dbece9b62717678f4f6","source":{"kind":"arxiv","id":"2504.07917","version":1},"attestation_state":"computed","paper":{"title":"SKK groups of manifolds and non-unitary invertible TQFTs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.GT","math.MP"],"primary_cat":"math.AT","authors_text":"Luuk Stehouwer, Renee S. Hoekzema, Simona Vesel\\'a","submitted_at":"2025-04-10T17:32:26Z","abstract_excerpt":"This work considers the computation of controllable cut-and-paste groups $\\mathrm{SKK}^{\\xi}_n$ of manifolds with tangential structure $\\xi:B_n\\to BO_n$. To this end, we apply the work of Galatius-Madsen-Tillman-Weiss, Genauer and Schommer-Pries, who showed that for a wide range of structures $\\xi$ these groups fit into a short exact sequence that relates them to bordism groups of $\\xi$-manifolds with kernel generated by the disc-bounding $\\xi$-sphere. The order of this sphere can be computed by knowing the possible values of the Euler characteristic of $\\xi$-manifolds. We are thus led to addr"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2504.07917","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AT","submitted_at":"2025-04-10T17:32:26Z","cross_cats_sorted":["math-ph","math.GT","math.MP"],"title_canon_sha256":"96fe0d12e98be462710175d29be32b591f231ee76817ff6d5f7f46477bbe3d43","abstract_canon_sha256":"13e93d0750303a08937abb57feadc152bb9e16c24a230fa386ddd765abb28e34"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:47:21.903708Z","signature_b64":"B42oJGQml8cis4cWIFMWQlzq3KO7ZconCEDrm4DLCyP5x7UgnGjGOpBx7N1/JZoLAF8uZQ3jrMjf91/X82cJCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"82c53dfb2402fe67e683c2ecf8decc5b4d2712231ed01dbece9b62717678f4f6","last_reissued_at":"2026-07-05T10:47:21.903189Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:47:21.903189Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"SKK groups of manifolds and non-unitary invertible TQFTs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.GT","math.MP"],"primary_cat":"math.AT","authors_text":"Luuk Stehouwer, Renee S. Hoekzema, Simona Vesel\\'a","submitted_at":"2025-04-10T17:32:26Z","abstract_excerpt":"This work considers the computation of controllable cut-and-paste groups $\\mathrm{SKK}^{\\xi}_n$ of manifolds with tangential structure $\\xi:B_n\\to BO_n$. To this end, we apply the work of Galatius-Madsen-Tillman-Weiss, Genauer and Schommer-Pries, who showed that for a wide range of structures $\\xi$ these groups fit into a short exact sequence that relates them to bordism groups of $\\xi$-manifolds with kernel generated by the disc-bounding $\\xi$-sphere. The order of this sphere can be computed by knowing the possible values of the Euler characteristic of $\\xi$-manifolds. We are thus led to addr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.07917","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/2504.07917/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2504.07917","created_at":"2026-07-05T10:47:21.903251+00:00"},{"alias_kind":"arxiv_version","alias_value":"2504.07917v1","created_at":"2026-07-05T10:47:21.903251+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2504.07917","created_at":"2026-07-05T10:47:21.903251+00:00"},{"alias_kind":"pith_short_12","alias_value":"QLCT36ZEAL7G","created_at":"2026-07-05T10:47:21.903251+00:00"},{"alias_kind":"pith_short_16","alias_value":"QLCT36ZEAL7GPZUD","created_at":"2026-07-05T10:47:21.903251+00:00"},{"alias_kind":"pith_short_8","alias_value":"QLCT36ZE","created_at":"2026-07-05T10:47:21.903251+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2507.08694","citing_title":"Free phases of Majorana fermions: Tenfold ways compared","ref_index":40,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/QLCT36ZEAL7GPZUDYLWPRXWMLN","json":"https://pith.science/pith/QLCT36ZEAL7GPZUDYLWPRXWMLN.json","graph_json":"https://pith.science/api/pith-number/QLCT36ZEAL7GPZUDYLWPRXWMLN/graph.json","events_json":"https://pith.science/api/pith-number/QLCT36ZEAL7GPZUDYLWPRXWMLN/events.json","paper":"https://pith.science/paper/QLCT36ZE"},"agent_actions":{"view_html":"https://pith.science/pith/QLCT36ZEAL7GPZUDYLWPRXWMLN","download_json":"https://pith.science/pith/QLCT36ZEAL7GPZUDYLWPRXWMLN.json","view_paper":"https://pith.science/paper/QLCT36ZE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2504.07917&json=true","fetch_graph":"https://pith.science/api/pith-number/QLCT36ZEAL7GPZUDYLWPRXWMLN/graph.json","fetch_events":"https://pith.science/api/pith-number/QLCT36ZEAL7GPZUDYLWPRXWMLN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QLCT36ZEAL7GPZUDYLWPRXWMLN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QLCT36ZEAL7GPZUDYLWPRXWMLN/action/storage_attestation","attest_author":"https://pith.science/pith/QLCT36ZEAL7GPZUDYLWPRXWMLN/action/author_attestation","sign_citation":"https://pith.science/pith/QLCT36ZEAL7GPZUDYLWPRXWMLN/action/citation_signature","submit_replication":"https://pith.science/pith/QLCT36ZEAL7GPZUDYLWPRXWMLN/action/replication_record"}},"created_at":"2026-07-05T10:47:21.903251+00:00","updated_at":"2026-07-05T10:47:21.903251+00:00"}