{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:IOKE2EKP3AKZRCZRL4MVKJS63U","short_pith_number":"pith:IOKE2EKP","schema_version":"1.0","canonical_sha256":"43944d114fd815988b315f1955265edd24ef790f1dd0d5688d973a4f4d12d8bd","source":{"kind":"arxiv","id":"1503.01989","version":1},"attestation_state":"computed","paper":{"title":"Non Hyperbolic Free-By-Cyclic and One-Relator Groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.GR","authors_text":"Jack Button, Robert Kropholler","submitted_at":"2015-03-06T15:25:39Z","abstract_excerpt":"We show that the free-by-cyclic groups of the form F(2)-by-Z act properly cocompactly on CAT(0) square complexes. We also show using generalised Baumslag-Solitar groups that all known groups defined by a 2-generator 1-relator presentation are either SQ-universal or are cyclic or isomorphic to BS(1,j). Finally we consider free-by-cyclic groups which are not relatively hyperbolic with respect to any collection of subgroups."},"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":"1503.01989","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-03-06T15:25:39Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"5df7af85515d89eeb4ca6c3e1906face08cfdfa372944a4d8b93f579c16af4c6","abstract_canon_sha256":"05e0b2ab0bb9653450699fdf4eff88058b7fec1cab54abd887a6a13eae0c8ebc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:25:27.105935Z","signature_b64":"Zt2osOrWYpxcUCEtQkRRDSvWxJH4HGLBiqd4DENpsXpI1G5sRhMrbZ8v/wfa/tehduEkLskeTF1VZg55YwehCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"43944d114fd815988b315f1955265edd24ef790f1dd0d5688d973a4f4d12d8bd","last_reissued_at":"2026-05-18T02:25:27.105428Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:25:27.105428Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Non Hyperbolic Free-By-Cyclic and One-Relator Groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.GR","authors_text":"Jack Button, Robert Kropholler","submitted_at":"2015-03-06T15:25:39Z","abstract_excerpt":"We show that the free-by-cyclic groups of the form F(2)-by-Z act properly cocompactly on CAT(0) square complexes. We also show using generalised Baumslag-Solitar groups that all known groups defined by a 2-generator 1-relator presentation are either SQ-universal or are cyclic or isomorphic to BS(1,j). Finally we consider free-by-cyclic groups which are not relatively hyperbolic with respect to any collection of subgroups."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.01989","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":""},"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":"1503.01989","created_at":"2026-05-18T02:25:27.105516+00:00"},{"alias_kind":"arxiv_version","alias_value":"1503.01989v1","created_at":"2026-05-18T02:25:27.105516+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.01989","created_at":"2026-05-18T02:25:27.105516+00:00"},{"alias_kind":"pith_short_12","alias_value":"IOKE2EKP3AKZ","created_at":"2026-05-18T12:29:25.134429+00:00"},{"alias_kind":"pith_short_16","alias_value":"IOKE2EKP3AKZRCZR","created_at":"2026-05-18T12:29:25.134429+00:00"},{"alias_kind":"pith_short_8","alias_value":"IOKE2EKP","created_at":"2026-05-18T12:29:25.134429+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/IOKE2EKP3AKZRCZRL4MVKJS63U","json":"https://pith.science/pith/IOKE2EKP3AKZRCZRL4MVKJS63U.json","graph_json":"https://pith.science/api/pith-number/IOKE2EKP3AKZRCZRL4MVKJS63U/graph.json","events_json":"https://pith.science/api/pith-number/IOKE2EKP3AKZRCZRL4MVKJS63U/events.json","paper":"https://pith.science/paper/IOKE2EKP"},"agent_actions":{"view_html":"https://pith.science/pith/IOKE2EKP3AKZRCZRL4MVKJS63U","download_json":"https://pith.science/pith/IOKE2EKP3AKZRCZRL4MVKJS63U.json","view_paper":"https://pith.science/paper/IOKE2EKP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1503.01989&json=true","fetch_graph":"https://pith.science/api/pith-number/IOKE2EKP3AKZRCZRL4MVKJS63U/graph.json","fetch_events":"https://pith.science/api/pith-number/IOKE2EKP3AKZRCZRL4MVKJS63U/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IOKE2EKP3AKZRCZRL4MVKJS63U/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IOKE2EKP3AKZRCZRL4MVKJS63U/action/storage_attestation","attest_author":"https://pith.science/pith/IOKE2EKP3AKZRCZRL4MVKJS63U/action/author_attestation","sign_citation":"https://pith.science/pith/IOKE2EKP3AKZRCZRL4MVKJS63U/action/citation_signature","submit_replication":"https://pith.science/pith/IOKE2EKP3AKZRCZRL4MVKJS63U/action/replication_record"}},"created_at":"2026-05-18T02:25:27.105516+00:00","updated_at":"2026-05-18T02:25:27.105516+00:00"}