{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:TW6A4F6SUNWBLNNCHWS65KME7U","short_pith_number":"pith:TW6A4F6S","schema_version":"1.0","canonical_sha256":"9dbc0e17d2a36c15b5a23da5eea984fd303a89d0322a43c6bd3871f91f2dc50d","source":{"kind":"arxiv","id":"1407.6850","version":1},"attestation_state":"computed","paper":{"title":"Finite index subgroups without unique product in graphical small cancellation groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Alexandre Martin, Dominik Gruber, Markus Steenbock","submitted_at":"2014-07-25T11:08:18Z","abstract_excerpt":"We construct torsion-free hyperbolic groups without unique product whose subgroups up to some given finite index are themselves non-unique product groups. This is achieved by generalising a construction of Comerford to graphical small cancellation presentations, showing that for every subgroup $H$ of a graphical small cancellation group there exists a free group $F$ such that $H*F$ admits a graphical small cancellation presentation."},"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":"1407.6850","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-07-25T11:08:18Z","cross_cats_sorted":[],"title_canon_sha256":"8cb2e50c1e3524d3a00a33f01f63301e8570561a64de06158b3e228d86911684","abstract_canon_sha256":"74d671629678993c3cf4edea5521a8c6d153269d93732805883a9426078ff141"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:44:28.900873Z","signature_b64":"0CsLVTpPtN4p0gz8bzOst5mJRlSoVmP6G81bQeIOaKeCFRqE6hCT1J/Byc1NlNa9g/+HbDjm6DJkYx0BYCD3Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9dbc0e17d2a36c15b5a23da5eea984fd303a89d0322a43c6bd3871f91f2dc50d","last_reissued_at":"2026-05-18T00:44:28.900361Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:44:28.900361Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Finite index subgroups without unique product in graphical small cancellation groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Alexandre Martin, Dominik Gruber, Markus Steenbock","submitted_at":"2014-07-25T11:08:18Z","abstract_excerpt":"We construct torsion-free hyperbolic groups without unique product whose subgroups up to some given finite index are themselves non-unique product groups. This is achieved by generalising a construction of Comerford to graphical small cancellation presentations, showing that for every subgroup $H$ of a graphical small cancellation group there exists a free group $F$ such that $H*F$ admits a graphical small cancellation presentation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.6850","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":"1407.6850","created_at":"2026-05-18T00:44:28.900446+00:00"},{"alias_kind":"arxiv_version","alias_value":"1407.6850v1","created_at":"2026-05-18T00:44:28.900446+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.6850","created_at":"2026-05-18T00:44:28.900446+00:00"},{"alias_kind":"pith_short_12","alias_value":"TW6A4F6SUNWB","created_at":"2026-05-18T12:28:52.271510+00:00"},{"alias_kind":"pith_short_16","alias_value":"TW6A4F6SUNWBLNNC","created_at":"2026-05-18T12:28:52.271510+00:00"},{"alias_kind":"pith_short_8","alias_value":"TW6A4F6S","created_at":"2026-05-18T12:28:52.271510+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/TW6A4F6SUNWBLNNCHWS65KME7U","json":"https://pith.science/pith/TW6A4F6SUNWBLNNCHWS65KME7U.json","graph_json":"https://pith.science/api/pith-number/TW6A4F6SUNWBLNNCHWS65KME7U/graph.json","events_json":"https://pith.science/api/pith-number/TW6A4F6SUNWBLNNCHWS65KME7U/events.json","paper":"https://pith.science/paper/TW6A4F6S"},"agent_actions":{"view_html":"https://pith.science/pith/TW6A4F6SUNWBLNNCHWS65KME7U","download_json":"https://pith.science/pith/TW6A4F6SUNWBLNNCHWS65KME7U.json","view_paper":"https://pith.science/paper/TW6A4F6S","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1407.6850&json=true","fetch_graph":"https://pith.science/api/pith-number/TW6A4F6SUNWBLNNCHWS65KME7U/graph.json","fetch_events":"https://pith.science/api/pith-number/TW6A4F6SUNWBLNNCHWS65KME7U/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TW6A4F6SUNWBLNNCHWS65KME7U/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TW6A4F6SUNWBLNNCHWS65KME7U/action/storage_attestation","attest_author":"https://pith.science/pith/TW6A4F6SUNWBLNNCHWS65KME7U/action/author_attestation","sign_citation":"https://pith.science/pith/TW6A4F6SUNWBLNNCHWS65KME7U/action/citation_signature","submit_replication":"https://pith.science/pith/TW6A4F6SUNWBLNNCHWS65KME7U/action/replication_record"}},"created_at":"2026-05-18T00:44:28.900446+00:00","updated_at":"2026-05-18T00:44:28.900446+00:00"}