{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:UC6OAH3SXTEGG5H3OS2G4DSKR2","short_pith_number":"pith:UC6OAH3S","schema_version":"1.0","canonical_sha256":"a0bce01f72bcc86374fb74b46e0e4a8eaeee9ac779a14d172b534acecbc1d9ce","source":{"kind":"arxiv","id":"1210.6183","version":3},"attestation_state":"computed","paper":{"title":"The hyperbolicity of the sphere complex via surgery paths","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.GT","authors_text":"Arnaud Hilion, Camille Horbez","submitted_at":"2012-10-23T10:27:42Z","abstract_excerpt":"Handel and Mosher have proved that the free splitting complex FS for the free group is Gromov hyperbolic. This is a deep and much sought-after result, since it establishes FS as a good analogue of the curve complex for surfaces.\n  We give a shorter alternative proof of this theorem, using surgery paths in Hatcher's sphere complex (another model for the free splitting complex), instead of Handel and Mosher's fold paths. As a byproduct, we get that surgery paths are unparameterized quasi-geodesics in the sphere complex.\n  We explain how to deduce from our proof the hyperbolicity of some other co"},"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":"1210.6183","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-10-23T10:27:42Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"4f45d97351a318d331d7e83411cfeaaa007561daa6c0d9eec0e2c8784f1525dd","abstract_canon_sha256":"d5d134596c9244e333b6511047bb01ff0b7fd88bc54870be542c5a01ac40350a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:26:32.304233Z","signature_b64":"saoE35X/GkDzL7jj0L0OqkmsxCFr9soIwr8rXKgiU7K0+Ys8e4+hsjZSBsfLUbVTPIdKhdYBsh+MGyXj7BYyCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a0bce01f72bcc86374fb74b46e0e4a8eaeee9ac779a14d172b534acecbc1d9ce","last_reissued_at":"2026-05-18T03:26:32.303681Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:26:32.303681Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The hyperbolicity of the sphere complex via surgery paths","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.GT","authors_text":"Arnaud Hilion, Camille Horbez","submitted_at":"2012-10-23T10:27:42Z","abstract_excerpt":"Handel and Mosher have proved that the free splitting complex FS for the free group is Gromov hyperbolic. This is a deep and much sought-after result, since it establishes FS as a good analogue of the curve complex for surfaces.\n  We give a shorter alternative proof of this theorem, using surgery paths in Hatcher's sphere complex (another model for the free splitting complex), instead of Handel and Mosher's fold paths. As a byproduct, we get that surgery paths are unparameterized quasi-geodesics in the sphere complex.\n  We explain how to deduce from our proof the hyperbolicity of some other co"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.6183","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":""},"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":"1210.6183","created_at":"2026-05-18T03:26:32.303779+00:00"},{"alias_kind":"arxiv_version","alias_value":"1210.6183v3","created_at":"2026-05-18T03:26:32.303779+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.6183","created_at":"2026-05-18T03:26:32.303779+00:00"},{"alias_kind":"pith_short_12","alias_value":"UC6OAH3SXTEG","created_at":"2026-05-18T12:27:23.164592+00:00"},{"alias_kind":"pith_short_16","alias_value":"UC6OAH3SXTEGG5H3","created_at":"2026-05-18T12:27:23.164592+00:00"},{"alias_kind":"pith_short_8","alias_value":"UC6OAH3S","created_at":"2026-05-18T12:27:23.164592+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/UC6OAH3SXTEGG5H3OS2G4DSKR2","json":"https://pith.science/pith/UC6OAH3SXTEGG5H3OS2G4DSKR2.json","graph_json":"https://pith.science/api/pith-number/UC6OAH3SXTEGG5H3OS2G4DSKR2/graph.json","events_json":"https://pith.science/api/pith-number/UC6OAH3SXTEGG5H3OS2G4DSKR2/events.json","paper":"https://pith.science/paper/UC6OAH3S"},"agent_actions":{"view_html":"https://pith.science/pith/UC6OAH3SXTEGG5H3OS2G4DSKR2","download_json":"https://pith.science/pith/UC6OAH3SXTEGG5H3OS2G4DSKR2.json","view_paper":"https://pith.science/paper/UC6OAH3S","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1210.6183&json=true","fetch_graph":"https://pith.science/api/pith-number/UC6OAH3SXTEGG5H3OS2G4DSKR2/graph.json","fetch_events":"https://pith.science/api/pith-number/UC6OAH3SXTEGG5H3OS2G4DSKR2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UC6OAH3SXTEGG5H3OS2G4DSKR2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UC6OAH3SXTEGG5H3OS2G4DSKR2/action/storage_attestation","attest_author":"https://pith.science/pith/UC6OAH3SXTEGG5H3OS2G4DSKR2/action/author_attestation","sign_citation":"https://pith.science/pith/UC6OAH3SXTEGG5H3OS2G4DSKR2/action/citation_signature","submit_replication":"https://pith.science/pith/UC6OAH3SXTEGG5H3OS2G4DSKR2/action/replication_record"}},"created_at":"2026-05-18T03:26:32.303779+00:00","updated_at":"2026-05-18T03:26:32.303779+00:00"}