{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:Q6BWRWT7UL354SH64C2SV3723T","short_pith_number":"pith:Q6BWRWT7","schema_version":"1.0","canonical_sha256":"878368da7fa2f7de48fee0b52aeffadcc09693edd5b8e026c639dbe0aac98078","source":{"kind":"arxiv","id":"1212.3160","version":2},"attestation_state":"computed","paper":{"title":"Uniform Hyperbolicity of the Graphs of Curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.GT","authors_text":"Tarik Aougab","submitted_at":"2012-12-13T12:56:35Z","abstract_excerpt":"Let $\\mathcal{C}(S_{g,p})$ denote the curve complex of the closed orientable surface of genus $g$ with $p$ punctures. Masur-Minksy and subsequently Bowditch showed that $\\mathcal{C}(S_{g,p})$ is $\\delta$-hyperbolic for some $\\delta=\\delta(g,p)$. In this paper, we show that there exists some $\\delta>0$ independent of $g,p$ such that the curve graph $\\mathcal{C}_{1}(S_{g,p})$ is $\\delta$-hyperbolic. Furthermore, we use the main tool in the proof of this theorem to show uniform boundedness of two other quantities which a priori grow with $g$ and $p$: the curve complex distance between two vertex "},"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":"1212.3160","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-12-13T12:56:35Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"47c13dda49bbdd810311e604e59e4241090a39b5533c5e3993ee44ad7d786669","abstract_canon_sha256":"da02c70dff1479a14fb4743071d411505cdbfd676b5311507a8889d8426ee4be"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:38:22.871794Z","signature_b64":"x+mpM13+y4dqqN2hjy6hh12qF2O4HXGCK0iT1ggZA2TweYOLHreU1TTWzEnyISxJYeU7N3Zz/C93qSQet596DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"878368da7fa2f7de48fee0b52aeffadcc09693edd5b8e026c639dbe0aac98078","last_reissued_at":"2026-05-18T03:38:22.871386Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:38:22.871386Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Uniform Hyperbolicity of the Graphs of Curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.GT","authors_text":"Tarik Aougab","submitted_at":"2012-12-13T12:56:35Z","abstract_excerpt":"Let $\\mathcal{C}(S_{g,p})$ denote the curve complex of the closed orientable surface of genus $g$ with $p$ punctures. Masur-Minksy and subsequently Bowditch showed that $\\mathcal{C}(S_{g,p})$ is $\\delta$-hyperbolic for some $\\delta=\\delta(g,p)$. In this paper, we show that there exists some $\\delta>0$ independent of $g,p$ such that the curve graph $\\mathcal{C}_{1}(S_{g,p})$ is $\\delta$-hyperbolic. Furthermore, we use the main tool in the proof of this theorem to show uniform boundedness of two other quantities which a priori grow with $g$ and $p$: the curve complex distance between two vertex "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.3160","kind":"arxiv","version":2},"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":"1212.3160","created_at":"2026-05-18T03:38:22.871455+00:00"},{"alias_kind":"arxiv_version","alias_value":"1212.3160v2","created_at":"2026-05-18T03:38:22.871455+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.3160","created_at":"2026-05-18T03:38:22.871455+00:00"},{"alias_kind":"pith_short_12","alias_value":"Q6BWRWT7UL35","created_at":"2026-05-18T12:27:18.751474+00:00"},{"alias_kind":"pith_short_16","alias_value":"Q6BWRWT7UL354SH6","created_at":"2026-05-18T12:27:18.751474+00:00"},{"alias_kind":"pith_short_8","alias_value":"Q6BWRWT7","created_at":"2026-05-18T12:27:18.751474+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/Q6BWRWT7UL354SH64C2SV3723T","json":"https://pith.science/pith/Q6BWRWT7UL354SH64C2SV3723T.json","graph_json":"https://pith.science/api/pith-number/Q6BWRWT7UL354SH64C2SV3723T/graph.json","events_json":"https://pith.science/api/pith-number/Q6BWRWT7UL354SH64C2SV3723T/events.json","paper":"https://pith.science/paper/Q6BWRWT7"},"agent_actions":{"view_html":"https://pith.science/pith/Q6BWRWT7UL354SH64C2SV3723T","download_json":"https://pith.science/pith/Q6BWRWT7UL354SH64C2SV3723T.json","view_paper":"https://pith.science/paper/Q6BWRWT7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1212.3160&json=true","fetch_graph":"https://pith.science/api/pith-number/Q6BWRWT7UL354SH64C2SV3723T/graph.json","fetch_events":"https://pith.science/api/pith-number/Q6BWRWT7UL354SH64C2SV3723T/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Q6BWRWT7UL354SH64C2SV3723T/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Q6BWRWT7UL354SH64C2SV3723T/action/storage_attestation","attest_author":"https://pith.science/pith/Q6BWRWT7UL354SH64C2SV3723T/action/author_attestation","sign_citation":"https://pith.science/pith/Q6BWRWT7UL354SH64C2SV3723T/action/citation_signature","submit_replication":"https://pith.science/pith/Q6BWRWT7UL354SH64C2SV3723T/action/replication_record"}},"created_at":"2026-05-18T03:38:22.871455+00:00","updated_at":"2026-05-18T03:38:22.871455+00:00"}