{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:NIWXLWDSNE6HYRVMTHNUHSJ6G3","short_pith_number":"pith:NIWXLWDS","schema_version":"1.0","canonical_sha256":"6a2d75d872693c7c46ac99db43c93e36fdc7297ef475478428eaaac18da48912","source":{"kind":"arxiv","id":"1310.4711","version":2},"attestation_state":"computed","paper":{"title":"Small intersection numbers in the curve graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Samuel J. Taylor, Tarik Aougab","submitted_at":"2013-10-17T14:23:07Z","abstract_excerpt":"Let $S_{g,p}$ denote the genus $g$ orientable surface with $p \\ge 0$ punctures, and let $\\omega(g,p)= 3g+p-4$. We prove the existence of infinitely long geodesic rays $\\left\\{v_{0},v_{1}, v_{2}, ...\\right\\}$ in the curve graph satisfying the following optimal intersection property: for any natural number $k$, the endpoints $v_{i},v_{i+k}$ of any length $k$ subsegment intersect $O(\\omega^{k-2})$ times. By combining this with work of the first author, we answer a question of Dan Margalit."},"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":"1310.4711","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-10-17T14:23:07Z","cross_cats_sorted":[],"title_canon_sha256":"3511438f0a1a66e2dd73d1f1ab93374ab82e8f14e9fafdb786ea158a68350dce","abstract_canon_sha256":"0c228b879434ad5a04220dcd7844999293587a9062ebe91fa7c236cad0d06882"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:44:29.422812Z","signature_b64":"dUG0A5v2jQKOfQxDnN8dc3QZ1gIlnr/F1LCTSMJ40Gfz8DDwhfbVafDBTvbtmG2/4rT9SEtDQu5FsNhod0ZiCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6a2d75d872693c7c46ac99db43c93e36fdc7297ef475478428eaaac18da48912","last_reissued_at":"2026-05-18T00:44:29.422398Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:44:29.422398Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Small intersection numbers in the curve graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Samuel J. Taylor, Tarik Aougab","submitted_at":"2013-10-17T14:23:07Z","abstract_excerpt":"Let $S_{g,p}$ denote the genus $g$ orientable surface with $p \\ge 0$ punctures, and let $\\omega(g,p)= 3g+p-4$. We prove the existence of infinitely long geodesic rays $\\left\\{v_{0},v_{1}, v_{2}, ...\\right\\}$ in the curve graph satisfying the following optimal intersection property: for any natural number $k$, the endpoints $v_{i},v_{i+k}$ of any length $k$ subsegment intersect $O(\\omega^{k-2})$ times. By combining this with work of the first author, we answer a question of Dan Margalit."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.4711","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":"1310.4711","created_at":"2026-05-18T00:44:29.422451+00:00"},{"alias_kind":"arxiv_version","alias_value":"1310.4711v2","created_at":"2026-05-18T00:44:29.422451+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.4711","created_at":"2026-05-18T00:44:29.422451+00:00"},{"alias_kind":"pith_short_12","alias_value":"NIWXLWDSNE6H","created_at":"2026-05-18T12:27:52.871228+00:00"},{"alias_kind":"pith_short_16","alias_value":"NIWXLWDSNE6HYRVM","created_at":"2026-05-18T12:27:52.871228+00:00"},{"alias_kind":"pith_short_8","alias_value":"NIWXLWDS","created_at":"2026-05-18T12:27:52.871228+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/NIWXLWDSNE6HYRVMTHNUHSJ6G3","json":"https://pith.science/pith/NIWXLWDSNE6HYRVMTHNUHSJ6G3.json","graph_json":"https://pith.science/api/pith-number/NIWXLWDSNE6HYRVMTHNUHSJ6G3/graph.json","events_json":"https://pith.science/api/pith-number/NIWXLWDSNE6HYRVMTHNUHSJ6G3/events.json","paper":"https://pith.science/paper/NIWXLWDS"},"agent_actions":{"view_html":"https://pith.science/pith/NIWXLWDSNE6HYRVMTHNUHSJ6G3","download_json":"https://pith.science/pith/NIWXLWDSNE6HYRVMTHNUHSJ6G3.json","view_paper":"https://pith.science/paper/NIWXLWDS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1310.4711&json=true","fetch_graph":"https://pith.science/api/pith-number/NIWXLWDSNE6HYRVMTHNUHSJ6G3/graph.json","fetch_events":"https://pith.science/api/pith-number/NIWXLWDSNE6HYRVMTHNUHSJ6G3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NIWXLWDSNE6HYRVMTHNUHSJ6G3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NIWXLWDSNE6HYRVMTHNUHSJ6G3/action/storage_attestation","attest_author":"https://pith.science/pith/NIWXLWDSNE6HYRVMTHNUHSJ6G3/action/author_attestation","sign_citation":"https://pith.science/pith/NIWXLWDSNE6HYRVMTHNUHSJ6G3/action/citation_signature","submit_replication":"https://pith.science/pith/NIWXLWDSNE6HYRVMTHNUHSJ6G3/action/replication_record"}},"created_at":"2026-05-18T00:44:29.422451+00:00","updated_at":"2026-05-18T00:44:29.422451+00:00"}