{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:EXECH6FW4HGTQZDLRTEZ7QOB5F","short_pith_number":"pith:EXECH6FW","schema_version":"1.0","canonical_sha256":"25c823f8b6e1cd38646b8cc99fc1c1e950142b43a681b0fa447e2e1afb2c5ec9","source":{"kind":"arxiv","id":"2305.00638","version":2},"attestation_state":"computed","paper":{"title":"Nonsimple closed geodesics with given intersection number on hyperbolic surfaces","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Wujie Shen","submitted_at":"2023-05-01T03:01:09Z","abstract_excerpt":"We prove that the minimal length of a closed geodesic with self-intersection number $k$ on any finite-type hyperbolic surface is $2\\cosh^{-1}(1+2k)$ for $k>1750$. This improves the previously known threshold $k > 10^{13350}$. Our proof is independent of it."},"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":"2305.00638","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GT","submitted_at":"2023-05-01T03:01:09Z","cross_cats_sorted":[],"title_canon_sha256":"8453737920f2861071e11488dc91b03af384d37477a0f3f1f6c49ab683f91646","abstract_canon_sha256":"06c3bd0fb9f4f5dd86c1a1193aae309a6c194eea19127f3f531090bdc033dfe0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:47:09.467783Z","signature_b64":"MDAHaGOqCYgyfG6fReBYIIZmmgyBGgon9tVknp0z6ZB9hgwi2UmnmI1TZnfyqrtS6GUo+hsx2l11ZugYF+pKAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"25c823f8b6e1cd38646b8cc99fc1c1e950142b43a681b0fa447e2e1afb2c5ec9","last_reissued_at":"2026-07-05T11:47:09.467292Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:47:09.467292Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Nonsimple closed geodesics with given intersection number on hyperbolic surfaces","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Wujie Shen","submitted_at":"2023-05-01T03:01:09Z","abstract_excerpt":"We prove that the minimal length of a closed geodesic with self-intersection number $k$ on any finite-type hyperbolic surface is $2\\cosh^{-1}(1+2k)$ for $k>1750$. This improves the previously known threshold $k > 10^{13350}$. Our proof is independent of it."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2305.00638","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2305.00638/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2305.00638","created_at":"2026-07-05T11:47:09.467356+00:00"},{"alias_kind":"arxiv_version","alias_value":"2305.00638v2","created_at":"2026-07-05T11:47:09.467356+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2305.00638","created_at":"2026-07-05T11:47:09.467356+00:00"},{"alias_kind":"pith_short_12","alias_value":"EXECH6FW4HGT","created_at":"2026-07-05T11:47:09.467356+00:00"},{"alias_kind":"pith_short_16","alias_value":"EXECH6FW4HGTQZDL","created_at":"2026-07-05T11:47:09.467356+00:00"},{"alias_kind":"pith_short_8","alias_value":"EXECH6FW","created_at":"2026-07-05T11:47:09.467356+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2506.12465","citing_title":"Shortest filling geodesics on hyperbolic surfaces","ref_index":31,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/EXECH6FW4HGTQZDLRTEZ7QOB5F","json":"https://pith.science/pith/EXECH6FW4HGTQZDLRTEZ7QOB5F.json","graph_json":"https://pith.science/api/pith-number/EXECH6FW4HGTQZDLRTEZ7QOB5F/graph.json","events_json":"https://pith.science/api/pith-number/EXECH6FW4HGTQZDLRTEZ7QOB5F/events.json","paper":"https://pith.science/paper/EXECH6FW"},"agent_actions":{"view_html":"https://pith.science/pith/EXECH6FW4HGTQZDLRTEZ7QOB5F","download_json":"https://pith.science/pith/EXECH6FW4HGTQZDLRTEZ7QOB5F.json","view_paper":"https://pith.science/paper/EXECH6FW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2305.00638&json=true","fetch_graph":"https://pith.science/api/pith-number/EXECH6FW4HGTQZDLRTEZ7QOB5F/graph.json","fetch_events":"https://pith.science/api/pith-number/EXECH6FW4HGTQZDLRTEZ7QOB5F/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EXECH6FW4HGTQZDLRTEZ7QOB5F/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EXECH6FW4HGTQZDLRTEZ7QOB5F/action/storage_attestation","attest_author":"https://pith.science/pith/EXECH6FW4HGTQZDLRTEZ7QOB5F/action/author_attestation","sign_citation":"https://pith.science/pith/EXECH6FW4HGTQZDLRTEZ7QOB5F/action/citation_signature","submit_replication":"https://pith.science/pith/EXECH6FW4HGTQZDLRTEZ7QOB5F/action/replication_record"}},"created_at":"2026-07-05T11:47:09.467356+00:00","updated_at":"2026-07-05T11:47:09.467356+00:00"}