{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:EXECH6FW4HGTQZDLRTEZ7QOB5F","short_pith_number":"pith:EXECH6FW","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"},"canonical_sha256":"25c823f8b6e1cd38646b8cc99fc1c1e950142b43a681b0fa447e2e1afb2c5ec9","source":{"kind":"arxiv","id":"2305.00638","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2305.00638","created_at":"2026-07-05T11:47:09Z"},{"alias_kind":"arxiv_version","alias_value":"2305.00638v2","created_at":"2026-07-05T11:47:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2305.00638","created_at":"2026-07-05T11:47:09Z"},{"alias_kind":"pith_short_12","alias_value":"EXECH6FW4HGT","created_at":"2026-07-05T11:47:09Z"},{"alias_kind":"pith_short_16","alias_value":"EXECH6FW4HGTQZDL","created_at":"2026-07-05T11:47:09Z"},{"alias_kind":"pith_short_8","alias_value":"EXECH6FW","created_at":"2026-07-05T11:47:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:EXECH6FW4HGTQZDLRTEZ7QOB5F","target":"record","payload":{"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"},"canonical_sha256":"25c823f8b6e1cd38646b8cc99fc1c1e950142b43a681b0fa447e2e1afb2c5ec9","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"},"source_kind":"arxiv","source_id":"2305.00638","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:47:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NnEMVo6eR2Vegcyng9omlxs+pwUxIKR4m2WkkYF7CyiMq1AFADk50TSWGuYiwJi4ZdCyBaOptl1L/OiCwAV2Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T23:17:47.227385Z"},"content_sha256":"efd8784338670e4e9614c94ded469a7a8f1c438ead3d1018fbc096f219790957","schema_version":"1.0","event_id":"sha256:efd8784338670e4e9614c94ded469a7a8f1c438ead3d1018fbc096f219790957"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:EXECH6FW4HGTQZDLRTEZ7QOB5F","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:47:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qQJpOGwKfGKtoQdliWEn1V4bQ5zeBacCUEMsf7wpNJK0JyY+ufkDTYO5e227O3A2rgxkaBjN+IlFYyqpTDl/Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T23:17:47.227888Z"},"content_sha256":"536caa5954bb273407cc01f70ad3fd69bb1c81f88b351ec16e8b9469dbb78ea1","schema_version":"1.0","event_id":"sha256:536caa5954bb273407cc01f70ad3fd69bb1c81f88b351ec16e8b9469dbb78ea1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EXECH6FW4HGTQZDLRTEZ7QOB5F/bundle.json","state_url":"https://pith.science/pith/EXECH6FW4HGTQZDLRTEZ7QOB5F/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EXECH6FW4HGTQZDLRTEZ7QOB5F/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-12T23:17:47Z","links":{"resolver":"https://pith.science/pith/EXECH6FW4HGTQZDLRTEZ7QOB5F","bundle":"https://pith.science/pith/EXECH6FW4HGTQZDLRTEZ7QOB5F/bundle.json","state":"https://pith.science/pith/EXECH6FW4HGTQZDLRTEZ7QOB5F/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EXECH6FW4HGTQZDLRTEZ7QOB5F/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:EXECH6FW4HGTQZDLRTEZ7QOB5F","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"06c3bd0fb9f4f5dd86c1a1193aae309a6c194eea19127f3f531090bdc033dfe0","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GT","submitted_at":"2023-05-01T03:01:09Z","title_canon_sha256":"8453737920f2861071e11488dc91b03af384d37477a0f3f1f6c49ab683f91646"},"schema_version":"1.0","source":{"id":"2305.00638","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2305.00638","created_at":"2026-07-05T11:47:09Z"},{"alias_kind":"arxiv_version","alias_value":"2305.00638v2","created_at":"2026-07-05T11:47:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2305.00638","created_at":"2026-07-05T11:47:09Z"},{"alias_kind":"pith_short_12","alias_value":"EXECH6FW4HGT","created_at":"2026-07-05T11:47:09Z"},{"alias_kind":"pith_short_16","alias_value":"EXECH6FW4HGTQZDL","created_at":"2026-07-05T11:47:09Z"},{"alias_kind":"pith_short_8","alias_value":"EXECH6FW","created_at":"2026-07-05T11:47:09Z"}],"graph_snapshots":[{"event_id":"sha256:536caa5954bb273407cc01f70ad3fd69bb1c81f88b351ec16e8b9469dbb78ea1","target":"graph","created_at":"2026-07-05T11:47:09Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2305.00638/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"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.","authors_text":"Wujie Shen","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GT","submitted_at":"2023-05-01T03:01:09Z","title":"Nonsimple closed geodesics with given intersection number on hyperbolic surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2305.00638","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:efd8784338670e4e9614c94ded469a7a8f1c438ead3d1018fbc096f219790957","target":"record","created_at":"2026-07-05T11:47:09Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"06c3bd0fb9f4f5dd86c1a1193aae309a6c194eea19127f3f531090bdc033dfe0","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GT","submitted_at":"2023-05-01T03:01:09Z","title_canon_sha256":"8453737920f2861071e11488dc91b03af384d37477a0f3f1f6c49ab683f91646"},"schema_version":"1.0","source":{"id":"2305.00638","kind":"arxiv","version":2}},"canonical_sha256":"25c823f8b6e1cd38646b8cc99fc1c1e950142b43a681b0fa447e2e1afb2c5ec9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"25c823f8b6e1cd38646b8cc99fc1c1e950142b43a681b0fa447e2e1afb2c5ec9","first_computed_at":"2026-07-05T11:47:09.467292Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:47:09.467292Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MDAHaGOqCYgyfG6fReBYIIZmmgyBGgon9tVknp0z6ZB9hgwi2UmnmI1TZnfyqrtS6GUo+hsx2l11ZugYF+pKAg==","signature_status":"signed_v1","signed_at":"2026-07-05T11:47:09.467783Z","signed_message":"canonical_sha256_bytes"},"source_id":"2305.00638","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:efd8784338670e4e9614c94ded469a7a8f1c438ead3d1018fbc096f219790957","sha256:536caa5954bb273407cc01f70ad3fd69bb1c81f88b351ec16e8b9469dbb78ea1"],"state_sha256":"2ba35c573577f8209c8dd712da1452ef501d270e9255e8e6c84c756ec7248799"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZbSAFEQRJWFQP3fyhcInPYZrv2k8w7d7/VMOhvPkrbk6VT+rpJjOGiGbBy1JbJK14yL7MyzBfvJ+p7knBbF4CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-12T23:17:47.231370Z","bundle_sha256":"8c1412b69f3892660e8f3bd8945e9a550a2db5914d1fa6e32a847e1d999f682a"}}