{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:PJMBWVPOLXXNGZXUCJZN2AONWQ","short_pith_number":"pith:PJMBWVPO","canonical_record":{"source":{"id":"1102.4838","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-02-23T20:35:18Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"90a52022e4f948a76b27d8e9cf9aabda790cdac98b2f6cb3bd5006c0702a0edf","abstract_canon_sha256":"cb463be578ff144bf089f4326345e08924d78234d9c8604c22b313abf219461d"},"schema_version":"1.0"},"canonical_sha256":"7a581b55ee5deed366f41272dd01cdb4194cdf9b17188d58dde29f5dc58e0578","source":{"kind":"arxiv","id":"1102.4838","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.4838","created_at":"2026-05-18T04:28:07Z"},{"alias_kind":"arxiv_version","alias_value":"1102.4838v1","created_at":"2026-05-18T04:28:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.4838","created_at":"2026-05-18T04:28:07Z"},{"alias_kind":"pith_short_12","alias_value":"PJMBWVPOLXXN","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"PJMBWVPOLXXNGZXU","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"PJMBWVPO","created_at":"2026-05-18T12:26:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:PJMBWVPOLXXNGZXUCJZN2AONWQ","target":"record","payload":{"canonical_record":{"source":{"id":"1102.4838","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-02-23T20:35:18Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"90a52022e4f948a76b27d8e9cf9aabda790cdac98b2f6cb3bd5006c0702a0edf","abstract_canon_sha256":"cb463be578ff144bf089f4326345e08924d78234d9c8604c22b313abf219461d"},"schema_version":"1.0"},"canonical_sha256":"7a581b55ee5deed366f41272dd01cdb4194cdf9b17188d58dde29f5dc58e0578","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:28:07.222724Z","signature_b64":"QVEw+5pm0obmZZm3Jv3L2ANNrpGV9qk+CveRYuVaLo070WKEmd4y/vfP+oNRVRLac/sPCN9XW6Ks/O5BBVriCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7a581b55ee5deed366f41272dd01cdb4194cdf9b17188d58dde29f5dc58e0578","last_reissued_at":"2026-05-18T04:28:07.222083Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:28:07.222083Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1102.4838","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:28:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VcgD9c5+cHCp2Mfz8FivrWJiUqImYpydhOuWUhW2WxUyLuawKs7Ysr8+Guvsov3WrwrS47PZtCBEuQsEQ384BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T01:49:41.252412Z"},"content_sha256":"6e317b5d34b435058d7443334a003e3f81f60aa6029769d6468a4eead19ae8c0","schema_version":"1.0","event_id":"sha256:6e317b5d34b435058d7443334a003e3f81f60aa6029769d6468a4eead19ae8c0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:PJMBWVPOLXXNGZXUCJZN2AONWQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Excursion and return times of a geodesics to a subset of a hyperbolic Riemann surface","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.DS","authors_text":"Andrew Haas","submitted_at":"2011-02-23T20:35:18Z","abstract_excerpt":"We calculate the asymptotic average rate at which a generic geodesic on a finite area hyperbolic 2-orbifold returns to a subsurface with geodesic boundary. As a consequence we get the average time a generic geodesic spends in such a subsurface. Related results are obtained for excursions into a collar neighborhood of a simple closed geodesic and the associated distribution of excursion depths."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.4838","kind":"arxiv","version":1},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:28:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rDQjdQlMQIOLUMa6f01kwez+z875nLdHHed0UhOdcmqEsqnXhkofcNI2pHlEImPPDyuRbw6j1+KxTrxnHGH5AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T01:49:41.253138Z"},"content_sha256":"1cc46ff4ef1428675368f0fc259f191a35b98632850431f7d631769ead88611b","schema_version":"1.0","event_id":"sha256:1cc46ff4ef1428675368f0fc259f191a35b98632850431f7d631769ead88611b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PJMBWVPOLXXNGZXUCJZN2AONWQ/bundle.json","state_url":"https://pith.science/pith/PJMBWVPOLXXNGZXUCJZN2AONWQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PJMBWVPOLXXNGZXUCJZN2AONWQ/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":"2026-06-10T01:49:41Z","links":{"resolver":"https://pith.science/pith/PJMBWVPOLXXNGZXUCJZN2AONWQ","bundle":"https://pith.science/pith/PJMBWVPOLXXNGZXUCJZN2AONWQ/bundle.json","state":"https://pith.science/pith/PJMBWVPOLXXNGZXUCJZN2AONWQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PJMBWVPOLXXNGZXUCJZN2AONWQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:PJMBWVPOLXXNGZXUCJZN2AONWQ","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":"cb463be578ff144bf089f4326345e08924d78234d9c8604c22b313abf219461d","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-02-23T20:35:18Z","title_canon_sha256":"90a52022e4f948a76b27d8e9cf9aabda790cdac98b2f6cb3bd5006c0702a0edf"},"schema_version":"1.0","source":{"id":"1102.4838","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.4838","created_at":"2026-05-18T04:28:07Z"},{"alias_kind":"arxiv_version","alias_value":"1102.4838v1","created_at":"2026-05-18T04:28:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.4838","created_at":"2026-05-18T04:28:07Z"},{"alias_kind":"pith_short_12","alias_value":"PJMBWVPOLXXN","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"PJMBWVPOLXXNGZXU","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"PJMBWVPO","created_at":"2026-05-18T12:26:39Z"}],"graph_snapshots":[{"event_id":"sha256:1cc46ff4ef1428675368f0fc259f191a35b98632850431f7d631769ead88611b","target":"graph","created_at":"2026-05-18T04:28:07Z","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"},"paper":{"abstract_excerpt":"We calculate the asymptotic average rate at which a generic geodesic on a finite area hyperbolic 2-orbifold returns to a subsurface with geodesic boundary. As a consequence we get the average time a generic geodesic spends in such a subsurface. Related results are obtained for excursions into a collar neighborhood of a simple closed geodesic and the associated distribution of excursion depths.","authors_text":"Andrew Haas","cross_cats":["math.CV"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-02-23T20:35:18Z","title":"Excursion and return times of a geodesics to a subset of a hyperbolic Riemann surface"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.4838","kind":"arxiv","version":1},"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":"sha256:6e317b5d34b435058d7443334a003e3f81f60aa6029769d6468a4eead19ae8c0","target":"record","created_at":"2026-05-18T04:28:07Z","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":"cb463be578ff144bf089f4326345e08924d78234d9c8604c22b313abf219461d","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-02-23T20:35:18Z","title_canon_sha256":"90a52022e4f948a76b27d8e9cf9aabda790cdac98b2f6cb3bd5006c0702a0edf"},"schema_version":"1.0","source":{"id":"1102.4838","kind":"arxiv","version":1}},"canonical_sha256":"7a581b55ee5deed366f41272dd01cdb4194cdf9b17188d58dde29f5dc58e0578","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7a581b55ee5deed366f41272dd01cdb4194cdf9b17188d58dde29f5dc58e0578","first_computed_at":"2026-05-18T04:28:07.222083Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:28:07.222083Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QVEw+5pm0obmZZm3Jv3L2ANNrpGV9qk+CveRYuVaLo070WKEmd4y/vfP+oNRVRLac/sPCN9XW6Ks/O5BBVriCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:28:07.222724Z","signed_message":"canonical_sha256_bytes"},"source_id":"1102.4838","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6e317b5d34b435058d7443334a003e3f81f60aa6029769d6468a4eead19ae8c0","sha256:1cc46ff4ef1428675368f0fc259f191a35b98632850431f7d631769ead88611b"],"state_sha256":"4b6eb0c99a883e2a824f9c50000469f304ae6c54675d2d69e13682b9ec42a175"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tz7a6YlOdR7HXo9XWOWmXPPfArTyLIGvZ8XdNyl/AKQTnNUrFE6FblyaxYeoEf36Xu1+OKVyPKDSOzcywawqCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T01:49:41.257157Z","bundle_sha256":"118fd808dd5c293b3193463770e0b50826153af71faf35f76e7fea0ed74ca0b9"}}