{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:OEO3RHVDEC5Y4FU5QWSXXQHDSV","short_pith_number":"pith:OEO3RHVD","canonical_record":{"source":{"id":"1209.1696","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-09-08T07:20:15Z","cross_cats_sorted":[],"title_canon_sha256":"e691dc68c58c200fa1414a688c8f5d608205026c81bde9e2923608385e2f75a8","abstract_canon_sha256":"7cd41218e2ac436a1826a6a940e5e04c1074ef9888631ac594d88673386a18da"},"schema_version":"1.0"},"canonical_sha256":"711db89ea320bb8e169d85a57bc0e395625fe876135717d998ebf0fafe0880de","source":{"kind":"arxiv","id":"1209.1696","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.1696","created_at":"2026-05-18T03:28:17Z"},{"alias_kind":"arxiv_version","alias_value":"1209.1696v2","created_at":"2026-05-18T03:28:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.1696","created_at":"2026-05-18T03:28:17Z"},{"alias_kind":"pith_short_12","alias_value":"OEO3RHVDEC5Y","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"OEO3RHVDEC5Y4FU5","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"OEO3RHVD","created_at":"2026-05-18T12:27:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:OEO3RHVDEC5Y4FU5QWSXXQHDSV","target":"record","payload":{"canonical_record":{"source":{"id":"1209.1696","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-09-08T07:20:15Z","cross_cats_sorted":[],"title_canon_sha256":"e691dc68c58c200fa1414a688c8f5d608205026c81bde9e2923608385e2f75a8","abstract_canon_sha256":"7cd41218e2ac436a1826a6a940e5e04c1074ef9888631ac594d88673386a18da"},"schema_version":"1.0"},"canonical_sha256":"711db89ea320bb8e169d85a57bc0e395625fe876135717d998ebf0fafe0880de","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:28:17.430900Z","signature_b64":"dHBeyvaoECkDlZmDoR+wOKcZ7QjrKhV3TbHnbr8K2887y9W/GM1M1a8SDj1aBrua3C2/0mn09JTX2p7/+N3BDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"711db89ea320bb8e169d85a57bc0e395625fe876135717d998ebf0fafe0880de","last_reissued_at":"2026-05-18T03:28:17.430302Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:28:17.430302Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1209.1696","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":"2026-05-18T03:28:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ty9qLzNqdhbA4BZ2OrihoATFCJNle7OvPhbSEaWNoF8tLs4ATuE//DhKbPlMFqUHVrdHI4YifWD9KjEeD2lQBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T07:01:28.703783Z"},"content_sha256":"22544ba58706051584880fb46e7ab7ff612be7dc12a18834dcea755f8efe6a37","schema_version":"1.0","event_id":"sha256:22544ba58706051584880fb46e7ab7ff612be7dc12a18834dcea755f8efe6a37"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:OEO3RHVDEC5Y4FU5QWSXXQHDSV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Topics in special functions III","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Glen D. Anderson, Matti Vuorinen, Xiaohui Zhang","submitted_at":"2012-09-08T07:20:15Z","abstract_excerpt":"The authors survey recent results in special functions of classical analysis and geometric function theory, in particular the circular and hyperbolic functions, the gamma function, the elliptic integrals, the Gaussian hypergeometric function, power series, and mean values."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.1696","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:28:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cqdpl8kuhNgZ4Iz5u5UiHzdHSf39/8yGfBHHDITY4J5GIE4+v98IL8i85ug5W4um5kkNAeLjGeVHXjGZz51TDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T07:01:28.704115Z"},"content_sha256":"a5328fa538665d7837d52d4418c9c805a56b0afbc451b82e367e10c573dddfda","schema_version":"1.0","event_id":"sha256:a5328fa538665d7837d52d4418c9c805a56b0afbc451b82e367e10c573dddfda"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OEO3RHVDEC5Y4FU5QWSXXQHDSV/bundle.json","state_url":"https://pith.science/pith/OEO3RHVDEC5Y4FU5QWSXXQHDSV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OEO3RHVDEC5Y4FU5QWSXXQHDSV/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":"2026-06-21T07:01:28Z","links":{"resolver":"https://pith.science/pith/OEO3RHVDEC5Y4FU5QWSXXQHDSV","bundle":"https://pith.science/pith/OEO3RHVDEC5Y4FU5QWSXXQHDSV/bundle.json","state":"https://pith.science/pith/OEO3RHVDEC5Y4FU5QWSXXQHDSV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OEO3RHVDEC5Y4FU5QWSXXQHDSV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:OEO3RHVDEC5Y4FU5QWSXXQHDSV","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":"7cd41218e2ac436a1826a6a940e5e04c1074ef9888631ac594d88673386a18da","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-09-08T07:20:15Z","title_canon_sha256":"e691dc68c58c200fa1414a688c8f5d608205026c81bde9e2923608385e2f75a8"},"schema_version":"1.0","source":{"id":"1209.1696","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.1696","created_at":"2026-05-18T03:28:17Z"},{"alias_kind":"arxiv_version","alias_value":"1209.1696v2","created_at":"2026-05-18T03:28:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.1696","created_at":"2026-05-18T03:28:17Z"},{"alias_kind":"pith_short_12","alias_value":"OEO3RHVDEC5Y","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"OEO3RHVDEC5Y4FU5","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"OEO3RHVD","created_at":"2026-05-18T12:27:16Z"}],"graph_snapshots":[{"event_id":"sha256:a5328fa538665d7837d52d4418c9c805a56b0afbc451b82e367e10c573dddfda","target":"graph","created_at":"2026-05-18T03:28:17Z","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":"The authors survey recent results in special functions of classical analysis and geometric function theory, in particular the circular and hyperbolic functions, the gamma function, the elliptic integrals, the Gaussian hypergeometric function, power series, and mean values.","authors_text":"Glen D. Anderson, Matti Vuorinen, Xiaohui Zhang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-09-08T07:20:15Z","title":"Topics in special functions III"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.1696","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":"sha256:22544ba58706051584880fb46e7ab7ff612be7dc12a18834dcea755f8efe6a37","target":"record","created_at":"2026-05-18T03:28:17Z","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":"7cd41218e2ac436a1826a6a940e5e04c1074ef9888631ac594d88673386a18da","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-09-08T07:20:15Z","title_canon_sha256":"e691dc68c58c200fa1414a688c8f5d608205026c81bde9e2923608385e2f75a8"},"schema_version":"1.0","source":{"id":"1209.1696","kind":"arxiv","version":2}},"canonical_sha256":"711db89ea320bb8e169d85a57bc0e395625fe876135717d998ebf0fafe0880de","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"711db89ea320bb8e169d85a57bc0e395625fe876135717d998ebf0fafe0880de","first_computed_at":"2026-05-18T03:28:17.430302Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:28:17.430302Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dHBeyvaoECkDlZmDoR+wOKcZ7QjrKhV3TbHnbr8K2887y9W/GM1M1a8SDj1aBrua3C2/0mn09JTX2p7/+N3BDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:28:17.430900Z","signed_message":"canonical_sha256_bytes"},"source_id":"1209.1696","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:22544ba58706051584880fb46e7ab7ff612be7dc12a18834dcea755f8efe6a37","sha256:a5328fa538665d7837d52d4418c9c805a56b0afbc451b82e367e10c573dddfda"],"state_sha256":"39fc65faee3380d970410ec017b48726d79d02f155d84315bdc621734c08353a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YU5bkvsPYdZrIncJEQOimmprRJzmP5IC007pKjUR9pgWunkyXBEtqSUK9fgfzP+vvG2XkueXSutjeV4Jy+7dAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T07:01:28.705986Z","bundle_sha256":"e995a90e9d9cee1eebcd2816c6414fc3ec73e0b230561ab9845b4a098f587806"}}