{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:5V4L2D5IMSDHOSPZ5AL6Q6YNXC","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":"9f80189cd5098419f7ccd027af29cf860d6abeb6cf45a56a6f3ac2947509ba87","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2010-03-26T20:00:47Z","title_canon_sha256":"cf2753844a425d0f0a3e7c87229975a33fedf30385c5801a4890d641b03007d2"},"schema_version":"1.0","source":{"id":"1003.5216","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1003.5216","created_at":"2026-05-18T04:42:33Z"},{"alias_kind":"arxiv_version","alias_value":"1003.5216v2","created_at":"2026-05-18T04:42:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1003.5216","created_at":"2026-05-18T04:42:33Z"},{"alias_kind":"pith_short_12","alias_value":"5V4L2D5IMSDH","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"5V4L2D5IMSDHOSPZ","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"5V4L2D5I","created_at":"2026-05-18T12:26:04Z"}],"graph_snapshots":[{"event_id":"sha256:e5eae852ca48d1ff737f3d49ed1e7fdd4b1a7c7986de166c3fb7fface0144b65","target":"graph","created_at":"2026-05-18T04:42:33Z","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":"In this paper we will give a proof of a certain summation formula for Gamma functions utilizing Gegenbauer polynomials.","authors_text":"Susanna Dann","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2010-03-26T20:00:47Z","title":"An interesting application of Gegebauer Polynomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.5216","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":"sha256:23489ebfc3b33cbfbe558ea84b2abd739f0d9fa46e33fa9899034166cf27ce6f","target":"record","created_at":"2026-05-18T04:42:33Z","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":"9f80189cd5098419f7ccd027af29cf860d6abeb6cf45a56a6f3ac2947509ba87","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2010-03-26T20:00:47Z","title_canon_sha256":"cf2753844a425d0f0a3e7c87229975a33fedf30385c5801a4890d641b03007d2"},"schema_version":"1.0","source":{"id":"1003.5216","kind":"arxiv","version":2}},"canonical_sha256":"ed78bd0fa864867749f9e817e87b0db8b67908df6bc7f548cd2e99461c487f7f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ed78bd0fa864867749f9e817e87b0db8b67908df6bc7f548cd2e99461c487f7f","first_computed_at":"2026-05-18T04:42:33.661813Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:42:33.661813Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CTYybB2zdEaSF+PlsU/V/A/agFk28XbH/nzOVEIAm7wwVEteq8At/YpE4UbWK7oZ6BeZuiZJmHV29JUsDopjBw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:42:33.662495Z","signed_message":"canonical_sha256_bytes"},"source_id":"1003.5216","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:23489ebfc3b33cbfbe558ea84b2abd739f0d9fa46e33fa9899034166cf27ce6f","sha256:e5eae852ca48d1ff737f3d49ed1e7fdd4b1a7c7986de166c3fb7fface0144b65"],"state_sha256":"9b43fead79e636d959dfce1c4ad941b177cad49ea40fa981c830ad95209d682b"}