{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:F7PL7CEK553M4VDT7V2H7BZKD2","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":"72abc077e123e03a835415d03bd4244c696da460c52e068ce94492345d5d6816","cross_cats_sorted":["math-ph","math.CV","math.MP"],"license":"","primary_cat":"math.CA","submitted_at":"2005-05-11T02:38:01Z","title_canon_sha256":"6ba304e9c521ccf21fdb460f605a167eb81b59c2a29fe85bc72eea187fe0ab93"},"schema_version":"1.0","source":{"id":"math/0505202","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0505202","created_at":"2026-05-18T03:25:14Z"},{"alias_kind":"arxiv_version","alias_value":"math/0505202v1","created_at":"2026-05-18T03:25:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0505202","created_at":"2026-05-18T03:25:14Z"},{"alias_kind":"pith_short_12","alias_value":"F7PL7CEK553M","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"F7PL7CEK553M4VDT","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"F7PL7CEK","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:9bfca2dfa82b5ea3fa2971f6b9924aedfd380a7c43525ded0ab1479580285819","target":"graph","created_at":"2026-05-18T03:25:14Z","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":"A new expansion for integral powers of the hypergeometric function corresponding to a special case of the incomplete beta function is summarized, and consequences, including two new sums involving digamma (psi) functions are presented.","authors_text":"Michael Milgram","cross_cats":["math-ph","math.CV","math.MP"],"headline":"","license":"","primary_cat":"math.CA","submitted_at":"2005-05-11T02:38:01Z","title":"On Powers of a Hypergeometric Function"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0505202","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:e4a4222faa958ca6aacdd1cfef9d2f310d26848d10a04c4f024348ffe4ad5892","target":"record","created_at":"2026-05-18T03:25:14Z","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":"72abc077e123e03a835415d03bd4244c696da460c52e068ce94492345d5d6816","cross_cats_sorted":["math-ph","math.CV","math.MP"],"license":"","primary_cat":"math.CA","submitted_at":"2005-05-11T02:38:01Z","title_canon_sha256":"6ba304e9c521ccf21fdb460f605a167eb81b59c2a29fe85bc72eea187fe0ab93"},"schema_version":"1.0","source":{"id":"math/0505202","kind":"arxiv","version":1}},"canonical_sha256":"2fdebf888aef76ce5473fd747f872a1e88fb90229e1a4bb5f8a63ba8a99b986d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2fdebf888aef76ce5473fd747f872a1e88fb90229e1a4bb5f8a63ba8a99b986d","first_computed_at":"2026-05-18T03:25:14.921306Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:25:14.921306Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gi9qjtvbg4vW9fx7caspQgIdeTMILj3KsgB2OUG70I7wYHeSTqmoXVKYfXsRUjkDvpLnZAJ/F0a3qyvkWSBeAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:25:14.921934Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0505202","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e4a4222faa958ca6aacdd1cfef9d2f310d26848d10a04c4f024348ffe4ad5892","sha256:9bfca2dfa82b5ea3fa2971f6b9924aedfd380a7c43525ded0ab1479580285819"],"state_sha256":"befceeec796a99d5db03f8c46dcdb1fcd3a35dafb6e4ff7e84e4fc060761b5ab"}