{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1994:O3E2IJIVAAZWM3E6RJU27VDK33","short_pith_number":"pith:O3E2IJIV","canonical_record":{"source":{"id":"math/9404220","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.CA","submitted_at":"1994-04-19T00:00:00Z","cross_cats_sorted":[],"title_canon_sha256":"af6dc0974a6fabc4f260317e76bf88f19ad9e1974df0cd3464d03bf43cfbf46b","abstract_canon_sha256":"b9d8bd0d6701d3668313f9d6b5f2650d8d91ffc10570e2a487bb574f452ebe9c"},"schema_version":"1.0"},"canonical_sha256":"76c9a425150033666c9e8a69afd46adeff7fceb546573314c0091dc2a5daa5b6","source":{"kind":"arxiv","id":"math/9404220","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/9404220","created_at":"2026-05-18T01:05:51Z"},{"alias_kind":"arxiv_version","alias_value":"math/9404220v1","created_at":"2026-05-18T01:05:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9404220","created_at":"2026-05-18T01:05:51Z"},{"alias_kind":"pith_short_12","alias_value":"O3E2IJIVAAZW","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_16","alias_value":"O3E2IJIVAAZWM3E6","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_8","alias_value":"O3E2IJIV","created_at":"2026-05-18T12:25:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1994:O3E2IJIVAAZWM3E6RJU27VDK33","target":"record","payload":{"canonical_record":{"source":{"id":"math/9404220","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.CA","submitted_at":"1994-04-19T00:00:00Z","cross_cats_sorted":[],"title_canon_sha256":"af6dc0974a6fabc4f260317e76bf88f19ad9e1974df0cd3464d03bf43cfbf46b","abstract_canon_sha256":"b9d8bd0d6701d3668313f9d6b5f2650d8d91ffc10570e2a487bb574f452ebe9c"},"schema_version":"1.0"},"canonical_sha256":"76c9a425150033666c9e8a69afd46adeff7fceb546573314c0091dc2a5daa5b6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:51.463934Z","signature_b64":"kf5ozl8b55ESmfa5oEKLuaLTyfnKfTUW6L3lBXq7tmvwcqdezjj0qbJnJw4mw1mJWq+hNN8hu61e25Xn1BcaDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"76c9a425150033666c9e8a69afd46adeff7fceb546573314c0091dc2a5daa5b6","last_reissued_at":"2026-05-18T01:05:51.463361Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:51.463361Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/9404220","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":"2026-05-18T01:05:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ct54tw0HC/sPNfd5RZQheqSTnbTJi2cWyiVnfI9DNuq5SeZA7eeEhWd1g+ddmMUAvMlXqP5P4C/zt8+fFCdhDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T18:57:59.121796Z"},"content_sha256":"cf57355a2712e024c451b4b6574a5dd9593636bffb7ed5b9876b398a0b21794c","schema_version":"1.0","event_id":"sha256:cf57355a2712e024c451b4b6574a5dd9593636bffb7ed5b9876b398a0b21794c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1994:O3E2IJIVAAZWM3E6RJU27VDK33","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Algorithmic work with orthogonal polynomials and special functions","license":"","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Wolfram Koepf","submitted_at":"1994-04-19T00:00:00Z","abstract_excerpt":"In this article we present a method to implement orthogonal polynomials and many other special functions in Computer Algebra systems enabling the user to work with those functions appropriately, and in particular to verify different types of identities for those functions. Some of these identities like differential equations, power series representations, and hypergeometric representations can even dealt with algorithmically, i.\\ e.\\ they can be computed by the Computer Algebra system, rather than only verified.\n  The types of functions that can be treated by the given technique cover the gene"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9404220","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":"2026-05-18T01:05:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7Ool6n6DEJo/x02W1zagnS4h1GyRE70mp8FuItXdASY7L/PrNXVHLIJtGTqcyFfO6zwm6XlKQGsBur6uY3wwCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T18:57:59.122133Z"},"content_sha256":"65db601cd0dd44fe5887245f341fec4855d3d9de96dc898590ac6354689bcea2","schema_version":"1.0","event_id":"sha256:65db601cd0dd44fe5887245f341fec4855d3d9de96dc898590ac6354689bcea2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/O3E2IJIVAAZWM3E6RJU27VDK33/bundle.json","state_url":"https://pith.science/pith/O3E2IJIVAAZWM3E6RJU27VDK33/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/O3E2IJIVAAZWM3E6RJU27VDK33/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":"2026-07-01T18:57:59Z","links":{"resolver":"https://pith.science/pith/O3E2IJIVAAZWM3E6RJU27VDK33","bundle":"https://pith.science/pith/O3E2IJIVAAZWM3E6RJU27VDK33/bundle.json","state":"https://pith.science/pith/O3E2IJIVAAZWM3E6RJU27VDK33/state.json","well_known_bundle":"https://pith.science/.well-known/pith/O3E2IJIVAAZWM3E6RJU27VDK33/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1994:O3E2IJIVAAZWM3E6RJU27VDK33","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":"b9d8bd0d6701d3668313f9d6b5f2650d8d91ffc10570e2a487bb574f452ebe9c","cross_cats_sorted":[],"license":"","primary_cat":"math.CA","submitted_at":"1994-04-19T00:00:00Z","title_canon_sha256":"af6dc0974a6fabc4f260317e76bf88f19ad9e1974df0cd3464d03bf43cfbf46b"},"schema_version":"1.0","source":{"id":"math/9404220","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/9404220","created_at":"2026-05-18T01:05:51Z"},{"alias_kind":"arxiv_version","alias_value":"math/9404220v1","created_at":"2026-05-18T01:05:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9404220","created_at":"2026-05-18T01:05:51Z"},{"alias_kind":"pith_short_12","alias_value":"O3E2IJIVAAZW","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_16","alias_value":"O3E2IJIVAAZWM3E6","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_8","alias_value":"O3E2IJIV","created_at":"2026-05-18T12:25:47Z"}],"graph_snapshots":[{"event_id":"sha256:65db601cd0dd44fe5887245f341fec4855d3d9de96dc898590ac6354689bcea2","target":"graph","created_at":"2026-05-18T01:05:51Z","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 article we present a method to implement orthogonal polynomials and many other special functions in Computer Algebra systems enabling the user to work with those functions appropriately, and in particular to verify different types of identities for those functions. Some of these identities like differential equations, power series representations, and hypergeometric representations can even dealt with algorithmically, i.\\ e.\\ they can be computed by the Computer Algebra system, rather than only verified.\n  The types of functions that can be treated by the given technique cover the gene","authors_text":"Wolfram Koepf","cross_cats":[],"headline":"","license":"","primary_cat":"math.CA","submitted_at":"1994-04-19T00:00:00Z","title":"Algorithmic work with orthogonal polynomials and special functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9404220","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:cf57355a2712e024c451b4b6574a5dd9593636bffb7ed5b9876b398a0b21794c","target":"record","created_at":"2026-05-18T01:05:51Z","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":"b9d8bd0d6701d3668313f9d6b5f2650d8d91ffc10570e2a487bb574f452ebe9c","cross_cats_sorted":[],"license":"","primary_cat":"math.CA","submitted_at":"1994-04-19T00:00:00Z","title_canon_sha256":"af6dc0974a6fabc4f260317e76bf88f19ad9e1974df0cd3464d03bf43cfbf46b"},"schema_version":"1.0","source":{"id":"math/9404220","kind":"arxiv","version":1}},"canonical_sha256":"76c9a425150033666c9e8a69afd46adeff7fceb546573314c0091dc2a5daa5b6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"76c9a425150033666c9e8a69afd46adeff7fceb546573314c0091dc2a5daa5b6","first_computed_at":"2026-05-18T01:05:51.463361Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:05:51.463361Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kf5ozl8b55ESmfa5oEKLuaLTyfnKfTUW6L3lBXq7tmvwcqdezjj0qbJnJw4mw1mJWq+hNN8hu61e25Xn1BcaDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:05:51.463934Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/9404220","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cf57355a2712e024c451b4b6574a5dd9593636bffb7ed5b9876b398a0b21794c","sha256:65db601cd0dd44fe5887245f341fec4855d3d9de96dc898590ac6354689bcea2"],"state_sha256":"fa4d8d7363a99f854ddc1c8b85beffa8a4d9a64ab7c174c7425707ecfb036940"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oQyNF8ccIPXO+PE2A0IdoJfRLXxQFataLff6euk6KZz+h8v0gmcDNVyK1pIqtX2uhaV2zsM5ExWfESiluy23Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-01T18:57:59.124013Z","bundle_sha256":"b49db4ab40da4bc581d5b9fbf02a6516396ce7ef8dabde0b0ecb2e70901b818f"}}