{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1993:3K7GSNSC4MB7STSL2BJNRBQ2WV","short_pith_number":"pith:3K7GSNSC","canonical_record":{"source":{"id":"math/9307217","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.CA","submitted_at":"1993-07-09T00:00:00Z","cross_cats_sorted":[],"title_canon_sha256":"dad4839891ec9735d46fcc3f998b2831fc052575914723afc1d83710ebe9b655","abstract_canon_sha256":"64c5ede43f4f14d84c812c2ddd952976e5c57e01c50476fe81d6e7f0dce69b8a"},"schema_version":"1.0"},"canonical_sha256":"dabe693642e303f94e4bd052d8861ab56ef556942fe510236627f77b59e24b8c","source":{"kind":"arxiv","id":"math/9307217","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/9307217","created_at":"2026-05-18T01:05:52Z"},{"alias_kind":"arxiv_version","alias_value":"math/9307217v1","created_at":"2026-05-18T01:05:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9307217","created_at":"2026-05-18T01:05:52Z"},{"alias_kind":"pith_short_12","alias_value":"3K7GSNSC4MB7","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_16","alias_value":"3K7GSNSC4MB7STSL","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_8","alias_value":"3K7GSNSC","created_at":"2026-05-18T12:25:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1993:3K7GSNSC4MB7STSL2BJNRBQ2WV","target":"record","payload":{"canonical_record":{"source":{"id":"math/9307217","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.CA","submitted_at":"1993-07-09T00:00:00Z","cross_cats_sorted":[],"title_canon_sha256":"dad4839891ec9735d46fcc3f998b2831fc052575914723afc1d83710ebe9b655","abstract_canon_sha256":"64c5ede43f4f14d84c812c2ddd952976e5c57e01c50476fe81d6e7f0dce69b8a"},"schema_version":"1.0"},"canonical_sha256":"dabe693642e303f94e4bd052d8861ab56ef556942fe510236627f77b59e24b8c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:52.062607Z","signature_b64":"2mNPd0wpG2/9efdFzVhoQoaGqumm11i12LK6xBOUwFZJv1G5weBvCfnIA68pN6IQbuRaMUgcl3aGp+G9JmMUDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dabe693642e303f94e4bd052d8861ab56ef556942fe510236627f77b59e24b8c","last_reissued_at":"2026-05-18T01:05:52.061858Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:52.061858Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/9307217","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":"2026-05-18T01:05:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PK2DhwEMmaHqDdEcRTissYqmsRnWpisCmXFAvP/OoF9BSb4CwJUQGi402wq1MVpoxT6UWyi32OaDKO1Q2zuYAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T07:04:38.014196Z"},"content_sha256":"174bf02082a0d8d75ebe2c234417838e9ab87e2ec12db44bc62461517de28ecb","schema_version":"1.0","event_id":"sha256:174bf02082a0d8d75ebe2c234417838e9ab87e2ec12db44bc62461517de28ecb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1993:3K7GSNSC4MB7STSL2BJNRBQ2WV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Some results on co-recursive associated Laguerre and Jacobi polynomials","license":"","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Jean Letessier","submitted_at":"1993-07-09T00:00:00Z","abstract_excerpt":"We present results on co-recursive associated Laguerre and Jacobi polynomials which are of interest for the solution of the Chapman-Kolmogorov equations of some birth and death processes with or without absorption. Explicit forms, generating functions, and absolutely continuous part of the spectral measures are given. We derive fourth-order differential equations satisfied by the polynomials with a special attention to some simple limiting cases."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9307217","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":"2026-05-18T01:05:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+53ZBS4u7H6TImj1zf8lc4cy0mgfVrLUYbk7sOGHxoNB1bmPM2WAuQ6GEPuZgB4SdvHakzbes2QP3xC88TuIDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T07:04:38.014909Z"},"content_sha256":"d5081e0eab9ba6f8806c0d9d30286622d8f809bdfff85bda74d440d7fef7ebde","schema_version":"1.0","event_id":"sha256:d5081e0eab9ba6f8806c0d9d30286622d8f809bdfff85bda74d440d7fef7ebde"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3K7GSNSC4MB7STSL2BJNRBQ2WV/bundle.json","state_url":"https://pith.science/pith/3K7GSNSC4MB7STSL2BJNRBQ2WV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3K7GSNSC4MB7STSL2BJNRBQ2WV/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":"2026-05-26T07:04:38Z","links":{"resolver":"https://pith.science/pith/3K7GSNSC4MB7STSL2BJNRBQ2WV","bundle":"https://pith.science/pith/3K7GSNSC4MB7STSL2BJNRBQ2WV/bundle.json","state":"https://pith.science/pith/3K7GSNSC4MB7STSL2BJNRBQ2WV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3K7GSNSC4MB7STSL2BJNRBQ2WV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1993:3K7GSNSC4MB7STSL2BJNRBQ2WV","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":"64c5ede43f4f14d84c812c2ddd952976e5c57e01c50476fe81d6e7f0dce69b8a","cross_cats_sorted":[],"license":"","primary_cat":"math.CA","submitted_at":"1993-07-09T00:00:00Z","title_canon_sha256":"dad4839891ec9735d46fcc3f998b2831fc052575914723afc1d83710ebe9b655"},"schema_version":"1.0","source":{"id":"math/9307217","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/9307217","created_at":"2026-05-18T01:05:52Z"},{"alias_kind":"arxiv_version","alias_value":"math/9307217v1","created_at":"2026-05-18T01:05:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9307217","created_at":"2026-05-18T01:05:52Z"},{"alias_kind":"pith_short_12","alias_value":"3K7GSNSC4MB7","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_16","alias_value":"3K7GSNSC4MB7STSL","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_8","alias_value":"3K7GSNSC","created_at":"2026-05-18T12:25:47Z"}],"graph_snapshots":[{"event_id":"sha256:d5081e0eab9ba6f8806c0d9d30286622d8f809bdfff85bda74d440d7fef7ebde","target":"graph","created_at":"2026-05-18T01:05:52Z","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 present results on co-recursive associated Laguerre and Jacobi polynomials which are of interest for the solution of the Chapman-Kolmogorov equations of some birth and death processes with or without absorption. Explicit forms, generating functions, and absolutely continuous part of the spectral measures are given. We derive fourth-order differential equations satisfied by the polynomials with a special attention to some simple limiting cases.","authors_text":"Jean Letessier","cross_cats":[],"headline":"","license":"","primary_cat":"math.CA","submitted_at":"1993-07-09T00:00:00Z","title":"Some results on co-recursive associated Laguerre and Jacobi polynomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9307217","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":"sha256:174bf02082a0d8d75ebe2c234417838e9ab87e2ec12db44bc62461517de28ecb","target":"record","created_at":"2026-05-18T01:05:52Z","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":"64c5ede43f4f14d84c812c2ddd952976e5c57e01c50476fe81d6e7f0dce69b8a","cross_cats_sorted":[],"license":"","primary_cat":"math.CA","submitted_at":"1993-07-09T00:00:00Z","title_canon_sha256":"dad4839891ec9735d46fcc3f998b2831fc052575914723afc1d83710ebe9b655"},"schema_version":"1.0","source":{"id":"math/9307217","kind":"arxiv","version":1}},"canonical_sha256":"dabe693642e303f94e4bd052d8861ab56ef556942fe510236627f77b59e24b8c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dabe693642e303f94e4bd052d8861ab56ef556942fe510236627f77b59e24b8c","first_computed_at":"2026-05-18T01:05:52.061858Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:05:52.061858Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2mNPd0wpG2/9efdFzVhoQoaGqumm11i12LK6xBOUwFZJv1G5weBvCfnIA68pN6IQbuRaMUgcl3aGp+G9JmMUDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:05:52.062607Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/9307217","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:174bf02082a0d8d75ebe2c234417838e9ab87e2ec12db44bc62461517de28ecb","sha256:d5081e0eab9ba6f8806c0d9d30286622d8f809bdfff85bda74d440d7fef7ebde"],"state_sha256":"9dfb0816877b0e58df7d4e5085d317cedebd38571f210e38a99a61152a1f669e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"H8l3rbBD76zlRyjbkKYN7YkLtxOEL86pWDlNuk3iPdVRwMFHlj4GAihXN2E9kvXZyMnTl7M9yUqPdkuhFjDmBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T07:04:38.018459Z","bundle_sha256":"52a1fd6066d7c3a249f0e51c1f9e8e94348af2d3d66d509c412b5ffddbe4b95b"}}