{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:VG4ZCRZB6TTSO5DK2HIYRYNILD","short_pith_number":"pith:VG4ZCRZB","schema_version":"1.0","canonical_sha256":"a9b9914721f4e727746ad1d188e1a858ffb75824bd5708e8c0237b97f6289caf","source":{"kind":"arxiv","id":"1610.09691","version":2},"attestation_state":"computed","paper":{"title":"Jacobi Type Continued Fractions for the Ordinary Generating Functions of Generalized Factorial Functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Maxie D. Schmidt","submitted_at":"2016-10-30T18:34:48Z","abstract_excerpt":"The article studies a class of generalized factorial functions and symbolic product sequences through Jacobi type continued fractions (J-fractions) that formally enumerate the divergent ordinary generating functions of these sequences. The more general definitions of these J-fractions extend the known expansions of the continued fractions originally proved by Flajolet that generate the rising factorial function, or Pochhammer symbol, $(x)_n$, at any fixed non-zero indeterminate $x \\in \\mathbb{C}$. The rational convergents of these generalized J-fractions provide formal power series approximati"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1610.09691","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-10-30T18:34:48Z","cross_cats_sorted":[],"title_canon_sha256":"a92943c905500d53e4c049701faeada58a0036079d7da95ea0f3c0be50051cd3","abstract_canon_sha256":"737f7cc3c790f6758bfd145bd4000701ac9a99f118981223ebb4c95a9eb39393"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:45:47.730216Z","signature_b64":"avpPexIWSudm6qgIn4W8O4H5jSRvUkZJLuKtybWqSINSxJKnYyMQ6KOfaWdtQAJcBXsGnQyMfDWdPjwTeFxXCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a9b9914721f4e727746ad1d188e1a858ffb75824bd5708e8c0237b97f6289caf","last_reissued_at":"2026-05-18T00:45:47.729714Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:45:47.729714Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Jacobi Type Continued Fractions for the Ordinary Generating Functions of Generalized Factorial Functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Maxie D. Schmidt","submitted_at":"2016-10-30T18:34:48Z","abstract_excerpt":"The article studies a class of generalized factorial functions and symbolic product sequences through Jacobi type continued fractions (J-fractions) that formally enumerate the divergent ordinary generating functions of these sequences. The more general definitions of these J-fractions extend the known expansions of the continued fractions originally proved by Flajolet that generate the rising factorial function, or Pochhammer symbol, $(x)_n$, at any fixed non-zero indeterminate $x \\in \\mathbb{C}$. The rational convergents of these generalized J-fractions provide formal power series approximati"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.09691","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1610.09691","created_at":"2026-05-18T00:45:47.729797+00:00"},{"alias_kind":"arxiv_version","alias_value":"1610.09691v2","created_at":"2026-05-18T00:45:47.729797+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.09691","created_at":"2026-05-18T00:45:47.729797+00:00"},{"alias_kind":"pith_short_12","alias_value":"VG4ZCRZB6TTS","created_at":"2026-05-18T12:30:48.956258+00:00"},{"alias_kind":"pith_short_16","alias_value":"VG4ZCRZB6TTSO5DK","created_at":"2026-05-18T12:30:48.956258+00:00"},{"alias_kind":"pith_short_8","alias_value":"VG4ZCRZB","created_at":"2026-05-18T12:30:48.956258+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/VG4ZCRZB6TTSO5DK2HIYRYNILD","json":"https://pith.science/pith/VG4ZCRZB6TTSO5DK2HIYRYNILD.json","graph_json":"https://pith.science/api/pith-number/VG4ZCRZB6TTSO5DK2HIYRYNILD/graph.json","events_json":"https://pith.science/api/pith-number/VG4ZCRZB6TTSO5DK2HIYRYNILD/events.json","paper":"https://pith.science/paper/VG4ZCRZB"},"agent_actions":{"view_html":"https://pith.science/pith/VG4ZCRZB6TTSO5DK2HIYRYNILD","download_json":"https://pith.science/pith/VG4ZCRZB6TTSO5DK2HIYRYNILD.json","view_paper":"https://pith.science/paper/VG4ZCRZB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1610.09691&json=true","fetch_graph":"https://pith.science/api/pith-number/VG4ZCRZB6TTSO5DK2HIYRYNILD/graph.json","fetch_events":"https://pith.science/api/pith-number/VG4ZCRZB6TTSO5DK2HIYRYNILD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VG4ZCRZB6TTSO5DK2HIYRYNILD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VG4ZCRZB6TTSO5DK2HIYRYNILD/action/storage_attestation","attest_author":"https://pith.science/pith/VG4ZCRZB6TTSO5DK2HIYRYNILD/action/author_attestation","sign_citation":"https://pith.science/pith/VG4ZCRZB6TTSO5DK2HIYRYNILD/action/citation_signature","submit_replication":"https://pith.science/pith/VG4ZCRZB6TTSO5DK2HIYRYNILD/action/replication_record"}},"created_at":"2026-05-18T00:45:47.729797+00:00","updated_at":"2026-05-18T00:45:47.729797+00:00"}