{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:UU2OIVEQDF7IS5PGUBEPRVJMH4","short_pith_number":"pith:UU2OIVEQ","schema_version":"1.0","canonical_sha256":"a534e45490197e8975e6a048f8d52c3f29b69afbb3a3e27d1a8236aca118aa8e","source":{"kind":"arxiv","id":"1307.3150","version":1},"attestation_state":"computed","paper":{"title":"Poweroids revisited - an old symbolic approach","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.CA","math.MP","math.NA"],"primary_cat":"math.CO","authors_text":"J.S.Dowker","submitted_at":"2013-07-11T15:53:41Z","abstract_excerpt":"Jeffery's 1861 computations using finite difference calculus are resurrected and extended from forward differences to general delta operators and used to neatly prove theorems in the Rota--Mullins theory of polynomials of binomial type (Steffensen's poweroids) allowing, for example, compact treatments of umbral composition, the binomial property and the connection constants. It is shown that it forms a legitimate alternative to the usual umbral device and also anticipates a number of results obtained more recently."},"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":"1307.3150","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-07-11T15:53:41Z","cross_cats_sorted":["math-ph","math.CA","math.MP","math.NA"],"title_canon_sha256":"b6768a2ebce01ef3febf88b8bd074f18b264a5293bd1bf21c00ebd0272c3d16f","abstract_canon_sha256":"867cd3ad6c64d210f5e35142c72a514eaf110fc931e44282addf7dff181de4df"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:18:07.694874Z","signature_b64":"8w0KIEIB7jX+6XzRg4btrxNE90LJR0M+kG6VIVeEYm2aa6Y+TZdxXVQkdQrSjcwkupgzid7LcZCN3AuQI406Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a534e45490197e8975e6a048f8d52c3f29b69afbb3a3e27d1a8236aca118aa8e","last_reissued_at":"2026-05-18T03:18:07.694243Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:18:07.694243Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Poweroids revisited - an old symbolic approach","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.CA","math.MP","math.NA"],"primary_cat":"math.CO","authors_text":"J.S.Dowker","submitted_at":"2013-07-11T15:53:41Z","abstract_excerpt":"Jeffery's 1861 computations using finite difference calculus are resurrected and extended from forward differences to general delta operators and used to neatly prove theorems in the Rota--Mullins theory of polynomials of binomial type (Steffensen's poweroids) allowing, for example, compact treatments of umbral composition, the binomial property and the connection constants. It is shown that it forms a legitimate alternative to the usual umbral device and also anticipates a number of results obtained more recently."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.3150","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1307.3150","created_at":"2026-05-18T03:18:07.694342+00:00"},{"alias_kind":"arxiv_version","alias_value":"1307.3150v1","created_at":"2026-05-18T03:18:07.694342+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.3150","created_at":"2026-05-18T03:18:07.694342+00:00"},{"alias_kind":"pith_short_12","alias_value":"UU2OIVEQDF7I","created_at":"2026-05-18T12:28:02.375192+00:00"},{"alias_kind":"pith_short_16","alias_value":"UU2OIVEQDF7IS5PG","created_at":"2026-05-18T12:28:02.375192+00:00"},{"alias_kind":"pith_short_8","alias_value":"UU2OIVEQ","created_at":"2026-05-18T12:28:02.375192+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/UU2OIVEQDF7IS5PGUBEPRVJMH4","json":"https://pith.science/pith/UU2OIVEQDF7IS5PGUBEPRVJMH4.json","graph_json":"https://pith.science/api/pith-number/UU2OIVEQDF7IS5PGUBEPRVJMH4/graph.json","events_json":"https://pith.science/api/pith-number/UU2OIVEQDF7IS5PGUBEPRVJMH4/events.json","paper":"https://pith.science/paper/UU2OIVEQ"},"agent_actions":{"view_html":"https://pith.science/pith/UU2OIVEQDF7IS5PGUBEPRVJMH4","download_json":"https://pith.science/pith/UU2OIVEQDF7IS5PGUBEPRVJMH4.json","view_paper":"https://pith.science/paper/UU2OIVEQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1307.3150&json=true","fetch_graph":"https://pith.science/api/pith-number/UU2OIVEQDF7IS5PGUBEPRVJMH4/graph.json","fetch_events":"https://pith.science/api/pith-number/UU2OIVEQDF7IS5PGUBEPRVJMH4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UU2OIVEQDF7IS5PGUBEPRVJMH4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UU2OIVEQDF7IS5PGUBEPRVJMH4/action/storage_attestation","attest_author":"https://pith.science/pith/UU2OIVEQDF7IS5PGUBEPRVJMH4/action/author_attestation","sign_citation":"https://pith.science/pith/UU2OIVEQDF7IS5PGUBEPRVJMH4/action/citation_signature","submit_replication":"https://pith.science/pith/UU2OIVEQDF7IS5PGUBEPRVJMH4/action/replication_record"}},"created_at":"2026-05-18T03:18:07.694342+00:00","updated_at":"2026-05-18T03:18:07.694342+00:00"}