{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:F3Z74JKKZLRZEQONDQSOOSVRX5","short_pith_number":"pith:F3Z74JKK","schema_version":"1.0","canonical_sha256":"2ef3fe254acae39241cd1c24e74ab1bf7aed383be8576b54b45fc00d8418ad1b","source":{"kind":"arxiv","id":"1102.5434","version":2},"attestation_state":"computed","paper":{"title":"(Discrete) Almansi Type Decompositions: An umbral calculus framework based on $\\mathfrak{osp}(1|2)$ symmetries","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.CV","authors_text":"Guangbin Ren, Nelson Faustino","submitted_at":"2011-02-26T18:35:43Z","abstract_excerpt":"We introduce the umbral calculus formalism for hypercomplex variables starting from the fact that the algebra of multivariate polynomials $\\BR[\\underline{x}]$ shall be described in terms of the generators of the Weyl-Heisenberg algebra. The extension of $\\BR[\\underline{x}]$ to the algebra of Clifford-valued polynomials $\\mathcal{P}$ gives rise to an algebra of Clifford-valued operators whose canonical generators are isomorphic to the orthosymplectic Lie algebra $\\mathfrak{osp}(1|2)$.\n  This extension provides an effective framework in continuity and discreteness that allow us to establish an a"},"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":"1102.5434","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2011-02-26T18:35:43Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"3c0844f808e0bbaa7827300c841ff8845e18e5842ce08425a5c99488107fdb72","abstract_canon_sha256":"536866e8be25fffc95ec343f76076907a07f08443f99fa1efdfceafb869179ad"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:41:19.005053Z","signature_b64":"gUNlAwiURa65IZHKGsSHjN4kdbxiaHjRLIYsmPC0k543cc8X+Y6Jv2KEIu6sEJQOdc1fNXLDIsYnUtXyBdrdAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2ef3fe254acae39241cd1c24e74ab1bf7aed383be8576b54b45fc00d8418ad1b","last_reissued_at":"2026-05-18T02:41:19.004556Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:41:19.004556Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"(Discrete) Almansi Type Decompositions: An umbral calculus framework based on $\\mathfrak{osp}(1|2)$ symmetries","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.CV","authors_text":"Guangbin Ren, Nelson Faustino","submitted_at":"2011-02-26T18:35:43Z","abstract_excerpt":"We introduce the umbral calculus formalism for hypercomplex variables starting from the fact that the algebra of multivariate polynomials $\\BR[\\underline{x}]$ shall be described in terms of the generators of the Weyl-Heisenberg algebra. The extension of $\\BR[\\underline{x}]$ to the algebra of Clifford-valued polynomials $\\mathcal{P}$ gives rise to an algebra of Clifford-valued operators whose canonical generators are isomorphic to the orthosymplectic Lie algebra $\\mathfrak{osp}(1|2)$.\n  This extension provides an effective framework in continuity and discreteness that allow us to establish an a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.5434","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":"1102.5434","created_at":"2026-05-18T02:41:19.004634+00:00"},{"alias_kind":"arxiv_version","alias_value":"1102.5434v2","created_at":"2026-05-18T02:41:19.004634+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.5434","created_at":"2026-05-18T02:41:19.004634+00:00"},{"alias_kind":"pith_short_12","alias_value":"F3Z74JKKZLRZ","created_at":"2026-05-18T12:26:28.662955+00:00"},{"alias_kind":"pith_short_16","alias_value":"F3Z74JKKZLRZEQON","created_at":"2026-05-18T12:26:28.662955+00:00"},{"alias_kind":"pith_short_8","alias_value":"F3Z74JKK","created_at":"2026-05-18T12:26:28.662955+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/F3Z74JKKZLRZEQONDQSOOSVRX5","json":"https://pith.science/pith/F3Z74JKKZLRZEQONDQSOOSVRX5.json","graph_json":"https://pith.science/api/pith-number/F3Z74JKKZLRZEQONDQSOOSVRX5/graph.json","events_json":"https://pith.science/api/pith-number/F3Z74JKKZLRZEQONDQSOOSVRX5/events.json","paper":"https://pith.science/paper/F3Z74JKK"},"agent_actions":{"view_html":"https://pith.science/pith/F3Z74JKKZLRZEQONDQSOOSVRX5","download_json":"https://pith.science/pith/F3Z74JKKZLRZEQONDQSOOSVRX5.json","view_paper":"https://pith.science/paper/F3Z74JKK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1102.5434&json=true","fetch_graph":"https://pith.science/api/pith-number/F3Z74JKKZLRZEQONDQSOOSVRX5/graph.json","fetch_events":"https://pith.science/api/pith-number/F3Z74JKKZLRZEQONDQSOOSVRX5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/F3Z74JKKZLRZEQONDQSOOSVRX5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/F3Z74JKKZLRZEQONDQSOOSVRX5/action/storage_attestation","attest_author":"https://pith.science/pith/F3Z74JKKZLRZEQONDQSOOSVRX5/action/author_attestation","sign_citation":"https://pith.science/pith/F3Z74JKKZLRZEQONDQSOOSVRX5/action/citation_signature","submit_replication":"https://pith.science/pith/F3Z74JKKZLRZEQONDQSOOSVRX5/action/replication_record"}},"created_at":"2026-05-18T02:41:19.004634+00:00","updated_at":"2026-05-18T02:41:19.004634+00:00"}