{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:AWXISDLJWVTMEHNA4ZHKMBLHNX","short_pith_number":"pith:AWXISDLJ","schema_version":"1.0","canonical_sha256":"05ae890d69b566c21da0e64ea605676ddf5c7a476dd47da298dfdefc77faf6c5","source":{"kind":"arxiv","id":"1511.04039","version":1},"attestation_state":"computed","paper":{"title":"Generalized Goncarov polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.CO","authors_text":"Catherine H. Yan, Rudolph Lorentz, Salvatore Tringali","submitted_at":"2015-11-12T20:06:12Z","abstract_excerpt":"We introduce the sequence of generalized Gon\\v{c}arov polynomials, which is a basis for the solutions to the Gon\\v{c}arov interpolation problem with respect to a delta operator. Explicitly, a generalized Gon\\v{c}arov basis is a sequence $(t_n(x))_{n \\ge 0}$ of polynomials defined by the biorthogonality relation $\\varepsilon_{z_i}(\\mathfrak d^{i}(t_n(x))) = n! \\;\\! \\delta_{i,n}$ for all $i,n \\in \\mathbf N$, where $\\mathfrak d$ is a delta operator, $\\mathcal Z = (z_i)_{i \\ge 0}$ a sequence of scalars, and $\\varepsilon_{z_i}$ the evaluation at $z_i$. We present algebraic and analytic properties o"},"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":"1511.04039","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-11-12T20:06:12Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"2350b088dd0bd7c602cbd84a161814fd48cd9a980c1de2828e2633db1515e707","abstract_canon_sha256":"15812398810bb6395dbf8f2df9b5742827ef73f4504a2424da26e122c3b126a7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:51:06.480830Z","signature_b64":"y3WZYGcjN10RTO2PfAdmjnu0DR6OruChZ8E6XvEuAQPcOdmOMHFfiTDm8ehp5Jg5oDS1PdVma+GQODxJ0PYGCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"05ae890d69b566c21da0e64ea605676ddf5c7a476dd47da298dfdefc77faf6c5","last_reissued_at":"2026-05-17T23:51:06.480307Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:51:06.480307Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Generalized Goncarov polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.CO","authors_text":"Catherine H. Yan, Rudolph Lorentz, Salvatore Tringali","submitted_at":"2015-11-12T20:06:12Z","abstract_excerpt":"We introduce the sequence of generalized Gon\\v{c}arov polynomials, which is a basis for the solutions to the Gon\\v{c}arov interpolation problem with respect to a delta operator. Explicitly, a generalized Gon\\v{c}arov basis is a sequence $(t_n(x))_{n \\ge 0}$ of polynomials defined by the biorthogonality relation $\\varepsilon_{z_i}(\\mathfrak d^{i}(t_n(x))) = n! \\;\\! \\delta_{i,n}$ for all $i,n \\in \\mathbf N$, where $\\mathfrak d$ is a delta operator, $\\mathcal Z = (z_i)_{i \\ge 0}$ a sequence of scalars, and $\\varepsilon_{z_i}$ the evaluation at $z_i$. We present algebraic and analytic properties o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.04039","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":"1511.04039","created_at":"2026-05-17T23:51:06.480412+00:00"},{"alias_kind":"arxiv_version","alias_value":"1511.04039v1","created_at":"2026-05-17T23:51:06.480412+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.04039","created_at":"2026-05-17T23:51:06.480412+00:00"},{"alias_kind":"pith_short_12","alias_value":"AWXISDLJWVTM","created_at":"2026-05-18T12:29:10.953037+00:00"},{"alias_kind":"pith_short_16","alias_value":"AWXISDLJWVTMEHNA","created_at":"2026-05-18T12:29:10.953037+00:00"},{"alias_kind":"pith_short_8","alias_value":"AWXISDLJ","created_at":"2026-05-18T12:29:10.953037+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/AWXISDLJWVTMEHNA4ZHKMBLHNX","json":"https://pith.science/pith/AWXISDLJWVTMEHNA4ZHKMBLHNX.json","graph_json":"https://pith.science/api/pith-number/AWXISDLJWVTMEHNA4ZHKMBLHNX/graph.json","events_json":"https://pith.science/api/pith-number/AWXISDLJWVTMEHNA4ZHKMBLHNX/events.json","paper":"https://pith.science/paper/AWXISDLJ"},"agent_actions":{"view_html":"https://pith.science/pith/AWXISDLJWVTMEHNA4ZHKMBLHNX","download_json":"https://pith.science/pith/AWXISDLJWVTMEHNA4ZHKMBLHNX.json","view_paper":"https://pith.science/paper/AWXISDLJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1511.04039&json=true","fetch_graph":"https://pith.science/api/pith-number/AWXISDLJWVTMEHNA4ZHKMBLHNX/graph.json","fetch_events":"https://pith.science/api/pith-number/AWXISDLJWVTMEHNA4ZHKMBLHNX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AWXISDLJWVTMEHNA4ZHKMBLHNX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AWXISDLJWVTMEHNA4ZHKMBLHNX/action/storage_attestation","attest_author":"https://pith.science/pith/AWXISDLJWVTMEHNA4ZHKMBLHNX/action/author_attestation","sign_citation":"https://pith.science/pith/AWXISDLJWVTMEHNA4ZHKMBLHNX/action/citation_signature","submit_replication":"https://pith.science/pith/AWXISDLJWVTMEHNA4ZHKMBLHNX/action/replication_record"}},"created_at":"2026-05-17T23:51:06.480412+00:00","updated_at":"2026-05-17T23:51:06.480412+00:00"}