{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:522VI56QQ32EIFGVUJRPXJ6USF","short_pith_number":"pith:522VI56Q","schema_version":"1.0","canonical_sha256":"eeb55477d086f44414d5a262fba7d4916578992f5ed83e1650442ded80ca673c","source":{"kind":"arxiv","id":"2506.03003","version":1},"attestation_state":"computed","paper":{"title":"Newtonian potentials of Legendre polynomials on rectangles have displacement structure","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Sheehan Olver","submitted_at":"2025-06-03T15:42:31Z","abstract_excerpt":"Particular solutions of the Poisson equation can be constructed via Newtonian potentials, integrals involving the corresponding Green's function which in two-dimensions has a logarithmic singularity. The singularity represents a significant challenge for computing the integrals, which is typically overcome via specially designed quadrature methods involving a large number of evaluations of the function and kernel. We present an attractive alternative: we show that Newtonian potentials (and their gradient) applied to (tensor products of) Legendre polynomials can be expressed in terms of complex"},"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":"2506.03003","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2025-06-03T15:42:31Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"e27f033f051f421ed436bd23c21b73a7583f95a33a8f727d15cc069e56d54eab","abstract_canon_sha256":"b99352e3fb34c83f9692f0114570488872f8f3ffa70e39bedf16e4dea796d669"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:15:13.177874Z","signature_b64":"N9xLj+eZOcy3OHqbrk9DVqAutFy0S0kPsO6pKneheU/+Tm1a9XL/nAWE22k/B3mbacFV72mqf8f76I2VJCwrCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"eeb55477d086f44414d5a262fba7d4916578992f5ed83e1650442ded80ca673c","last_reissued_at":"2026-07-05T11:15:13.177433Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:15:13.177433Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Newtonian potentials of Legendre polynomials on rectangles have displacement structure","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Sheehan Olver","submitted_at":"2025-06-03T15:42:31Z","abstract_excerpt":"Particular solutions of the Poisson equation can be constructed via Newtonian potentials, integrals involving the corresponding Green's function which in two-dimensions has a logarithmic singularity. The singularity represents a significant challenge for computing the integrals, which is typically overcome via specially designed quadrature methods involving a large number of evaluations of the function and kernel. We present an attractive alternative: we show that Newtonian potentials (and their gradient) applied to (tensor products of) Legendre polynomials can be expressed in terms of complex"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.03003","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2506.03003/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2506.03003","created_at":"2026-07-05T11:15:13.177507+00:00"},{"alias_kind":"arxiv_version","alias_value":"2506.03003v1","created_at":"2026-07-05T11:15:13.177507+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.03003","created_at":"2026-07-05T11:15:13.177507+00:00"},{"alias_kind":"pith_short_12","alias_value":"522VI56QQ32E","created_at":"2026-07-05T11:15:13.177507+00:00"},{"alias_kind":"pith_short_16","alias_value":"522VI56QQ32EIFGV","created_at":"2026-07-05T11:15:13.177507+00:00"},{"alias_kind":"pith_short_8","alias_value":"522VI56Q","created_at":"2026-07-05T11:15:13.177507+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/522VI56QQ32EIFGVUJRPXJ6USF","json":"https://pith.science/pith/522VI56QQ32EIFGVUJRPXJ6USF.json","graph_json":"https://pith.science/api/pith-number/522VI56QQ32EIFGVUJRPXJ6USF/graph.json","events_json":"https://pith.science/api/pith-number/522VI56QQ32EIFGVUJRPXJ6USF/events.json","paper":"https://pith.science/paper/522VI56Q"},"agent_actions":{"view_html":"https://pith.science/pith/522VI56QQ32EIFGVUJRPXJ6USF","download_json":"https://pith.science/pith/522VI56QQ32EIFGVUJRPXJ6USF.json","view_paper":"https://pith.science/paper/522VI56Q","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2506.03003&json=true","fetch_graph":"https://pith.science/api/pith-number/522VI56QQ32EIFGVUJRPXJ6USF/graph.json","fetch_events":"https://pith.science/api/pith-number/522VI56QQ32EIFGVUJRPXJ6USF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/522VI56QQ32EIFGVUJRPXJ6USF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/522VI56QQ32EIFGVUJRPXJ6USF/action/storage_attestation","attest_author":"https://pith.science/pith/522VI56QQ32EIFGVUJRPXJ6USF/action/author_attestation","sign_citation":"https://pith.science/pith/522VI56QQ32EIFGVUJRPXJ6USF/action/citation_signature","submit_replication":"https://pith.science/pith/522VI56QQ32EIFGVUJRPXJ6USF/action/replication_record"}},"created_at":"2026-07-05T11:15:13.177507+00:00","updated_at":"2026-07-05T11:15:13.177507+00:00"}