{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:522VI56QQ32EIFGVUJRPXJ6USF","short_pith_number":"pith:522VI56Q","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"},"canonical_sha256":"eeb55477d086f44414d5a262fba7d4916578992f5ed83e1650442ded80ca673c","source":{"kind":"arxiv","id":"2506.03003","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.03003","created_at":"2026-07-05T11:15:13Z"},{"alias_kind":"arxiv_version","alias_value":"2506.03003v1","created_at":"2026-07-05T11:15:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.03003","created_at":"2026-07-05T11:15:13Z"},{"alias_kind":"pith_short_12","alias_value":"522VI56QQ32E","created_at":"2026-07-05T11:15:13Z"},{"alias_kind":"pith_short_16","alias_value":"522VI56QQ32EIFGV","created_at":"2026-07-05T11:15:13Z"},{"alias_kind":"pith_short_8","alias_value":"522VI56Q","created_at":"2026-07-05T11:15:13Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:522VI56QQ32EIFGVUJRPXJ6USF","target":"record","payload":{"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"},"canonical_sha256":"eeb55477d086f44414d5a262fba7d4916578992f5ed83e1650442ded80ca673c","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"},"source_kind":"arxiv","source_id":"2506.03003","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:15:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HE7oh8Z1nrz7Xrnkt3tyHUep3Dz10uqXDfPXGunun5eeVyxrbmI1AdBRg4LCKvVaYUn+nKFz2RS4L4S6CCauAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T11:48:39.800031Z"},"content_sha256":"431c595fe0cd914e54a0d122452eb4c4322cc710fbc1cab61b841f9ed878f2c0","schema_version":"1.0","event_id":"sha256:431c595fe0cd914e54a0d122452eb4c4322cc710fbc1cab61b841f9ed878f2c0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:522VI56QQ32EIFGVUJRPXJ6USF","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:15:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Sn/P/xJvV9u4X6wOV3Bv2pJGFZFPlVmwgHDSsR/3cefL2pAR1nB/BSkMhsR9Oy/vVr6fhJ840v0dxkSd77NgAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T11:48:39.801085Z"},"content_sha256":"8830832e906a4004b4591eb508e0f03d4cc08e107a99a5bf34d12a3eb2a7076e","schema_version":"1.0","event_id":"sha256:8830832e906a4004b4591eb508e0f03d4cc08e107a99a5bf34d12a3eb2a7076e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/522VI56QQ32EIFGVUJRPXJ6USF/bundle.json","state_url":"https://pith.science/pith/522VI56QQ32EIFGVUJRPXJ6USF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/522VI56QQ32EIFGVUJRPXJ6USF/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-08T11:48:39Z","links":{"resolver":"https://pith.science/pith/522VI56QQ32EIFGVUJRPXJ6USF","bundle":"https://pith.science/pith/522VI56QQ32EIFGVUJRPXJ6USF/bundle.json","state":"https://pith.science/pith/522VI56QQ32EIFGVUJRPXJ6USF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/522VI56QQ32EIFGVUJRPXJ6USF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:522VI56QQ32EIFGVUJRPXJ6USF","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"b99352e3fb34c83f9692f0114570488872f8f3ffa70e39bedf16e4dea796d669","cross_cats_sorted":["cs.NA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2025-06-03T15:42:31Z","title_canon_sha256":"e27f033f051f421ed436bd23c21b73a7583f95a33a8f727d15cc069e56d54eab"},"schema_version":"1.0","source":{"id":"2506.03003","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.03003","created_at":"2026-07-05T11:15:13Z"},{"alias_kind":"arxiv_version","alias_value":"2506.03003v1","created_at":"2026-07-05T11:15:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.03003","created_at":"2026-07-05T11:15:13Z"},{"alias_kind":"pith_short_12","alias_value":"522VI56QQ32E","created_at":"2026-07-05T11:15:13Z"},{"alias_kind":"pith_short_16","alias_value":"522VI56QQ32EIFGV","created_at":"2026-07-05T11:15:13Z"},{"alias_kind":"pith_short_8","alias_value":"522VI56Q","created_at":"2026-07-05T11:15:13Z"}],"graph_snapshots":[{"event_id":"sha256:8830832e906a4004b4591eb508e0f03d4cc08e107a99a5bf34d12a3eb2a7076e","target":"graph","created_at":"2026-07-05T11:15:13Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2506.03003/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"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","authors_text":"Sheehan Olver","cross_cats":["cs.NA"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2025-06-03T15:42:31Z","title":"Newtonian potentials of Legendre polynomials on rectangles have displacement structure"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.03003","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:431c595fe0cd914e54a0d122452eb4c4322cc710fbc1cab61b841f9ed878f2c0","target":"record","created_at":"2026-07-05T11:15:13Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"b99352e3fb34c83f9692f0114570488872f8f3ffa70e39bedf16e4dea796d669","cross_cats_sorted":["cs.NA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2025-06-03T15:42:31Z","title_canon_sha256":"e27f033f051f421ed436bd23c21b73a7583f95a33a8f727d15cc069e56d54eab"},"schema_version":"1.0","source":{"id":"2506.03003","kind":"arxiv","version":1}},"canonical_sha256":"eeb55477d086f44414d5a262fba7d4916578992f5ed83e1650442ded80ca673c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eeb55477d086f44414d5a262fba7d4916578992f5ed83e1650442ded80ca673c","first_computed_at":"2026-07-05T11:15:13.177433Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:15:13.177433Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"N9xLj+eZOcy3OHqbrk9DVqAutFy0S0kPsO6pKneheU/+Tm1a9XL/nAWE22k/B3mbacFV72mqf8f76I2VJCwrCg==","signature_status":"signed_v1","signed_at":"2026-07-05T11:15:13.177874Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.03003","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:431c595fe0cd914e54a0d122452eb4c4322cc710fbc1cab61b841f9ed878f2c0","sha256:8830832e906a4004b4591eb508e0f03d4cc08e107a99a5bf34d12a3eb2a7076e"],"state_sha256":"77f13bb724b715984360ba97cc4a8af2c8dee8b3357b48f3f1549c0691ccf1ee"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"phy6npKUOiHBVdVtNFpxiu7QQRbaKKU6iWRBAtpS/9GUMX8Lt31rYX/XC5XmWBzw7ZDJLsQJh6XZ2fPBnlcXAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T11:48:39.807291Z","bundle_sha256":"b3d4bf81ed59bb083dfb7431da7a7e9af5f4816e03dcfd87c9186525ac2ffdfc"}}