{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:ERAZJCVGO5CQQXDMQEPQGSZB52","short_pith_number":"pith:ERAZJCVG","schema_version":"1.0","canonical_sha256":"2441948aa67745085c6c811f034b21ee8d9a3defd5a6ee4e3b31a131bd3ca6f8","source":{"kind":"arxiv","id":"2506.04918","version":1},"attestation_state":"computed","paper":{"title":"Orthogonality of polar Legendre polynomials and approximation","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Abdelhamid Rehouma","submitted_at":"2025-06-05T11:53:00Z","abstract_excerpt":"Let $\\{Q_{n}(x)\\}$ be a system of integral Legendre polynomials of degree exactly n,and let $\\{P_{n}(x)\\}$ be polar polynomials primitives of integral Legendre polynomials. We derive some identities and relations and extremal problems and minimization involving of polar integral Legendre polynomials."},"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":"2506.04918","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.CV","submitted_at":"2025-06-05T11:53:00Z","cross_cats_sorted":[],"title_canon_sha256":"f97aedeca2710f343d4f7886e4c4b4e11f30de5537590f2efdcf8db7a758fa5f","abstract_canon_sha256":"d98a8ffecf33b5eca3bac5d3150f55720ffef1273bb512dbb8f5f5c893c75a06"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:16:39.083501Z","signature_b64":"jLkbC3A49EMULy1gBsstaiR9f5QHCDfVcTK+//BZEsoauY/P8yyFZZVLJDHmOyoXeCIno8v3YR/Qvu4Lq3opCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2441948aa67745085c6c811f034b21ee8d9a3defd5a6ee4e3b31a131bd3ca6f8","last_reissued_at":"2026-07-05T11:16:39.082992Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:16:39.082992Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Orthogonality of polar Legendre polynomials and approximation","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Abdelhamid Rehouma","submitted_at":"2025-06-05T11:53:00Z","abstract_excerpt":"Let $\\{Q_{n}(x)\\}$ be a system of integral Legendre polynomials of degree exactly n,and let $\\{P_{n}(x)\\}$ be polar polynomials primitives of integral Legendre polynomials. We derive some identities and relations and extremal problems and minimization involving of polar integral Legendre polynomials."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.04918","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/2506.04918/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":"2506.04918","created_at":"2026-07-05T11:16:39.083055+00:00"},{"alias_kind":"arxiv_version","alias_value":"2506.04918v1","created_at":"2026-07-05T11:16:39.083055+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.04918","created_at":"2026-07-05T11:16:39.083055+00:00"},{"alias_kind":"pith_short_12","alias_value":"ERAZJCVGO5CQ","created_at":"2026-07-05T11:16:39.083055+00:00"},{"alias_kind":"pith_short_16","alias_value":"ERAZJCVGO5CQQXDM","created_at":"2026-07-05T11:16:39.083055+00:00"},{"alias_kind":"pith_short_8","alias_value":"ERAZJCVG","created_at":"2026-07-05T11:16:39.083055+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/ERAZJCVGO5CQQXDMQEPQGSZB52","json":"https://pith.science/pith/ERAZJCVGO5CQQXDMQEPQGSZB52.json","graph_json":"https://pith.science/api/pith-number/ERAZJCVGO5CQQXDMQEPQGSZB52/graph.json","events_json":"https://pith.science/api/pith-number/ERAZJCVGO5CQQXDMQEPQGSZB52/events.json","paper":"https://pith.science/paper/ERAZJCVG"},"agent_actions":{"view_html":"https://pith.science/pith/ERAZJCVGO5CQQXDMQEPQGSZB52","download_json":"https://pith.science/pith/ERAZJCVGO5CQQXDMQEPQGSZB52.json","view_paper":"https://pith.science/paper/ERAZJCVG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2506.04918&json=true","fetch_graph":"https://pith.science/api/pith-number/ERAZJCVGO5CQQXDMQEPQGSZB52/graph.json","fetch_events":"https://pith.science/api/pith-number/ERAZJCVGO5CQQXDMQEPQGSZB52/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ERAZJCVGO5CQQXDMQEPQGSZB52/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ERAZJCVGO5CQQXDMQEPQGSZB52/action/storage_attestation","attest_author":"https://pith.science/pith/ERAZJCVGO5CQQXDMQEPQGSZB52/action/author_attestation","sign_citation":"https://pith.science/pith/ERAZJCVGO5CQQXDMQEPQGSZB52/action/citation_signature","submit_replication":"https://pith.science/pith/ERAZJCVGO5CQQXDMQEPQGSZB52/action/replication_record"}},"created_at":"2026-07-05T11:16:39.083055+00:00","updated_at":"2026-07-05T11:16:39.083055+00:00"}