{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:WG57OFB5A7YCRN7UYX2BBT5IAM","short_pith_number":"pith:WG57OFB5","schema_version":"1.0","canonical_sha256":"b1bbf7143d07f028b7f4c5f410cfa8030df1403d8bff8f40c0d8c23e358e36ed","source":{"kind":"arxiv","id":"1907.08309","version":1},"attestation_state":"computed","paper":{"title":"A roadmap for Generalized Plane Waves and their interpolation properties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Guillaume Sylvand, Lise-Marie Imbert-Gerard","submitted_at":"2019-07-18T22:15:30Z","abstract_excerpt":"This work focuses on the study of partial differential equation (PDE) based basis function for Discontinuous Galerkin methods to solve numerically wave-related boundary value problems with variable coefficients. To tackle problems with constant coefficients, wave-based methods have been widely studied in the literature: they rely on the concept of Trefftz functions, i.e. local solutions to the governing PDE, using oscillating basis functions rather than polynomial functions to represent the numerical solution. Generalized Plane Waves (GPWs) are an alternative developed to tackle problems with "},"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":"1907.08309","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-07-18T22:15:30Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"0893c035cd5c4095abe6f7ce95de72afabca580826df36a4e43bc84f43782e62","abstract_canon_sha256":"7ccc696a6f68374679b5d289cf90d116503afdf55de0e320f2ffffdce2bacba6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:40:10.258680Z","signature_b64":"A8HJQJ4jQ46nRfo26J+lvRcOpK45SENH1mf0iKxU8NXEXr/fBwwtv4gNH8HmsmUfX++HpVBgOg+CCzeizbQfDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b1bbf7143d07f028b7f4c5f410cfa8030df1403d8bff8f40c0d8c23e358e36ed","last_reissued_at":"2026-05-17T23:40:10.258117Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:40:10.258117Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A roadmap for Generalized Plane Waves and their interpolation properties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Guillaume Sylvand, Lise-Marie Imbert-Gerard","submitted_at":"2019-07-18T22:15:30Z","abstract_excerpt":"This work focuses on the study of partial differential equation (PDE) based basis function for Discontinuous Galerkin methods to solve numerically wave-related boundary value problems with variable coefficients. To tackle problems with constant coefficients, wave-based methods have been widely studied in the literature: they rely on the concept of Trefftz functions, i.e. local solutions to the governing PDE, using oscillating basis functions rather than polynomial functions to represent the numerical solution. Generalized Plane Waves (GPWs) are an alternative developed to tackle problems with "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.08309","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":"1907.08309","created_at":"2026-05-17T23:40:10.258193+00:00"},{"alias_kind":"arxiv_version","alias_value":"1907.08309v1","created_at":"2026-05-17T23:40:10.258193+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.08309","created_at":"2026-05-17T23:40:10.258193+00:00"},{"alias_kind":"pith_short_12","alias_value":"WG57OFB5A7YC","created_at":"2026-05-18T12:33:30.264802+00:00"},{"alias_kind":"pith_short_16","alias_value":"WG57OFB5A7YCRN7U","created_at":"2026-05-18T12:33:30.264802+00:00"},{"alias_kind":"pith_short_8","alias_value":"WG57OFB5","created_at":"2026-05-18T12:33:30.264802+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/WG57OFB5A7YCRN7UYX2BBT5IAM","json":"https://pith.science/pith/WG57OFB5A7YCRN7UYX2BBT5IAM.json","graph_json":"https://pith.science/api/pith-number/WG57OFB5A7YCRN7UYX2BBT5IAM/graph.json","events_json":"https://pith.science/api/pith-number/WG57OFB5A7YCRN7UYX2BBT5IAM/events.json","paper":"https://pith.science/paper/WG57OFB5"},"agent_actions":{"view_html":"https://pith.science/pith/WG57OFB5A7YCRN7UYX2BBT5IAM","download_json":"https://pith.science/pith/WG57OFB5A7YCRN7UYX2BBT5IAM.json","view_paper":"https://pith.science/paper/WG57OFB5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1907.08309&json=true","fetch_graph":"https://pith.science/api/pith-number/WG57OFB5A7YCRN7UYX2BBT5IAM/graph.json","fetch_events":"https://pith.science/api/pith-number/WG57OFB5A7YCRN7UYX2BBT5IAM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WG57OFB5A7YCRN7UYX2BBT5IAM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WG57OFB5A7YCRN7UYX2BBT5IAM/action/storage_attestation","attest_author":"https://pith.science/pith/WG57OFB5A7YCRN7UYX2BBT5IAM/action/author_attestation","sign_citation":"https://pith.science/pith/WG57OFB5A7YCRN7UYX2BBT5IAM/action/citation_signature","submit_replication":"https://pith.science/pith/WG57OFB5A7YCRN7UYX2BBT5IAM/action/replication_record"}},"created_at":"2026-05-17T23:40:10.258193+00:00","updated_at":"2026-05-17T23:40:10.258193+00:00"}