{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:236KXXN572LXWKNHVVYMCO3WWH","short_pith_number":"pith:236KXXN5","schema_version":"1.0","canonical_sha256":"d6fcabddbdfe977b29a7ad70c13b76b1eee44272a8540cb6f49d983d46c3110f","source":{"kind":"arxiv","id":"2605.29334","version":1},"attestation_state":"computed","paper":{"title":"Weighted Quadrature on Unstructured Splines","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Falai Chen, Ji Sheng, Xiaodong Wei","submitted_at":"2026-05-28T04:09:26Z","abstract_excerpt":"This work presents a weighted quadrature (WQ) method to fast assemble Galerkin matrices based on unstructured spline surfaces. The method is developed upon a particular variant of unstructured splines, namely the bicubic analysis-suitable unstructured T-splines (ASUTS). While existing WQ approaches have significant speedup for structured splines (e.g., B-splines), their extension to unstructured splines faces several challenges: (1) lack of a global parametric domain for defining quadrature points, (2) a varying number of basis functions across elements that complicates the determination of th"},"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":"2605.29334","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2026-05-28T04:09:26Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"c816f9e6c60ec1177d064678f7df2880c64842c3b08a52165f4f0163a3e95293","abstract_canon_sha256":"c07d3ac7c371acbba05431e708b4a33b11ca88594658d16cd89a84259c16bfa6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-29T01:05:33.361470Z","signature_b64":"nS8oONt6B75pjQA0LejTD+CHZ6zf39aXhYOcjvT9yCi/Meo4tIpTsq8OxU2wtqqYwfhwhArhXLbolq9GHz4fAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d6fcabddbdfe977b29a7ad70c13b76b1eee44272a8540cb6f49d983d46c3110f","last_reissued_at":"2026-05-29T01:05:33.360707Z","signature_status":"signed_v1","first_computed_at":"2026-05-29T01:05:33.360707Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Weighted Quadrature on Unstructured Splines","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Falai Chen, Ji Sheng, Xiaodong Wei","submitted_at":"2026-05-28T04:09:26Z","abstract_excerpt":"This work presents a weighted quadrature (WQ) method to fast assemble Galerkin matrices based on unstructured spline surfaces. The method is developed upon a particular variant of unstructured splines, namely the bicubic analysis-suitable unstructured T-splines (ASUTS). While existing WQ approaches have significant speedup for structured splines (e.g., B-splines), their extension to unstructured splines faces several challenges: (1) lack of a global parametric domain for defining quadrature points, (2) a varying number of basis functions across elements that complicates the determination of th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.29334","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/2605.29334/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":"2605.29334","created_at":"2026-05-29T01:05:33.360837+00:00"},{"alias_kind":"arxiv_version","alias_value":"2605.29334v1","created_at":"2026-05-29T01:05:33.360837+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.29334","created_at":"2026-05-29T01:05:33.360837+00:00"},{"alias_kind":"pith_short_12","alias_value":"236KXXN572LX","created_at":"2026-05-29T01:05:33.360837+00:00"},{"alias_kind":"pith_short_16","alias_value":"236KXXN572LXWKNH","created_at":"2026-05-29T01:05:33.360837+00:00"},{"alias_kind":"pith_short_8","alias_value":"236KXXN5","created_at":"2026-05-29T01:05:33.360837+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/236KXXN572LXWKNHVVYMCO3WWH","json":"https://pith.science/pith/236KXXN572LXWKNHVVYMCO3WWH.json","graph_json":"https://pith.science/api/pith-number/236KXXN572LXWKNHVVYMCO3WWH/graph.json","events_json":"https://pith.science/api/pith-number/236KXXN572LXWKNHVVYMCO3WWH/events.json","paper":"https://pith.science/paper/236KXXN5"},"agent_actions":{"view_html":"https://pith.science/pith/236KXXN572LXWKNHVVYMCO3WWH","download_json":"https://pith.science/pith/236KXXN572LXWKNHVVYMCO3WWH.json","view_paper":"https://pith.science/paper/236KXXN5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2605.29334&json=true","fetch_graph":"https://pith.science/api/pith-number/236KXXN572LXWKNHVVYMCO3WWH/graph.json","fetch_events":"https://pith.science/api/pith-number/236KXXN572LXWKNHVVYMCO3WWH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/236KXXN572LXWKNHVVYMCO3WWH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/236KXXN572LXWKNHVVYMCO3WWH/action/storage_attestation","attest_author":"https://pith.science/pith/236KXXN572LXWKNHVVYMCO3WWH/action/author_attestation","sign_citation":"https://pith.science/pith/236KXXN572LXWKNHVVYMCO3WWH/action/citation_signature","submit_replication":"https://pith.science/pith/236KXXN572LXWKNHVVYMCO3WWH/action/replication_record"}},"created_at":"2026-05-29T01:05:33.360837+00:00","updated_at":"2026-05-29T01:05:33.360837+00:00"}