{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:6RRKEN4RGKPRAYGKFPCG6WDQON","short_pith_number":"pith:6RRKEN4R","schema_version":"1.0","canonical_sha256":"f462a23791329f1060ca2bc46f587073463ef04a01c7ab19fb5e3a973e2a4799","source":{"kind":"arxiv","id":"2502.07795","version":1},"attestation_state":"computed","paper":{"title":"Stabilizer-free Weak Galerkin Methods for Quad-Curl Problems on polyhedral Meshes without Convexity Assumptions","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Chunmei Wang, Shangyou Zhang","submitted_at":"2025-01-27T14:00:00Z","abstract_excerpt":"This paper introduces an efficient stabilizer-free weak Galerkin (WG) finite element method for solving the three-dimensional quad-curl problem. Leveraging bubble functions as a key analytical tool, the method extends the applicability of stabilizer-free WG approaches to non-convex elements in finite element partitions-a notable advancement over existing methods, which are restricted to convex elements. The proposed method maintains a simple, symmetric, and positive definite formulation. It achieves optimal error estimates for the exact solution in a discrete norm, as well as an optimal-order "},"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":"2502.07795","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.NA","submitted_at":"2025-01-27T14:00:00Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"ac79c08da995896c37596ee8a5cd50228209b3587b1dabde7799686a2c68e631","abstract_canon_sha256":"727de1762480fc53f0ff81c479c8871a74b9d1b3401ead55ee2c8cbde5b799d8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:13:09.965676Z","signature_b64":"EgM/oDpl4vCBFPy3FcuD55jH4LbrJJcEMH1wneA7pIZ/8afiDsQ8O8jckjCoqif0MN8JiozhcDDfpKtaIVnQBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f462a23791329f1060ca2bc46f587073463ef04a01c7ab19fb5e3a973e2a4799","last_reissued_at":"2026-07-05T10:13:09.965064Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:13:09.965064Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Stabilizer-free Weak Galerkin Methods for Quad-Curl Problems on polyhedral Meshes without Convexity Assumptions","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Chunmei Wang, Shangyou Zhang","submitted_at":"2025-01-27T14:00:00Z","abstract_excerpt":"This paper introduces an efficient stabilizer-free weak Galerkin (WG) finite element method for solving the three-dimensional quad-curl problem. Leveraging bubble functions as a key analytical tool, the method extends the applicability of stabilizer-free WG approaches to non-convex elements in finite element partitions-a notable advancement over existing methods, which are restricted to convex elements. The proposed method maintains a simple, symmetric, and positive definite formulation. It achieves optimal error estimates for the exact solution in a discrete norm, as well as an optimal-order "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.07795","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/2502.07795/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":"2502.07795","created_at":"2026-07-05T10:13:09.965130+00:00"},{"alias_kind":"arxiv_version","alias_value":"2502.07795v1","created_at":"2026-07-05T10:13:09.965130+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.07795","created_at":"2026-07-05T10:13:09.965130+00:00"},{"alias_kind":"pith_short_12","alias_value":"6RRKEN4RGKPR","created_at":"2026-07-05T10:13:09.965130+00:00"},{"alias_kind":"pith_short_16","alias_value":"6RRKEN4RGKPRAYGK","created_at":"2026-07-05T10:13:09.965130+00:00"},{"alias_kind":"pith_short_8","alias_value":"6RRKEN4R","created_at":"2026-07-05T10:13:09.965130+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2507.18896","citing_title":"A Simple and Robust Weak Galerkin Method for the Brinkman Equations on Non-Convex Polytopal Meshes","ref_index":32,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/6RRKEN4RGKPRAYGKFPCG6WDQON","json":"https://pith.science/pith/6RRKEN4RGKPRAYGKFPCG6WDQON.json","graph_json":"https://pith.science/api/pith-number/6RRKEN4RGKPRAYGKFPCG6WDQON/graph.json","events_json":"https://pith.science/api/pith-number/6RRKEN4RGKPRAYGKFPCG6WDQON/events.json","paper":"https://pith.science/paper/6RRKEN4R"},"agent_actions":{"view_html":"https://pith.science/pith/6RRKEN4RGKPRAYGKFPCG6WDQON","download_json":"https://pith.science/pith/6RRKEN4RGKPRAYGKFPCG6WDQON.json","view_paper":"https://pith.science/paper/6RRKEN4R","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2502.07795&json=true","fetch_graph":"https://pith.science/api/pith-number/6RRKEN4RGKPRAYGKFPCG6WDQON/graph.json","fetch_events":"https://pith.science/api/pith-number/6RRKEN4RGKPRAYGKFPCG6WDQON/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6RRKEN4RGKPRAYGKFPCG6WDQON/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6RRKEN4RGKPRAYGKFPCG6WDQON/action/storage_attestation","attest_author":"https://pith.science/pith/6RRKEN4RGKPRAYGKFPCG6WDQON/action/author_attestation","sign_citation":"https://pith.science/pith/6RRKEN4RGKPRAYGKFPCG6WDQON/action/citation_signature","submit_replication":"https://pith.science/pith/6RRKEN4RGKPRAYGKFPCG6WDQON/action/replication_record"}},"created_at":"2026-07-05T10:13:09.965130+00:00","updated_at":"2026-07-05T10:13:09.965130+00:00"}