{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:BO5D62HU2WEGMLIEVQ53Q3KOJN","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":"fac14a348bfdaad9b8db1ec357bf95565aaff6ea1bdb6e9a11493737bd805c2b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2011-11-02T21:39:15Z","title_canon_sha256":"69543adaf1247d63e650e2ba5d92760de94e784b9bbe6efd5ee010a2952cc358"},"schema_version":"1.0","source":{"id":"1111.0671","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.0671","created_at":"2026-05-18T04:09:37Z"},{"alias_kind":"arxiv_version","alias_value":"1111.0671v1","created_at":"2026-05-18T04:09:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.0671","created_at":"2026-05-18T04:09:37Z"},{"alias_kind":"pith_short_12","alias_value":"BO5D62HU2WEG","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_16","alias_value":"BO5D62HU2WEGMLIE","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_8","alias_value":"BO5D62HU","created_at":"2026-05-18T12:26:24Z"}],"graph_snapshots":[{"event_id":"sha256:c1b801bb57ca943696f9121e6640f816354c4a91f7b956bbdac781be3d954163","target":"graph","created_at":"2026-05-18T04:09:37Z","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"},"paper":{"abstract_excerpt":"Weak Galerkin (WG) refers to general finite element methods for partial differential equations in which differential operators are approximated by weak forms through the usual integration by parts. In particular, WG methods allow the use of discontinuous finite element functions in the algorithm design. One of such examples was recently introduced by Wang and Ye for solving second order elliptic problems. The goal of this paper is to apply the WG method of Wang and Ye to the Helmholtz equation with high wave numbers. Several test scenarios are designed for a numerical investigation on the accu","authors_text":"Junping Wang, Lin Mu, Shan Zhao, Xiu Ye","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2011-11-02T21:39:15Z","title":"A Numerical Study on the Weak Galerkin Method for the Helmholtz Equation with Large Wave Numbers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.0671","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":"sha256:7c96e0af4a51a74e65c83a196e95c95cb2ac9516e0dca7f1215f03b6d9759ffe","target":"record","created_at":"2026-05-18T04:09:37Z","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":"fac14a348bfdaad9b8db1ec357bf95565aaff6ea1bdb6e9a11493737bd805c2b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2011-11-02T21:39:15Z","title_canon_sha256":"69543adaf1247d63e650e2ba5d92760de94e784b9bbe6efd5ee010a2952cc358"},"schema_version":"1.0","source":{"id":"1111.0671","kind":"arxiv","version":1}},"canonical_sha256":"0bba3f68f4d588662d04ac3bb86d4e4b48d1ad662b9b205e1d790efc77bf3a13","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0bba3f68f4d588662d04ac3bb86d4e4b48d1ad662b9b205e1d790efc77bf3a13","first_computed_at":"2026-05-18T04:09:37.176645Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:09:37.176645Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ps574m7X+b1ZSEqfbYfgabiu/SN8tk4EX6RIaSiwt4fDwX95yFfl795AvXLBFNR0kO1d4DTGQ3SHeILDRjJsDg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:09:37.177342Z","signed_message":"canonical_sha256_bytes"},"source_id":"1111.0671","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7c96e0af4a51a74e65c83a196e95c95cb2ac9516e0dca7f1215f03b6d9759ffe","sha256:c1b801bb57ca943696f9121e6640f816354c4a91f7b956bbdac781be3d954163"],"state_sha256":"be05d948c94372490264b0893f5809b4f11954f8e1cb56e74a6504a543b572fc"}