{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:GE7435ORMKKM6OQSVZ5XBV6FK2","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":"8d6bd7396dd52c6456fa325f65615ff53e5a56ab7dae00195a9633a237285b70","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-09-23T18:49:45Z","title_canon_sha256":"c8a6cf56746d522d2333f54a6693ae1addfb697b9b6144e8faae52a138ce9570"},"schema_version":"1.0","source":{"id":"1409.6692","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.6692","created_at":"2026-05-18T02:26:02Z"},{"alias_kind":"arxiv_version","alias_value":"1409.6692v2","created_at":"2026-05-18T02:26:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.6692","created_at":"2026-05-18T02:26:02Z"},{"alias_kind":"pith_short_12","alias_value":"GE7435ORMKKM","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_16","alias_value":"GE7435ORMKKM6OQS","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_8","alias_value":"GE7435OR","created_at":"2026-05-18T12:28:30Z"}],"graph_snapshots":[{"event_id":"sha256:b2f8ab7a1e0d4f9e3f8bbddcba80722c2df341de02fec5fd8420af5027ab1990","target":"graph","created_at":"2026-05-18T02:26:02Z","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":"We study semi-Lagrangian discontinuous Galerkin (SLDG) and Runge-Kutta discontinuous Galerkin (RKDG) schemes for some front propagation problems in the presence of an obstacle term, modeled by a nonlinear Hamilton-Jacobi equation of the form $\\min(u_t + c u_x, u - g(x))=0$, in one space dimension. New convergence results and error bounds are obtained for Lipschitz regular data. These \"low regularity\" assumptions are the natural ones for the solutions of the studied equations.","authors_text":"Chi-Wang Shu (DAM), Olivier Bokanowski (LJLL, UMA/OC), Yingda Cheng","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-09-23T18:49:45Z","title":"Convergence of discontinuous Galerkin schemes for front propagation with obstacles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.6692","kind":"arxiv","version":2},"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":"sha256:0c1f3843cada4ba57acadf60acff494adbd91cf18fc29992e72995a6d1ccfacb","target":"record","created_at":"2026-05-18T02:26:02Z","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":"8d6bd7396dd52c6456fa325f65615ff53e5a56ab7dae00195a9633a237285b70","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-09-23T18:49:45Z","title_canon_sha256":"c8a6cf56746d522d2333f54a6693ae1addfb697b9b6144e8faae52a138ce9570"},"schema_version":"1.0","source":{"id":"1409.6692","kind":"arxiv","version":2}},"canonical_sha256":"313fcdf5d16294cf3a12ae7b70d7c5569d6a1570ddcc31a3de00eb6e276bbd20","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"313fcdf5d16294cf3a12ae7b70d7c5569d6a1570ddcc31a3de00eb6e276bbd20","first_computed_at":"2026-05-18T02:26:02.557924Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:26:02.557924Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"V9MFl+aOdWn5zqiaK9kJZ0mFv7vxhaSYa9aOG1IgbUOzc56PjtsJ9GyFJOnaoivrJoE7OemoL0HdDvQplGYyBA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:26:02.558374Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.6692","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0c1f3843cada4ba57acadf60acff494adbd91cf18fc29992e72995a6d1ccfacb","sha256:b2f8ab7a1e0d4f9e3f8bbddcba80722c2df341de02fec5fd8420af5027ab1990"],"state_sha256":"af204d8f2e6022ce8b19f69a0d459be4c3b8d65f6e79dc688e42f23759a5df61"}