{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:G6NZ7QXW5DPF2BGDXSOOLC3ST4","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":"b39ba5e913e8830b340d9c55b3ec03ef2d87b2e82f806f138a3995a0deb65c9a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-02-02T17:08:24Z","title_canon_sha256":"58dbdd737bcd22fb90f9a6337c84e994fe23c66d0ee29c6a0d836ddf0882e1bc"},"schema_version":"1.0","source":{"id":"1102.0493","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.0493","created_at":"2026-05-18T03:45:21Z"},{"alias_kind":"arxiv_version","alias_value":"1102.0493v2","created_at":"2026-05-18T03:45:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.0493","created_at":"2026-05-18T03:45:21Z"},{"alias_kind":"pith_short_12","alias_value":"G6NZ7QXW5DPF","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_16","alias_value":"G6NZ7QXW5DPF2BGD","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_8","alias_value":"G6NZ7QXW","created_at":"2026-05-18T12:26:28Z"}],"graph_snapshots":[{"event_id":"sha256:418b2a2a55ab479e82bc7d5de23dfb8eab976c4b75ec6c5d11b623a5a99a2347","target":"graph","created_at":"2026-05-18T03:45:21Z","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 consider semi-discrete first-order finite difference schemes for a nonlinear degenerate convection-diffusion equations in one space dimension, and prove an L1 error estimate. Precisely, we show that the L1 loc difference between the approximate solution and the unique entropy solution converges at a rate O(\\Deltax 1/11), where \\Deltax is the spatial mesh size. If the diffusion is linear, we get the convergence rate O(\\Deltax 1/2), the point being that the O is independent of the size of the diffusion","authors_text":"K. H. Karlsen, N. H. Risebro, U. Koley","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-02-02T17:08:24Z","title":"An error estimate for the finite difference approximation to degenerate convection -diffusion equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.0493","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":"sha256:6dd7776d1017e31b8ca7c2c44fb3d287209b1558555a61a0bc3dea4c5b7ec773","target":"record","created_at":"2026-05-18T03:45:21Z","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":"b39ba5e913e8830b340d9c55b3ec03ef2d87b2e82f806f138a3995a0deb65c9a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-02-02T17:08:24Z","title_canon_sha256":"58dbdd737bcd22fb90f9a6337c84e994fe23c66d0ee29c6a0d836ddf0882e1bc"},"schema_version":"1.0","source":{"id":"1102.0493","kind":"arxiv","version":2}},"canonical_sha256":"379b9fc2f6e8de5d04c3bc9ce58b729f20be921269ea48fc00c0792e8a771ff1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"379b9fc2f6e8de5d04c3bc9ce58b729f20be921269ea48fc00c0792e8a771ff1","first_computed_at":"2026-05-18T03:45:21.768607Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:45:21.768607Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GiKcOMaLIUog5rz3RCUa4oLH7Pjcrv6aT/MPQWazxFzzGr2NXCJH4dgG7guc4iWH+LNIGsdwu2PMDR4Zy8baCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:45:21.769054Z","signed_message":"canonical_sha256_bytes"},"source_id":"1102.0493","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6dd7776d1017e31b8ca7c2c44fb3d287209b1558555a61a0bc3dea4c5b7ec773","sha256:418b2a2a55ab479e82bc7d5de23dfb8eab976c4b75ec6c5d11b623a5a99a2347"],"state_sha256":"dcda5bba1fe962849fc37c99344cb119d4064eaf7b30284347d7dce360b28b76"}