{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:UKQC26NFAGS57UXFQ4VCY6OMSW","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":"2d568b529b9e212d3c9872529b96ad87d87da988791d1f769b1989e800521bf9","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2009-08-30T16:51:38Z","title_canon_sha256":"4a2a2b09570720c52403e5f3f8bac6bcf30079212057d1bb4a4d6fdcdd8b34fa"},"schema_version":"1.0","source":{"id":"0908.4402","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0908.4402","created_at":"2026-06-03T23:06:28Z"},{"alias_kind":"arxiv_version","alias_value":"0908.4402v1","created_at":"2026-06-03T23:06:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0908.4402","created_at":"2026-06-03T23:06:28Z"},{"alias_kind":"pith_short_12","alias_value":"UKQC26NFAGS5","created_at":"2026-06-03T23:06:28Z"},{"alias_kind":"pith_short_16","alias_value":"UKQC26NFAGS57UXF","created_at":"2026-06-03T23:06:28Z"},{"alias_kind":"pith_short_8","alias_value":"UKQC26NF","created_at":"2026-06-03T23:06:28Z"}],"graph_snapshots":[{"event_id":"sha256:ed7a76855f53539df6ce6944541800f76794f64306f22ae6cf14075a454a59ae","target":"graph","created_at":"2026-06-03T23:06:28Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/0908.4402/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider 3-point numerical schemes for scalar Conservation Laws, that are oscillatory either to their dispersive or anti-diffusive nature. Oscillations are responsible for the increase of the Total Variation (TV); a bound on which is crucial for the stability of the numerical scheme. It has been noticed (\\cite{Arvanitis.2001}, \\cite{Arvanitis.2004}, \\cite{Sfakianakis.2008}) that the use of non-uniform adaptively redefined meshes, that take into account the geometry of the numerical solution itself, is capable of taming oscillations; hence improving the stability properties of the numerical ","authors_text":"Nikolaos Sfakianakis","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2009-08-30T16:51:38Z","title":"Adaptive mesh reconstruction: Total Variation Bound"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0908.4402","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":"sha256:2f1d9c49dbf0f2d0ea18fa369285eff402e9e7f5c75642c1dcbcb2419e8fa9bd","target":"record","created_at":"2026-06-03T23:06:28Z","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":"2d568b529b9e212d3c9872529b96ad87d87da988791d1f769b1989e800521bf9","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2009-08-30T16:51:38Z","title_canon_sha256":"4a2a2b09570720c52403e5f3f8bac6bcf30079212057d1bb4a4d6fdcdd8b34fa"},"schema_version":"1.0","source":{"id":"0908.4402","kind":"arxiv","version":1}},"canonical_sha256":"a2a02d79a501a5dfd2e5872a2c79cc95a985119df6eea4acb7ef99a012f70cfe","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a2a02d79a501a5dfd2e5872a2c79cc95a985119df6eea4acb7ef99a012f70cfe","first_computed_at":"2026-06-03T23:06:28.445947Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-03T23:06:28.445947Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YWHmG2aHp5SSBjrTqJeYEV0lh8or0N9H46fjBOkRW5knK92gDMrIBpV2MepD8LM9Ra5BAsDhl5UVWoVXibQrDA==","signature_status":"signed_v1","signed_at":"2026-06-03T23:06:28.446361Z","signed_message":"canonical_sha256_bytes"},"source_id":"0908.4402","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2f1d9c49dbf0f2d0ea18fa369285eff402e9e7f5c75642c1dcbcb2419e8fa9bd","sha256:ed7a76855f53539df6ce6944541800f76794f64306f22ae6cf14075a454a59ae"],"state_sha256":"e99963c4018fb7554f16cefa0cae6cc52dcf5524bb23ef5f745326084aead494"}