{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:PC7C7NMUBZARFRUUPE3ZAZQTM3","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":"ab9d4e43da7d879dc35fc6170e260a8c24989d9144886e52e7858f9622a941f1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-09-24T18:09:45Z","title_canon_sha256":"3f6714bf47608c09fdda8ba7112914a21c1f7b4772870d6fb22b940d77ceb5ed"},"schema_version":"1.0","source":{"id":"1509.07461","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.07461","created_at":"2026-05-18T01:32:08Z"},{"alias_kind":"arxiv_version","alias_value":"1509.07461v1","created_at":"2026-05-18T01:32:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.07461","created_at":"2026-05-18T01:32:08Z"},{"alias_kind":"pith_short_12","alias_value":"PC7C7NMUBZAR","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_16","alias_value":"PC7C7NMUBZARFRUU","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_8","alias_value":"PC7C7NMU","created_at":"2026-05-18T12:29:37Z"}],"graph_snapshots":[{"event_id":"sha256:f19c1fdaa5cd53691eb4256830ac5d6824adf9f79787d7b6b87b94f69f894af1","target":"graph","created_at":"2026-05-18T01:32:08Z","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 propose a numerical method to solve general hyperbolic systems in any space dimension using forward Euler time stepping and continuous finite elements on non-uniform grids. The properties of the method are based on the introduction of an artificial dissipation that is defined so that any convex invariant sets containing the initial data is an invariant domain for the method. The invariant domain property is proved for any hyperbolic system provided a CFL condition holds. The solution is also shown to satisfy a discrete entropy inequality for every admissible entropy of the system. The metho","authors_text":"Bojan Popov, Jean-Luc Guermond","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-09-24T18:09:45Z","title":"Invariant domains and first-order continuous finite element approximation for hyperbolic systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.07461","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:eb9c5b8b1f2ee431abe4c2f1a3e67d83800f5814627b90502d93de93e2af8d19","target":"record","created_at":"2026-05-18T01:32:08Z","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":"ab9d4e43da7d879dc35fc6170e260a8c24989d9144886e52e7858f9622a941f1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-09-24T18:09:45Z","title_canon_sha256":"3f6714bf47608c09fdda8ba7112914a21c1f7b4772870d6fb22b940d77ceb5ed"},"schema_version":"1.0","source":{"id":"1509.07461","kind":"arxiv","version":1}},"canonical_sha256":"78be2fb5940e4112c694793790661366c52ab74f456dd7674e02cb06b5081f3c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"78be2fb5940e4112c694793790661366c52ab74f456dd7674e02cb06b5081f3c","first_computed_at":"2026-05-18T01:32:08.898358Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:32:08.898358Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AeCuJzJyTEwxr0X6AYaM5baO0/zQFzBvnSsHctbne4LXCrzCT23xY65Ev8mce2cppVJFNZ4udtgjuPs2lhkgAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:32:08.898963Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.07461","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:eb9c5b8b1f2ee431abe4c2f1a3e67d83800f5814627b90502d93de93e2af8d19","sha256:f19c1fdaa5cd53691eb4256830ac5d6824adf9f79787d7b6b87b94f69f894af1"],"state_sha256":"72fd761ef033922dfbd990886a3f8b443fd55372a1ce89035a2bb19b141228de"}