{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:TGR3QPB7TCJKTMS4N3446YXJCH","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":"8b7c4e4c2d961570ed5daf39b3f4684d8d3c655d4b965505259c991ab5fe9901","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-10-03T02:42:45Z","title_canon_sha256":"87597d48e1a9be2448cb2d51975f9fe7faa9a9faa6d77910e6753e12f8d466ab"},"schema_version":"1.0","source":{"id":"1710.00964","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.00964","created_at":"2026-05-18T00:33:47Z"},{"alias_kind":"arxiv_version","alias_value":"1710.00964v1","created_at":"2026-05-18T00:33:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.00964","created_at":"2026-05-18T00:33:47Z"},{"alias_kind":"pith_short_12","alias_value":"TGR3QPB7TCJK","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_16","alias_value":"TGR3QPB7TCJKTMS4","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_8","alias_value":"TGR3QPB7","created_at":"2026-05-18T12:31:46Z"}],"graph_snapshots":[{"event_id":"sha256:58bcf7216ef43609faa29198f5ade22c620694c08ed52bc6990bd64c84d64faa","target":"graph","created_at":"2026-05-18T00:33:47Z","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 design, analyze and numerically validate a novel discontinuous Galerkin method for solving the coagulation-fragmentation equations. The DG discretization is applied to the conservative form of the model, with flux terms evaluated by Gaussian quadrature with $Q=k+1$ quadrature points for polynomials of degree $k$. The positivity of the numerical solution is enforced through a simple scaling limiter based on positive cell averages. The positivity of cell averages is propagated by the time discretization provided a proper time step restriction is imposed.","authors_text":"Gerald Warnecke, Hailiang Liu, Robin Gr\\\"opler","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-10-03T02:42:45Z","title":"A high order positivity preserving DG method for coagulation-fragmentation equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.00964","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":"sha256:716c725a6f59e0c46db3021f0b1b85dacc0f993171ecf0915de5bc49d1cda5de","target":"record","created_at":"2026-05-18T00:33:47Z","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":"8b7c4e4c2d961570ed5daf39b3f4684d8d3c655d4b965505259c991ab5fe9901","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-10-03T02:42:45Z","title_canon_sha256":"87597d48e1a9be2448cb2d51975f9fe7faa9a9faa6d77910e6753e12f8d466ab"},"schema_version":"1.0","source":{"id":"1710.00964","kind":"arxiv","version":1}},"canonical_sha256":"99a3b83c3f9892a9b25c6ef9cf62e911fa4b195cbbc8b5dbf75e6b91be7e3980","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"99a3b83c3f9892a9b25c6ef9cf62e911fa4b195cbbc8b5dbf75e6b91be7e3980","first_computed_at":"2026-05-18T00:33:47.364162Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:33:47.364162Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4EYiSDIkpvEs4TkHEtQyezLNmmPNfXZc696DpcFmz153IdwotvxosChyYLp7RdnE9mIvSZ31A1ev+9KGpnTYDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:33:47.364791Z","signed_message":"canonical_sha256_bytes"},"source_id":"1710.00964","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:716c725a6f59e0c46db3021f0b1b85dacc0f993171ecf0915de5bc49d1cda5de","sha256:58bcf7216ef43609faa29198f5ade22c620694c08ed52bc6990bd64c84d64faa"],"state_sha256":"1d48f18fc092f751e95f17d82e8f7df62094dfb8d3a2f03e2372d3f5f2c5fd29"}