{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:QPR3ZIDSRJ6MPHVQGO732MNA2W","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":"ecf52e329a8faaf99e19154fec56ae36b9bfdc89d58ac90715a3037f8fd5cb11","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.NA","submitted_at":"2014-02-18T09:08:04Z","title_canon_sha256":"ad185f0fd9aa043119e7b0e6f47aa46c64c44fb1ca0317fa52773342e846735b"},"schema_version":"1.0","source":{"id":"1402.4252","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.4252","created_at":"2026-05-18T01:44:36Z"},{"alias_kind":"arxiv_version","alias_value":"1402.4252v2","created_at":"2026-05-18T01:44:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.4252","created_at":"2026-05-18T01:44:36Z"},{"alias_kind":"pith_short_12","alias_value":"QPR3ZIDSRJ6M","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_16","alias_value":"QPR3ZIDSRJ6MPHVQ","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_8","alias_value":"QPR3ZIDS","created_at":"2026-05-18T12:28:46Z"}],"graph_snapshots":[{"event_id":"sha256:8d4856d8135886159a2a1f160959738ace01bb1da1fff0b0250f27b991a6fddc","target":"graph","created_at":"2026-05-18T01:44:36Z","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 positivity preserving entropy decreasing finite volume scheme for nonlinear nonlocal equations with a gradient flow structure. These properties allow for accurate computations of stationary states and long-time asymptotics demonstrated by suitably chosen test cases in which these features of the scheme are essential. The proposed scheme is able to cope with non-smooth stationary states, different time scales including metastability, as well as concentrations and self-similar behavior induced by singular nonlocal kernels. We use the scheme to explore properties of these equations b","authors_text":"Alina Chertock, Jos\\'e A. Carrillo, Yanghong Huang","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.NA","submitted_at":"2014-02-18T09:08:04Z","title":"A Finite-Volume Method for Nonlinear Nonlocal Equations with a Gradient Flow Structure"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.4252","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":"sha256:5ad2c644620fa2980e6535e2bd6e0f1e4b07374fb877ee1bfbd9255a27fcd52b","target":"record","created_at":"2026-05-18T01:44:36Z","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":"ecf52e329a8faaf99e19154fec56ae36b9bfdc89d58ac90715a3037f8fd5cb11","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.NA","submitted_at":"2014-02-18T09:08:04Z","title_canon_sha256":"ad185f0fd9aa043119e7b0e6f47aa46c64c44fb1ca0317fa52773342e846735b"},"schema_version":"1.0","source":{"id":"1402.4252","kind":"arxiv","version":2}},"canonical_sha256":"83e3bca0728a7cc79eb033bfbd31a0d5a403fb8a64d289cf14710ff67bdd8ddc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"83e3bca0728a7cc79eb033bfbd31a0d5a403fb8a64d289cf14710ff67bdd8ddc","first_computed_at":"2026-05-18T01:44:36.971364Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:44:36.971364Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aL6d9680XIRWCCgTB08SQfcMSq6EQxRd2iOSSv43zTii3Od8t2rqMxaXseHNRiNzDFhza2FlW/2bq1SX7pQlBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:44:36.971824Z","signed_message":"canonical_sha256_bytes"},"source_id":"1402.4252","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5ad2c644620fa2980e6535e2bd6e0f1e4b07374fb877ee1bfbd9255a27fcd52b","sha256:8d4856d8135886159a2a1f160959738ace01bb1da1fff0b0250f27b991a6fddc"],"state_sha256":"69eee1c2c4201b308922c6eedab4ee4f636f695348abb4e8fc705156014f7cc1"}