{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:QPR3ZIDSRJ6MPHVQGO732MNA2W","short_pith_number":"pith:QPR3ZIDS","canonical_record":{"source":{"id":"1402.4252","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.NA","submitted_at":"2014-02-18T09:08:04Z","cross_cats_sorted":[],"title_canon_sha256":"ad185f0fd9aa043119e7b0e6f47aa46c64c44fb1ca0317fa52773342e846735b","abstract_canon_sha256":"ecf52e329a8faaf99e19154fec56ae36b9bfdc89d58ac90715a3037f8fd5cb11"},"schema_version":"1.0"},"canonical_sha256":"83e3bca0728a7cc79eb033bfbd31a0d5a403fb8a64d289cf14710ff67bdd8ddc","source":{"kind":"arxiv","id":"1402.4252","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:QPR3ZIDSRJ6MPHVQGO732MNA2W","target":"record","payload":{"canonical_record":{"source":{"id":"1402.4252","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.NA","submitted_at":"2014-02-18T09:08:04Z","cross_cats_sorted":[],"title_canon_sha256":"ad185f0fd9aa043119e7b0e6f47aa46c64c44fb1ca0317fa52773342e846735b","abstract_canon_sha256":"ecf52e329a8faaf99e19154fec56ae36b9bfdc89d58ac90715a3037f8fd5cb11"},"schema_version":"1.0"},"canonical_sha256":"83e3bca0728a7cc79eb033bfbd31a0d5a403fb8a64d289cf14710ff67bdd8ddc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:44:36.971824Z","signature_b64":"aL6d9680XIRWCCgTB08SQfcMSq6EQxRd2iOSSv43zTii3Od8t2rqMxaXseHNRiNzDFhza2FlW/2bq1SX7pQlBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"83e3bca0728a7cc79eb033bfbd31a0d5a403fb8a64d289cf14710ff67bdd8ddc","last_reissued_at":"2026-05-18T01:44:36.971364Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:44:36.971364Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1402.4252","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:44:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mWwP3A92OtLqpRMqR/4PaaLLgWq7jxh1oe/uHpRe5kxOJIe+ooChJXXmYgaerVimEFeuUCTri7toh/GMcmJ3Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T16:23:57.724553Z"},"content_sha256":"5ad2c644620fa2980e6535e2bd6e0f1e4b07374fb877ee1bfbd9255a27fcd52b","schema_version":"1.0","event_id":"sha256:5ad2c644620fa2980e6535e2bd6e0f1e4b07374fb877ee1bfbd9255a27fcd52b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:QPR3ZIDSRJ6MPHVQGO732MNA2W","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Finite-Volume Method for Nonlinear Nonlocal Equations with a Gradient Flow Structure","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Alina Chertock, Jos\\'e A. Carrillo, Yanghong Huang","submitted_at":"2014-02-18T09:08:04Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.4252","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:44:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"h32/NHKO1KvGTVyrp6HpdliQAE3feSf/JqHu1asGJ4vY9uZd5+RB6rpBnzsVmlPZiPKkl8ltA51gkSC9uu6kAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T16:23:57.724894Z"},"content_sha256":"8d4856d8135886159a2a1f160959738ace01bb1da1fff0b0250f27b991a6fddc","schema_version":"1.0","event_id":"sha256:8d4856d8135886159a2a1f160959738ace01bb1da1fff0b0250f27b991a6fddc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QPR3ZIDSRJ6MPHVQGO732MNA2W/bundle.json","state_url":"https://pith.science/pith/QPR3ZIDSRJ6MPHVQGO732MNA2W/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QPR3ZIDSRJ6MPHVQGO732MNA2W/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-23T16:23:57Z","links":{"resolver":"https://pith.science/pith/QPR3ZIDSRJ6MPHVQGO732MNA2W","bundle":"https://pith.science/pith/QPR3ZIDSRJ6MPHVQGO732MNA2W/bundle.json","state":"https://pith.science/pith/QPR3ZIDSRJ6MPHVQGO732MNA2W/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QPR3ZIDSRJ6MPHVQGO732MNA2W/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UjdHjILaQJB6yYLhkISG8n2Ayu+/1V6Msj9Yxe2jwu9XirDRPtlFzzN+ZznJeSeNSohMhxJxMoqmz5/vQe1PCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T16:23:57.726748Z","bundle_sha256":"9e9f29df2790e6230bc4c561186a09a7dcc5d85499d2161ccaa484c63490f066"}}