{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:HKYAR2HA2E37R73BOS4CXYZISW","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":"034b8f4b7560e8e0f7856d28c287a2fcdcc2f6c0364f58f534ef30bacdde1c3d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-07-05T05:58:46Z","title_canon_sha256":"4cc4d7e27bc9b12eadd1c61296f11bd728c4c2cade237cf2ca8f3a6dd298c31d"},"schema_version":"1.0","source":{"id":"1107.0786","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.0786","created_at":"2026-05-18T04:07:07Z"},{"alias_kind":"arxiv_version","alias_value":"1107.0786v2","created_at":"2026-05-18T04:07:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.0786","created_at":"2026-05-18T04:07:07Z"},{"alias_kind":"pith_short_12","alias_value":"HKYAR2HA2E37","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"HKYAR2HA2E37R73B","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"HKYAR2HA","created_at":"2026-05-18T12:26:30Z"}],"graph_snapshots":[{"event_id":"sha256:13e62c590554a540e97da5fe9d196f3f73abb61d0765a3ee4dfd5370fbb8a7bf","target":"graph","created_at":"2026-05-18T04:07:07Z","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":"The hydrodynamic limit for a kinetic model of chemotaxis is investigated. The limit equation is a non local conservation law, for which finite time blow-up occurs, giving rise to measure-valued solutions and discontinuous velocities. An adaptation of the notion of duality solutions, introduced for linear equations with discontinuous coefficients, leads to an existence result. Uniqueness is obtained through a precise definition of the nonlinear flux as well as the complete dynamics of aggregates, i.e. combinations of Dirac masses. Finally a particle method is used to build an adapted numerical ","authors_text":"Fran\\c{c}ois James (MAPMO), INRIA Rocquencourt), Nicolas Vauchelet (LJLL","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-07-05T05:58:46Z","title":"Chemotaxis: from kinetic equations to aggregate dynamics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.0786","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:c22290c01977f1f1a43bdceff4443bb17a1bd9b9f13089acc3a8a1526ea8844f","target":"record","created_at":"2026-05-18T04:07:07Z","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":"034b8f4b7560e8e0f7856d28c287a2fcdcc2f6c0364f58f534ef30bacdde1c3d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-07-05T05:58:46Z","title_canon_sha256":"4cc4d7e27bc9b12eadd1c61296f11bd728c4c2cade237cf2ca8f3a6dd298c31d"},"schema_version":"1.0","source":{"id":"1107.0786","kind":"arxiv","version":2}},"canonical_sha256":"3ab008e8e0d137f8ff6174b82be32895a7363167a61d64c00ca1be55d3160248","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3ab008e8e0d137f8ff6174b82be32895a7363167a61d64c00ca1be55d3160248","first_computed_at":"2026-05-18T04:07:07.797160Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:07:07.797160Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TrBhTMrX2UnO/byYogmtiNhKHKJI1fU3nQbPD1LA4iD41kXZPwvWMRYKcCpfocYTNscIZhwF89/dXCBvR2qxCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:07:07.797705Z","signed_message":"canonical_sha256_bytes"},"source_id":"1107.0786","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c22290c01977f1f1a43bdceff4443bb17a1bd9b9f13089acc3a8a1526ea8844f","sha256:13e62c590554a540e97da5fe9d196f3f73abb61d0765a3ee4dfd5370fbb8a7bf"],"state_sha256":"dd6f255f1f6cfc0cc0ab4df75659d47c4e0c345b056deba2cc5ba98275dea636"}