{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:KZRBFSDPNG7NI2A7CKVDNWJBEA","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":"bf377e37d8d57abb4e3acf85dface1a2291ec75bf838521f4999ff3e08c0f177","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-07-10T13:54:29Z","title_canon_sha256":"7dd29a9d610f6a09cc8c7d79f8eceb547688317abcf7e42b3af7f32bf85d6d45"},"schema_version":"1.0","source":{"id":"1507.02900","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.02900","created_at":"2026-05-18T00:46:16Z"},{"alias_kind":"arxiv_version","alias_value":"1507.02900v2","created_at":"2026-05-18T00:46:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.02900","created_at":"2026-05-18T00:46:16Z"},{"alias_kind":"pith_short_12","alias_value":"KZRBFSDPNG7N","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_16","alias_value":"KZRBFSDPNG7NI2A7","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_8","alias_value":"KZRBFSDP","created_at":"2026-05-18T12:29:29Z"}],"graph_snapshots":[{"event_id":"sha256:7888b8cc9bda44adc057fb0e14e8cd2d2528e8fec8c26fd3dc520cb584812f67","target":"graph","created_at":"2026-05-18T00:46:16Z","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":"In this paper we present some basic uniqueness results for evolutive equations under density constraints. First, we develop a rigorous proof of a well-known result (among specialists) in the case where the spontaneous velocity field satisfies a monotonicity assumption: we prove the uniqueness of a solution for first order systems modeling crowd motion with hard congestion effects, introduced recently by \\emph{Maury et al.} The monotonicity of the velocity field implies that the $2-$Wasserstein distance along two solutions is $\\lambda$-contractive, which in particular implies uniqueness. In the","authors_text":"Alp\\'ar Rich\\'ard M\\'esz\\'aros, Simone Di Marino (SNS)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-07-10T13:54:29Z","title":"Uniqueness issues for evolution equations with density constraints"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.02900","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:f443bede1111e04ca398ba9061088f664f40d631987583535685b4496ad01880","target":"record","created_at":"2026-05-18T00:46:16Z","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":"bf377e37d8d57abb4e3acf85dface1a2291ec75bf838521f4999ff3e08c0f177","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-07-10T13:54:29Z","title_canon_sha256":"7dd29a9d610f6a09cc8c7d79f8eceb547688317abcf7e42b3af7f32bf85d6d45"},"schema_version":"1.0","source":{"id":"1507.02900","kind":"arxiv","version":2}},"canonical_sha256":"566212c86f69bed4681f12aa36d9212036a278eceaec2bd8d58625136c427faa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"566212c86f69bed4681f12aa36d9212036a278eceaec2bd8d58625136c427faa","first_computed_at":"2026-05-18T00:46:16.933304Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:46:16.933304Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TFif6Y938SqCZudHm+CiNXyPEmD3t0oCr/8aLJBVus0xsSz1mPqlWkSreoAagg321NUxZGrt3257+gRHiqBNCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:46:16.933757Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.02900","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f443bede1111e04ca398ba9061088f664f40d631987583535685b4496ad01880","sha256:7888b8cc9bda44adc057fb0e14e8cd2d2528e8fec8c26fd3dc520cb584812f67"],"state_sha256":"fc747ef80bcd3d777c79ed4fe5fcaa26ad847fcca6d50ce6ae61f01a2e1e5636"}