{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:KCALJZOUWKD5W2ZRD2MODPLNCD","short_pith_number":"pith:KCALJZOU","schema_version":"1.0","canonical_sha256":"5080b4e5d4b287db6b311e98e1bd6d10ee759dbac3d30d127123988a2db5b263","source":{"kind":"arxiv","id":"1503.02311","version":2},"attestation_state":"computed","paper":{"title":"Advection-diffusion equations with density constraints","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alp\\'ar Rich\\'ard M\\'esz\\'aros, Filippo Santambrogio","submitted_at":"2015-03-08T19:15:32Z","abstract_excerpt":"In the spirit of the macroscopic crowd motion models with hard congestion (i.e. a strong density constraint $\\rho\\leq 1$) introduced by Maury {\\it et al.} some years ago, we analyze a variant of the same models where diffusion of the agents is also taken into account. From the modeling point of view, this means that individuals try to follow a given spontaneous velocity, but are subject to a Brownian diffusion, and have to adapt to a density constraint which introduces a pressure term affecting the movement. From the PDE point of view, this corresponds to a modified Fokker-Planck equation, wit"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1503.02311","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-03-08T19:15:32Z","cross_cats_sorted":[],"title_canon_sha256":"667768549c83a506c210e4d349008e469230ffbef7f996fb17eb90f770675714","abstract_canon_sha256":"bd3fb5e5ed809d43bc5fd722a347c24476726d29ba0c5bdc4d67012c9f41e262"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:19:44.582768Z","signature_b64":"Uj2ScAfLS2PJ2I2qUr7UH/xTwjh809WVuMgZbMQzsAKQ7rhQDLckoUcDLDgZ+MAzQyMDK/J/BhlCBrTcFue5AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5080b4e5d4b287db6b311e98e1bd6d10ee759dbac3d30d127123988a2db5b263","last_reissued_at":"2026-05-18T01:19:44.582069Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:19:44.582069Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Advection-diffusion equations with density constraints","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alp\\'ar Rich\\'ard M\\'esz\\'aros, Filippo Santambrogio","submitted_at":"2015-03-08T19:15:32Z","abstract_excerpt":"In the spirit of the macroscopic crowd motion models with hard congestion (i.e. a strong density constraint $\\rho\\leq 1$) introduced by Maury {\\it et al.} some years ago, we analyze a variant of the same models where diffusion of the agents is also taken into account. From the modeling point of view, this means that individuals try to follow a given spontaneous velocity, but are subject to a Brownian diffusion, and have to adapt to a density constraint which introduces a pressure term affecting the movement. From the PDE point of view, this corresponds to a modified Fokker-Planck equation, wit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.02311","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1503.02311","created_at":"2026-05-18T01:19:44.582189+00:00"},{"alias_kind":"arxiv_version","alias_value":"1503.02311v2","created_at":"2026-05-18T01:19:44.582189+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.02311","created_at":"2026-05-18T01:19:44.582189+00:00"},{"alias_kind":"pith_short_12","alias_value":"KCALJZOUWKD5","created_at":"2026-05-18T12:29:27.538025+00:00"},{"alias_kind":"pith_short_16","alias_value":"KCALJZOUWKD5W2ZR","created_at":"2026-05-18T12:29:27.538025+00:00"},{"alias_kind":"pith_short_8","alias_value":"KCALJZOU","created_at":"2026-05-18T12:29:27.538025+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/KCALJZOUWKD5W2ZRD2MODPLNCD","json":"https://pith.science/pith/KCALJZOUWKD5W2ZRD2MODPLNCD.json","graph_json":"https://pith.science/api/pith-number/KCALJZOUWKD5W2ZRD2MODPLNCD/graph.json","events_json":"https://pith.science/api/pith-number/KCALJZOUWKD5W2ZRD2MODPLNCD/events.json","paper":"https://pith.science/paper/KCALJZOU"},"agent_actions":{"view_html":"https://pith.science/pith/KCALJZOUWKD5W2ZRD2MODPLNCD","download_json":"https://pith.science/pith/KCALJZOUWKD5W2ZRD2MODPLNCD.json","view_paper":"https://pith.science/paper/KCALJZOU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1503.02311&json=true","fetch_graph":"https://pith.science/api/pith-number/KCALJZOUWKD5W2ZRD2MODPLNCD/graph.json","fetch_events":"https://pith.science/api/pith-number/KCALJZOUWKD5W2ZRD2MODPLNCD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KCALJZOUWKD5W2ZRD2MODPLNCD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KCALJZOUWKD5W2ZRD2MODPLNCD/action/storage_attestation","attest_author":"https://pith.science/pith/KCALJZOUWKD5W2ZRD2MODPLNCD/action/author_attestation","sign_citation":"https://pith.science/pith/KCALJZOUWKD5W2ZRD2MODPLNCD/action/citation_signature","submit_replication":"https://pith.science/pith/KCALJZOUWKD5W2ZRD2MODPLNCD/action/replication_record"}},"created_at":"2026-05-18T01:19:44.582189+00:00","updated_at":"2026-05-18T01:19:44.582189+00:00"}