{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:NC2JQ2TOJGDDPFPWDNVMUCD2WW","short_pith_number":"pith:NC2JQ2TO","schema_version":"1.0","canonical_sha256":"68b4986a6e49863795f61b6aca087ab5a59efaa51ba9e984e93be3bcdaa95c59","source":{"kind":"arxiv","id":"1304.3072","version":1},"attestation_state":"computed","paper":{"title":"Quasi-static evolution and congested crowd transport","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Damon Alexander, Inwon Kim, Yao Yao","submitted_at":"2013-04-10T19:55:03Z","abstract_excerpt":"We consider the relationship between Hele-Shaw evolution with drift, the porous medium equation with superharmonic drift, and a congested crowd motion model originally proposed by [MRS]- [MRSV]. We first use viscosity solutions to show that the porous medium equation solutions converge to the Hele- Shaw solution as the exponent tends to infinity. Next, using of the gradient flow structure of both the porous medium equation and the crowd motion model, we prove that the porous medium equation solutions also converge to the congested crowd motion. Combining these results lets us deduce that in th"},"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":"1304.3072","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-04-10T19:55:03Z","cross_cats_sorted":[],"title_canon_sha256":"68a24fd1a8afc695141c0f874c9045142a0be0b7326dfd914b58ee649b5bfe82","abstract_canon_sha256":"c4c122b2d5bb3fd2b5ef8acb1033f20964c4c53d081c3a6c20f6727b259d12ac"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:50:40.230790Z","signature_b64":"LoegKey5AJEjhX00PiXSCeTV6zOHaj9pdkGiLrRBhPWMiq9hvZiUPum+e2Yi17ReH8yQOQE94uyBRwwoFSefCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"68b4986a6e49863795f61b6aca087ab5a59efaa51ba9e984e93be3bcdaa95c59","last_reissued_at":"2026-05-18T01:50:40.230103Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:50:40.230103Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Quasi-static evolution and congested crowd transport","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Damon Alexander, Inwon Kim, Yao Yao","submitted_at":"2013-04-10T19:55:03Z","abstract_excerpt":"We consider the relationship between Hele-Shaw evolution with drift, the porous medium equation with superharmonic drift, and a congested crowd motion model originally proposed by [MRS]- [MRSV]. We first use viscosity solutions to show that the porous medium equation solutions converge to the Hele- Shaw solution as the exponent tends to infinity. Next, using of the gradient flow structure of both the porous medium equation and the crowd motion model, we prove that the porous medium equation solutions also converge to the congested crowd motion. Combining these results lets us deduce that in th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.3072","kind":"arxiv","version":1},"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":"1304.3072","created_at":"2026-05-18T01:50:40.230207+00:00"},{"alias_kind":"arxiv_version","alias_value":"1304.3072v1","created_at":"2026-05-18T01:50:40.230207+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.3072","created_at":"2026-05-18T01:50:40.230207+00:00"},{"alias_kind":"pith_short_12","alias_value":"NC2JQ2TOJGDD","created_at":"2026-05-18T12:27:52.871228+00:00"},{"alias_kind":"pith_short_16","alias_value":"NC2JQ2TOJGDDPFPW","created_at":"2026-05-18T12:27:52.871228+00:00"},{"alias_kind":"pith_short_8","alias_value":"NC2JQ2TO","created_at":"2026-05-18T12:27:52.871228+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/NC2JQ2TOJGDDPFPWDNVMUCD2WW","json":"https://pith.science/pith/NC2JQ2TOJGDDPFPWDNVMUCD2WW.json","graph_json":"https://pith.science/api/pith-number/NC2JQ2TOJGDDPFPWDNVMUCD2WW/graph.json","events_json":"https://pith.science/api/pith-number/NC2JQ2TOJGDDPFPWDNVMUCD2WW/events.json","paper":"https://pith.science/paper/NC2JQ2TO"},"agent_actions":{"view_html":"https://pith.science/pith/NC2JQ2TOJGDDPFPWDNVMUCD2WW","download_json":"https://pith.science/pith/NC2JQ2TOJGDDPFPWDNVMUCD2WW.json","view_paper":"https://pith.science/paper/NC2JQ2TO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1304.3072&json=true","fetch_graph":"https://pith.science/api/pith-number/NC2JQ2TOJGDDPFPWDNVMUCD2WW/graph.json","fetch_events":"https://pith.science/api/pith-number/NC2JQ2TOJGDDPFPWDNVMUCD2WW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NC2JQ2TOJGDDPFPWDNVMUCD2WW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NC2JQ2TOJGDDPFPWDNVMUCD2WW/action/storage_attestation","attest_author":"https://pith.science/pith/NC2JQ2TOJGDDPFPWDNVMUCD2WW/action/author_attestation","sign_citation":"https://pith.science/pith/NC2JQ2TOJGDDPFPWDNVMUCD2WW/action/citation_signature","submit_replication":"https://pith.science/pith/NC2JQ2TOJGDDPFPWDNVMUCD2WW/action/replication_record"}},"created_at":"2026-05-18T01:50:40.230207+00:00","updated_at":"2026-05-18T01:50:40.230207+00:00"}