{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:7BUEYW3RR3DUVHTX5DVZZ6443Y","short_pith_number":"pith:7BUEYW3R","schema_version":"1.0","canonical_sha256":"f8684c5b718ec74a9e77e8eb9cfb9cde3823054a17dc6277f82fd583741cc99d","source":{"kind":"arxiv","id":"1304.5201","version":1},"attestation_state":"computed","paper":{"title":"Mean field games with nonlinear mobilities in pedestrian dynamics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC","nlin.AO"],"primary_cat":"math.AP","authors_text":"Marco Di Francesco, Marie-Therese Wolfram, Martin Burger, Peter Markowich","submitted_at":"2013-04-18T18:03:17Z","abstract_excerpt":"In this paper we present an optimal control approach modeling fast exit scenarios in pedestrian crowds. In particular we consider the case of a large human crowd trying to exit a room as fast as possible. The motion of every pedestrian is determined by minimizing a cost functional, which depends on his/her position, velocity, exit time and the overall density of people. This microscopic setup leads in the mean-field limit to a parabolic optimal control problem. We discuss the modeling of the macroscopic optimal control approach and show how the optimal conditions relate to Hughes model for ped"},"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":"1304.5201","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-04-18T18:03:17Z","cross_cats_sorted":["math.OC","nlin.AO"],"title_canon_sha256":"e0a9bd59b47e7e538a36a52ebd2363ec8f2528c2c1e217702f2a269b600cdf90","abstract_canon_sha256":"83fa6176703a0beaa8727ff58722d9863743bcd1e9958944627096c5abf17728"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:27:41.494829Z","signature_b64":"KJHZMESdiOPVho2nt/j96NBHzAxCpw7B5NDQASJYavCUD3d3HjRDDLsoHrTmc68JCkk9lViuwrwIBj20kRViAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f8684c5b718ec74a9e77e8eb9cfb9cde3823054a17dc6277f82fd583741cc99d","last_reissued_at":"2026-05-18T03:27:41.494126Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:27:41.494126Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Mean field games with nonlinear mobilities in pedestrian dynamics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC","nlin.AO"],"primary_cat":"math.AP","authors_text":"Marco Di Francesco, Marie-Therese Wolfram, Martin Burger, Peter Markowich","submitted_at":"2013-04-18T18:03:17Z","abstract_excerpt":"In this paper we present an optimal control approach modeling fast exit scenarios in pedestrian crowds. In particular we consider the case of a large human crowd trying to exit a room as fast as possible. The motion of every pedestrian is determined by minimizing a cost functional, which depends on his/her position, velocity, exit time and the overall density of people. This microscopic setup leads in the mean-field limit to a parabolic optimal control problem. We discuss the modeling of the macroscopic optimal control approach and show how the optimal conditions relate to Hughes model for ped"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.5201","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":"1304.5201","created_at":"2026-05-18T03:27:41.494260+00:00"},{"alias_kind":"arxiv_version","alias_value":"1304.5201v1","created_at":"2026-05-18T03:27:41.494260+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.5201","created_at":"2026-05-18T03:27:41.494260+00:00"},{"alias_kind":"pith_short_12","alias_value":"7BUEYW3RR3DU","created_at":"2026-05-18T12:27:36.564083+00:00"},{"alias_kind":"pith_short_16","alias_value":"7BUEYW3RR3DUVHTX","created_at":"2026-05-18T12:27:36.564083+00:00"},{"alias_kind":"pith_short_8","alias_value":"7BUEYW3R","created_at":"2026-05-18T12:27:36.564083+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/7BUEYW3RR3DUVHTX5DVZZ6443Y","json":"https://pith.science/pith/7BUEYW3RR3DUVHTX5DVZZ6443Y.json","graph_json":"https://pith.science/api/pith-number/7BUEYW3RR3DUVHTX5DVZZ6443Y/graph.json","events_json":"https://pith.science/api/pith-number/7BUEYW3RR3DUVHTX5DVZZ6443Y/events.json","paper":"https://pith.science/paper/7BUEYW3R"},"agent_actions":{"view_html":"https://pith.science/pith/7BUEYW3RR3DUVHTX5DVZZ6443Y","download_json":"https://pith.science/pith/7BUEYW3RR3DUVHTX5DVZZ6443Y.json","view_paper":"https://pith.science/paper/7BUEYW3R","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1304.5201&json=true","fetch_graph":"https://pith.science/api/pith-number/7BUEYW3RR3DUVHTX5DVZZ6443Y/graph.json","fetch_events":"https://pith.science/api/pith-number/7BUEYW3RR3DUVHTX5DVZZ6443Y/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7BUEYW3RR3DUVHTX5DVZZ6443Y/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7BUEYW3RR3DUVHTX5DVZZ6443Y/action/storage_attestation","attest_author":"https://pith.science/pith/7BUEYW3RR3DUVHTX5DVZZ6443Y/action/author_attestation","sign_citation":"https://pith.science/pith/7BUEYW3RR3DUVHTX5DVZZ6443Y/action/citation_signature","submit_replication":"https://pith.science/pith/7BUEYW3RR3DUVHTX5DVZZ6443Y/action/replication_record"}},"created_at":"2026-05-18T03:27:41.494260+00:00","updated_at":"2026-05-18T03:27:41.494260+00:00"}