{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:7BUEYW3RR3DUVHTX5DVZZ6443Y","short_pith_number":"pith:7BUEYW3R","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"},"canonical_sha256":"f8684c5b718ec74a9e77e8eb9cfb9cde3823054a17dc6277f82fd583741cc99d","source":{"kind":"arxiv","id":"1304.5201","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.5201","created_at":"2026-05-18T03:27:41Z"},{"alias_kind":"arxiv_version","alias_value":"1304.5201v1","created_at":"2026-05-18T03:27:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.5201","created_at":"2026-05-18T03:27:41Z"},{"alias_kind":"pith_short_12","alias_value":"7BUEYW3RR3DU","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_16","alias_value":"7BUEYW3RR3DUVHTX","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_8","alias_value":"7BUEYW3R","created_at":"2026-05-18T12:27:36Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:7BUEYW3RR3DUVHTX5DVZZ6443Y","target":"record","payload":{"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"},"canonical_sha256":"f8684c5b718ec74a9e77e8eb9cfb9cde3823054a17dc6277f82fd583741cc99d","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"},"source_kind":"arxiv","source_id":"1304.5201","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:27:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8eov6bFAimNJ2k0tVIAngKcWcSI9G41P9vCyBtuRq8qWpjnUrtCD/B5SSdgycAmcpNOrWPIkKUVGKmypBsOQBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T20:22:35.305158Z"},"content_sha256":"867dd5c88ae7f3df4aea3120392804128ce235bcab488334c75181c25027a869","schema_version":"1.0","event_id":"sha256:867dd5c88ae7f3df4aea3120392804128ce235bcab488334c75181c25027a869"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:7BUEYW3RR3DUVHTX5DVZZ6443Y","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:27:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eFyLcx5Bn076r4eleQYRyhKkBa1/XPd5fceeODqCudEtimpuGoMmXDKgT1AjTcIV5RJAU9zZfEVBQKaKOqo4CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T20:22:35.305533Z"},"content_sha256":"5d9f1eb6f1dc417ae3803f44d86514e2204744084af8bedf304efac1ea7596bb","schema_version":"1.0","event_id":"sha256:5d9f1eb6f1dc417ae3803f44d86514e2204744084af8bedf304efac1ea7596bb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7BUEYW3RR3DUVHTX5DVZZ6443Y/bundle.json","state_url":"https://pith.science/pith/7BUEYW3RR3DUVHTX5DVZZ6443Y/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7BUEYW3RR3DUVHTX5DVZZ6443Y/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-27T20:22:35Z","links":{"resolver":"https://pith.science/pith/7BUEYW3RR3DUVHTX5DVZZ6443Y","bundle":"https://pith.science/pith/7BUEYW3RR3DUVHTX5DVZZ6443Y/bundle.json","state":"https://pith.science/pith/7BUEYW3RR3DUVHTX5DVZZ6443Y/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7BUEYW3RR3DUVHTX5DVZZ6443Y/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:7BUEYW3RR3DUVHTX5DVZZ6443Y","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":"83fa6176703a0beaa8727ff58722d9863743bcd1e9958944627096c5abf17728","cross_cats_sorted":["math.OC","nlin.AO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-04-18T18:03:17Z","title_canon_sha256":"e0a9bd59b47e7e538a36a52ebd2363ec8f2528c2c1e217702f2a269b600cdf90"},"schema_version":"1.0","source":{"id":"1304.5201","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.5201","created_at":"2026-05-18T03:27:41Z"},{"alias_kind":"arxiv_version","alias_value":"1304.5201v1","created_at":"2026-05-18T03:27:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.5201","created_at":"2026-05-18T03:27:41Z"},{"alias_kind":"pith_short_12","alias_value":"7BUEYW3RR3DU","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_16","alias_value":"7BUEYW3RR3DUVHTX","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_8","alias_value":"7BUEYW3R","created_at":"2026-05-18T12:27:36Z"}],"graph_snapshots":[{"event_id":"sha256:5d9f1eb6f1dc417ae3803f44d86514e2204744084af8bedf304efac1ea7596bb","target":"graph","created_at":"2026-05-18T03:27:41Z","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 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","authors_text":"Marco Di Francesco, Marie-Therese Wolfram, Martin Burger, Peter Markowich","cross_cats":["math.OC","nlin.AO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-04-18T18:03:17Z","title":"Mean field games with nonlinear mobilities in pedestrian dynamics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.5201","kind":"arxiv","version":1},"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":"sha256:867dd5c88ae7f3df4aea3120392804128ce235bcab488334c75181c25027a869","target":"record","created_at":"2026-05-18T03:27:41Z","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":"83fa6176703a0beaa8727ff58722d9863743bcd1e9958944627096c5abf17728","cross_cats_sorted":["math.OC","nlin.AO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-04-18T18:03:17Z","title_canon_sha256":"e0a9bd59b47e7e538a36a52ebd2363ec8f2528c2c1e217702f2a269b600cdf90"},"schema_version":"1.0","source":{"id":"1304.5201","kind":"arxiv","version":1}},"canonical_sha256":"f8684c5b718ec74a9e77e8eb9cfb9cde3823054a17dc6277f82fd583741cc99d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f8684c5b718ec74a9e77e8eb9cfb9cde3823054a17dc6277f82fd583741cc99d","first_computed_at":"2026-05-18T03:27:41.494126Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:27:41.494126Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KJHZMESdiOPVho2nt/j96NBHzAxCpw7B5NDQASJYavCUD3d3HjRDDLsoHrTmc68JCkk9lViuwrwIBj20kRViAA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:27:41.494829Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.5201","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:867dd5c88ae7f3df4aea3120392804128ce235bcab488334c75181c25027a869","sha256:5d9f1eb6f1dc417ae3803f44d86514e2204744084af8bedf304efac1ea7596bb"],"state_sha256":"23b041c2aea31f2f9640179188119247d20e19616312d14e1750b063bed07367"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mxwLRc43gXvguS1FbuG769BjOzDLOhmpD9xrtS72zm+6+Gp0zaTBMiYLyumyOugexmLGNhS3zD9Wcfo9rcEJDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T20:22:35.308031Z","bundle_sha256":"bf8a22b9d3934dd6b97335a78e1e837e37022604f573bd18564b06e6bec46d0c"}}