{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:VSK3KCUAJLCE7TG6M3Q7AQKZCY","short_pith_number":"pith:VSK3KCUA","canonical_record":{"source":{"id":"1608.06432","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-08-23T09:27:29Z","cross_cats_sorted":[],"title_canon_sha256":"a1e9df18d632841f0c5c726b3693490677cbb3b64398574c6b6a1477111f4fe0","abstract_canon_sha256":"c988ee6684d44c5957974ff526d4fb372484a6b17d69346fb474de982936b5fe"},"schema_version":"1.0"},"canonical_sha256":"ac95b50a804ac44fccde66e1f041591621fcea08ddda67329de2901e2e385246","source":{"kind":"arxiv","id":"1608.06432","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.06432","created_at":"2026-05-18T00:56:45Z"},{"alias_kind":"arxiv_version","alias_value":"1608.06432v2","created_at":"2026-05-18T00:56:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.06432","created_at":"2026-05-18T00:56:45Z"},{"alias_kind":"pith_short_12","alias_value":"VSK3KCUAJLCE","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_16","alias_value":"VSK3KCUAJLCE7TG6","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_8","alias_value":"VSK3KCUA","created_at":"2026-05-18T12:30:48Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:VSK3KCUAJLCE7TG6M3Q7AQKZCY","target":"record","payload":{"canonical_record":{"source":{"id":"1608.06432","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-08-23T09:27:29Z","cross_cats_sorted":[],"title_canon_sha256":"a1e9df18d632841f0c5c726b3693490677cbb3b64398574c6b6a1477111f4fe0","abstract_canon_sha256":"c988ee6684d44c5957974ff526d4fb372484a6b17d69346fb474de982936b5fe"},"schema_version":"1.0"},"canonical_sha256":"ac95b50a804ac44fccde66e1f041591621fcea08ddda67329de2901e2e385246","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:56:45.591011Z","signature_b64":"5gEj8IOjK3mevhTMpNaEoMdHsw+TfqE52DaCi+4SSJMuDADzyQJZtVVNkxQrRPcgJjwjEZ6HDGh6lZaXCAPoDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ac95b50a804ac44fccde66e1f041591621fcea08ddda67329de2901e2e385246","last_reissued_at":"2026-05-18T00:56:45.590418Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:56:45.590418Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1608.06432","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:56:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9m7Jye3PRcKdB+0y7V7b46FtJvGolvHOzlh+KcKczwlpYAr33R49qYPRJ6nso6KL0kvfbC2A37twSZrqcJ9cCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T09:11:15.396932Z"},"content_sha256":"25ab4c3ef52acfe3ae5f591094efe20ae8457f0cb17a86e403ea87c80dd41ae2","schema_version":"1.0","event_id":"sha256:25ab4c3ef52acfe3ae5f591094efe20ae8457f0cb17a86e403ea87c80dd41ae2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:VSK3KCUAJLCE7TG6M3Q7AQKZCY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Mean Field Limit and Propagation of Chaos for a Pedestrian Flow Model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Li Chen, Qitao Yin, Simone G\\\"ottlich","submitted_at":"2016-08-23T09:27:29Z","abstract_excerpt":"In this paper a rigorous proof of the mean field limit for a pedestrian flow model in two dimensions is given by using a probabilistic method.\n  The model under investigation is an interacting particle system coupled to the eikonal equation on the microscopic scale.\n  For stochastic initial data, it is proved that the solution of the $N$-particle pedestrian flow system with properly chosen cut-off converges in the probability sense to the solution of the characteristics of the non-cut-off Vlasov equation.\n  Furthermore, the result on propagation of chaos is also deduced in terms of bounded Lip"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.06432","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:56:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bW+QFgC4f9vBaokh+eGBweYQLlOSTG6o3ZHTgsOo/rskImEySmXStB7vJ04C0fG6OhVjG69sGZlODxv/nYSaBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T09:11:15.397503Z"},"content_sha256":"ef7e1e2a2facbba31e840b4b3a3e52662bd8be1f0d9dccc95a3fb9f6a0abf324","schema_version":"1.0","event_id":"sha256:ef7e1e2a2facbba31e840b4b3a3e52662bd8be1f0d9dccc95a3fb9f6a0abf324"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VSK3KCUAJLCE7TG6M3Q7AQKZCY/bundle.json","state_url":"https://pith.science/pith/VSK3KCUAJLCE7TG6M3Q7AQKZCY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VSK3KCUAJLCE7TG6M3Q7AQKZCY/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":"2026-06-05T09:11:15Z","links":{"resolver":"https://pith.science/pith/VSK3KCUAJLCE7TG6M3Q7AQKZCY","bundle":"https://pith.science/pith/VSK3KCUAJLCE7TG6M3Q7AQKZCY/bundle.json","state":"https://pith.science/pith/VSK3KCUAJLCE7TG6M3Q7AQKZCY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VSK3KCUAJLCE7TG6M3Q7AQKZCY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:VSK3KCUAJLCE7TG6M3Q7AQKZCY","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":"c988ee6684d44c5957974ff526d4fb372484a6b17d69346fb474de982936b5fe","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-08-23T09:27:29Z","title_canon_sha256":"a1e9df18d632841f0c5c726b3693490677cbb3b64398574c6b6a1477111f4fe0"},"schema_version":"1.0","source":{"id":"1608.06432","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.06432","created_at":"2026-05-18T00:56:45Z"},{"alias_kind":"arxiv_version","alias_value":"1608.06432v2","created_at":"2026-05-18T00:56:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.06432","created_at":"2026-05-18T00:56:45Z"},{"alias_kind":"pith_short_12","alias_value":"VSK3KCUAJLCE","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_16","alias_value":"VSK3KCUAJLCE7TG6","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_8","alias_value":"VSK3KCUA","created_at":"2026-05-18T12:30:48Z"}],"graph_snapshots":[{"event_id":"sha256:ef7e1e2a2facbba31e840b4b3a3e52662bd8be1f0d9dccc95a3fb9f6a0abf324","target":"graph","created_at":"2026-05-18T00:56:45Z","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 a rigorous proof of the mean field limit for a pedestrian flow model in two dimensions is given by using a probabilistic method.\n  The model under investigation is an interacting particle system coupled to the eikonal equation on the microscopic scale.\n  For stochastic initial data, it is proved that the solution of the $N$-particle pedestrian flow system with properly chosen cut-off converges in the probability sense to the solution of the characteristics of the non-cut-off Vlasov equation.\n  Furthermore, the result on propagation of chaos is also deduced in terms of bounded Lip","authors_text":"Li Chen, Qitao Yin, Simone G\\\"ottlich","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-08-23T09:27:29Z","title":"Mean Field Limit and Propagation of Chaos for a Pedestrian Flow Model"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.06432","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":"sha256:25ab4c3ef52acfe3ae5f591094efe20ae8457f0cb17a86e403ea87c80dd41ae2","target":"record","created_at":"2026-05-18T00:56:45Z","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":"c988ee6684d44c5957974ff526d4fb372484a6b17d69346fb474de982936b5fe","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-08-23T09:27:29Z","title_canon_sha256":"a1e9df18d632841f0c5c726b3693490677cbb3b64398574c6b6a1477111f4fe0"},"schema_version":"1.0","source":{"id":"1608.06432","kind":"arxiv","version":2}},"canonical_sha256":"ac95b50a804ac44fccde66e1f041591621fcea08ddda67329de2901e2e385246","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ac95b50a804ac44fccde66e1f041591621fcea08ddda67329de2901e2e385246","first_computed_at":"2026-05-18T00:56:45.590418Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:56:45.590418Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5gEj8IOjK3mevhTMpNaEoMdHsw+TfqE52DaCi+4SSJMuDADzyQJZtVVNkxQrRPcgJjwjEZ6HDGh6lZaXCAPoDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:56:45.591011Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.06432","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:25ab4c3ef52acfe3ae5f591094efe20ae8457f0cb17a86e403ea87c80dd41ae2","sha256:ef7e1e2a2facbba31e840b4b3a3e52662bd8be1f0d9dccc95a3fb9f6a0abf324"],"state_sha256":"6e3a1cdf787916ee6f2d2215f9c18f5cc468ba28bafbbadaea08fbe5844f65a8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GhDYzjAgG2WxVqfGYtVqp7Ay94bxOC5YPs+H0LhhS7t9SQse4Xy7AmpizRR86qUO628MHjeWP1956PxeYYhDBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T09:11:15.400028Z","bundle_sha256":"72d536bca60de72a09071e3e76dfe23fa6416e8dd44e8b6508f77f8272d516eb"}}