{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:7L2YT674QKQZPN2FOQ5KVXXJGZ","short_pith_number":"pith:7L2YT674","canonical_record":{"source":{"id":"1802.08083","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-02-22T14:58:43Z","cross_cats_sorted":[],"title_canon_sha256":"0d216098b851699fc4c8c936e0ce43e9aea60f92e8a6aa553a8156ae09284199","abstract_canon_sha256":"82673ddc983e693035cc71aee8003d3b2f1dea5b37a1f922b275ed09d3a6b721"},"schema_version":"1.0"},"canonical_sha256":"faf589fbfc82a197b745743aaadee9364809ab82f4ec47997a78bf57d4d7b96b","source":{"kind":"arxiv","id":"1802.08083","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.08083","created_at":"2026-05-18T00:22:45Z"},{"alias_kind":"arxiv_version","alias_value":"1802.08083v1","created_at":"2026-05-18T00:22:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.08083","created_at":"2026-05-18T00:22:45Z"},{"alias_kind":"pith_short_12","alias_value":"7L2YT674QKQZ","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_16","alias_value":"7L2YT674QKQZPN2F","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_8","alias_value":"7L2YT674","created_at":"2026-05-18T12:32:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:7L2YT674QKQZPN2FOQ5KVXXJGZ","target":"record","payload":{"canonical_record":{"source":{"id":"1802.08083","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-02-22T14:58:43Z","cross_cats_sorted":[],"title_canon_sha256":"0d216098b851699fc4c8c936e0ce43e9aea60f92e8a6aa553a8156ae09284199","abstract_canon_sha256":"82673ddc983e693035cc71aee8003d3b2f1dea5b37a1f922b275ed09d3a6b721"},"schema_version":"1.0"},"canonical_sha256":"faf589fbfc82a197b745743aaadee9364809ab82f4ec47997a78bf57d4d7b96b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:22:45.597910Z","signature_b64":"FExU8v+Z+UZAyVsO8TP/BKWLQeoIjtt542+7p8aDOJhwwJxvzgsKR8PPLC3Gxoth1PhLcXdwy7E2wWkPj7FEBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"faf589fbfc82a197b745743aaadee9364809ab82f4ec47997a78bf57d4d7b96b","last_reissued_at":"2026-05-18T00:22:45.597392Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:22:45.597392Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1802.08083","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":"2026-05-18T00:22:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sAEkUpK+BK5Q0jrUrvMtAS3wdP/+GGL4cjED6R7goEnXMK/An/7VPhBX4xvbvlmKezWnLlWnxn/idXoVF+krCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T11:55:44.719630Z"},"content_sha256":"7e53cf5871d452b19475079fb898234868a0afdbc5f3130e4e154e54cf05db11","schema_version":"1.0","event_id":"sha256:7e53cf5871d452b19475079fb898234868a0afdbc5f3130e4e154e54cf05db11"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:7L2YT674QKQZPN2FOQ5KVXXJGZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Applications of Optimal Control of a Nonconvex Sweeping Process to Optimization of the Planar Crowd Motion Model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Boris Mordukhovich, Tan Cao","submitted_at":"2018-02-22T14:58:43Z","abstract_excerpt":"This paper concerns optimal control of a nonconvex perturbed sweeping process and its applications to optimization of the planar crowd motion model of traffic equilibria. The obtained theoretical results allow us to investigate a dynamic optimization problem for the microscopic planar crown motion model with finitely many participants and completely solve it analytically in the case of two participants."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.08083","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":"2026-05-18T00:22:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vO15+O3WbeV4hiQXJXpcHzAi7UdnS0z0dfp5B0P+1FwvQ/zOP/9qwYx3U3aT5Z5c9FAANcF+uKssEToxMM3/AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T11:55:44.719971Z"},"content_sha256":"23771d810c0e05e363e27ca2a30396ddd9c23420971d2382efa40ab43cd3bacc","schema_version":"1.0","event_id":"sha256:23771d810c0e05e363e27ca2a30396ddd9c23420971d2382efa40ab43cd3bacc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7L2YT674QKQZPN2FOQ5KVXXJGZ/bundle.json","state_url":"https://pith.science/pith/7L2YT674QKQZPN2FOQ5KVXXJGZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7L2YT674QKQZPN2FOQ5KVXXJGZ/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":"2026-06-25T11:55:44Z","links":{"resolver":"https://pith.science/pith/7L2YT674QKQZPN2FOQ5KVXXJGZ","bundle":"https://pith.science/pith/7L2YT674QKQZPN2FOQ5KVXXJGZ/bundle.json","state":"https://pith.science/pith/7L2YT674QKQZPN2FOQ5KVXXJGZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7L2YT674QKQZPN2FOQ5KVXXJGZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:7L2YT674QKQZPN2FOQ5KVXXJGZ","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":"82673ddc983e693035cc71aee8003d3b2f1dea5b37a1f922b275ed09d3a6b721","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-02-22T14:58:43Z","title_canon_sha256":"0d216098b851699fc4c8c936e0ce43e9aea60f92e8a6aa553a8156ae09284199"},"schema_version":"1.0","source":{"id":"1802.08083","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.08083","created_at":"2026-05-18T00:22:45Z"},{"alias_kind":"arxiv_version","alias_value":"1802.08083v1","created_at":"2026-05-18T00:22:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.08083","created_at":"2026-05-18T00:22:45Z"},{"alias_kind":"pith_short_12","alias_value":"7L2YT674QKQZ","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_16","alias_value":"7L2YT674QKQZPN2F","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_8","alias_value":"7L2YT674","created_at":"2026-05-18T12:32:11Z"}],"graph_snapshots":[{"event_id":"sha256:23771d810c0e05e363e27ca2a30396ddd9c23420971d2382efa40ab43cd3bacc","target":"graph","created_at":"2026-05-18T00:22:45Z","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":"This paper concerns optimal control of a nonconvex perturbed sweeping process and its applications to optimization of the planar crowd motion model of traffic equilibria. The obtained theoretical results allow us to investigate a dynamic optimization problem for the microscopic planar crown motion model with finitely many participants and completely solve it analytically in the case of two participants.","authors_text":"Boris Mordukhovich, Tan Cao","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-02-22T14:58:43Z","title":"Applications of Optimal Control of a Nonconvex Sweeping Process to Optimization of the Planar Crowd Motion Model"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.08083","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":"sha256:7e53cf5871d452b19475079fb898234868a0afdbc5f3130e4e154e54cf05db11","target":"record","created_at":"2026-05-18T00:22:45Z","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":"82673ddc983e693035cc71aee8003d3b2f1dea5b37a1f922b275ed09d3a6b721","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-02-22T14:58:43Z","title_canon_sha256":"0d216098b851699fc4c8c936e0ce43e9aea60f92e8a6aa553a8156ae09284199"},"schema_version":"1.0","source":{"id":"1802.08083","kind":"arxiv","version":1}},"canonical_sha256":"faf589fbfc82a197b745743aaadee9364809ab82f4ec47997a78bf57d4d7b96b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"faf589fbfc82a197b745743aaadee9364809ab82f4ec47997a78bf57d4d7b96b","first_computed_at":"2026-05-18T00:22:45.597392Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:22:45.597392Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FExU8v+Z+UZAyVsO8TP/BKWLQeoIjtt542+7p8aDOJhwwJxvzgsKR8PPLC3Gxoth1PhLcXdwy7E2wWkPj7FEBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:22:45.597910Z","signed_message":"canonical_sha256_bytes"},"source_id":"1802.08083","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7e53cf5871d452b19475079fb898234868a0afdbc5f3130e4e154e54cf05db11","sha256:23771d810c0e05e363e27ca2a30396ddd9c23420971d2382efa40ab43cd3bacc"],"state_sha256":"a73e8b8f9e9a7e5f60f4ec6337074bdc7d321df634e77f6160632d48fa0acf46"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FHYIZ/12Od0RS8H2TxInal8jJpmzq6f77nLDYqTFo6uBj6+MxbX4+BehFTP1DL5mXWP+KHL0z9HrVFbEVq/6AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T11:55:44.721800Z","bundle_sha256":"4b6cbf4d6cec69da14e4b003a7ccbc02e3e82b55d87d369ee0be958b626c6d8c"}}