{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:CTHWLRP5HCVVETNXMBVEPTQOOM","short_pith_number":"pith:CTHWLRP5","canonical_record":{"source":{"id":"2109.08457","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2021-09-17T10:34:01Z","cross_cats_sorted":[],"title_canon_sha256":"67dce0abcb3efffc51dc1e075a4240c83d210861c7c08d0d36dbad3205cd3d6a","abstract_canon_sha256":"360037b3b9f13c2eca7368b83f553e7e8fdde7788c8f554dbeed84c29458f4aa"},"schema_version":"1.0"},"canonical_sha256":"14cf65c5fd38ab524db7606a47ce0e731aa3c19e2c58b402278d2cfd5154b8e6","source":{"kind":"arxiv","id":"2109.08457","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2109.08457","created_at":"2026-07-05T03:46:22Z"},{"alias_kind":"arxiv_version","alias_value":"2109.08457v2","created_at":"2026-07-05T03:46:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2109.08457","created_at":"2026-07-05T03:46:22Z"},{"alias_kind":"pith_short_12","alias_value":"CTHWLRP5HCVV","created_at":"2026-07-05T03:46:22Z"},{"alias_kind":"pith_short_16","alias_value":"CTHWLRP5HCVVETNX","created_at":"2026-07-05T03:46:22Z"},{"alias_kind":"pith_short_8","alias_value":"CTHWLRP5","created_at":"2026-07-05T03:46:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:CTHWLRP5HCVVETNXMBVEPTQOOM","target":"record","payload":{"canonical_record":{"source":{"id":"2109.08457","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2021-09-17T10:34:01Z","cross_cats_sorted":[],"title_canon_sha256":"67dce0abcb3efffc51dc1e075a4240c83d210861c7c08d0d36dbad3205cd3d6a","abstract_canon_sha256":"360037b3b9f13c2eca7368b83f553e7e8fdde7788c8f554dbeed84c29458f4aa"},"schema_version":"1.0"},"canonical_sha256":"14cf65c5fd38ab524db7606a47ce0e731aa3c19e2c58b402278d2cfd5154b8e6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:46:22.411657Z","signature_b64":"ayU3vTtaaRog20TkG5LoE5qrvW6btnhyTb43vIVnfgVwKp3pw+QGCgO/lefwdf22lbYaY2BElB41fz6y0DcMCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"14cf65c5fd38ab524db7606a47ce0e731aa3c19e2c58b402278d2cfd5154b8e6","last_reissued_at":"2026-07-05T03:46:22.411233Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:46:22.411233Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2109.08457","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":"2026-07-05T03:46:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"haG0Kn52iKYxoOy2l7vUgHIZ7NL48C/uiY96p+epcEc/+tfClxs0lD5wXrZVp13qKTzcbVJ3h6SallutGr1ECQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-23T22:54:50.282256Z"},"content_sha256":"7de7dd24d749a847af206100b998fbaaf19c7eec0e969e18ea6635f58a92bd02","schema_version":"1.0","event_id":"sha256:7de7dd24d749a847af206100b998fbaaf19c7eec0e969e18ea6635f58a92bd02"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:CTHWLRP5HCVVETNXMBVEPTQOOM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Maximum Principle for a Time-Optimal Bilevel Sweeping Control Problem","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Fernando Lobo Pereira, Nathalie T. Khalil","submitted_at":"2021-09-17T10:34:01Z","abstract_excerpt":"In this article, we investigate a time-optimal state-constrained bilevel optimal control problem whose lower-level dynamics feature a sweeping control process involving a {\\it truncated normal cone}. By bilevel, it is meant that the optimization of the upper level problem is carried out over the solution set of the lower level problem.This problem instance arises in structured crowd motion control problems in a confined space. We establish the corresponding necessary optimality conditions in the Gamkrelidze's form. The analysis relies on the {\\it smooth approximation} of the lower level sweepi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2109.08457","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2109.08457/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T03:46:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VSFkbs+D6tWAelOSfTna2U2mAN+v5Ec/fNuvu/CA9bwd/4reBtyByzhzsmryTm8lU5g4sD5btOjiqGiReCm2Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-23T22:54:50.283238Z"},"content_sha256":"3bd0e08542fda322f9a6c4d855938f2159a0de0e7ea9079e830528a6bf5575b9","schema_version":"1.0","event_id":"sha256:3bd0e08542fda322f9a6c4d855938f2159a0de0e7ea9079e830528a6bf5575b9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CTHWLRP5HCVVETNXMBVEPTQOOM/bundle.json","state_url":"https://pith.science/pith/CTHWLRP5HCVVETNXMBVEPTQOOM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CTHWLRP5HCVVETNXMBVEPTQOOM/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":"2026-08-23T22:54:50Z","links":{"resolver":"https://pith.science/pith/CTHWLRP5HCVVETNXMBVEPTQOOM","bundle":"https://pith.science/pith/CTHWLRP5HCVVETNXMBVEPTQOOM/bundle.json","state":"https://pith.science/pith/CTHWLRP5HCVVETNXMBVEPTQOOM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CTHWLRP5HCVVETNXMBVEPTQOOM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:CTHWLRP5HCVVETNXMBVEPTQOOM","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":"360037b3b9f13c2eca7368b83f553e7e8fdde7788c8f554dbeed84c29458f4aa","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2021-09-17T10:34:01Z","title_canon_sha256":"67dce0abcb3efffc51dc1e075a4240c83d210861c7c08d0d36dbad3205cd3d6a"},"schema_version":"1.0","source":{"id":"2109.08457","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2109.08457","created_at":"2026-07-05T03:46:22Z"},{"alias_kind":"arxiv_version","alias_value":"2109.08457v2","created_at":"2026-07-05T03:46:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2109.08457","created_at":"2026-07-05T03:46:22Z"},{"alias_kind":"pith_short_12","alias_value":"CTHWLRP5HCVV","created_at":"2026-07-05T03:46:22Z"},{"alias_kind":"pith_short_16","alias_value":"CTHWLRP5HCVVETNX","created_at":"2026-07-05T03:46:22Z"},{"alias_kind":"pith_short_8","alias_value":"CTHWLRP5","created_at":"2026-07-05T03:46:22Z"}],"graph_snapshots":[{"event_id":"sha256:3bd0e08542fda322f9a6c4d855938f2159a0de0e7ea9079e830528a6bf5575b9","target":"graph","created_at":"2026-07-05T03:46:22Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2109.08457/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this article, we investigate a time-optimal state-constrained bilevel optimal control problem whose lower-level dynamics feature a sweeping control process involving a {\\it truncated normal cone}. By bilevel, it is meant that the optimization of the upper level problem is carried out over the solution set of the lower level problem.This problem instance arises in structured crowd motion control problems in a confined space. We establish the corresponding necessary optimality conditions in the Gamkrelidze's form. The analysis relies on the {\\it smooth approximation} of the lower level sweepi","authors_text":"Fernando Lobo Pereira, Nathalie T. Khalil","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2021-09-17T10:34:01Z","title":"A Maximum Principle for a Time-Optimal Bilevel Sweeping Control Problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2109.08457","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":"sha256:7de7dd24d749a847af206100b998fbaaf19c7eec0e969e18ea6635f58a92bd02","target":"record","created_at":"2026-07-05T03:46:22Z","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":"360037b3b9f13c2eca7368b83f553e7e8fdde7788c8f554dbeed84c29458f4aa","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2021-09-17T10:34:01Z","title_canon_sha256":"67dce0abcb3efffc51dc1e075a4240c83d210861c7c08d0d36dbad3205cd3d6a"},"schema_version":"1.0","source":{"id":"2109.08457","kind":"arxiv","version":2}},"canonical_sha256":"14cf65c5fd38ab524db7606a47ce0e731aa3c19e2c58b402278d2cfd5154b8e6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"14cf65c5fd38ab524db7606a47ce0e731aa3c19e2c58b402278d2cfd5154b8e6","first_computed_at":"2026-07-05T03:46:22.411233Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:46:22.411233Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ayU3vTtaaRog20TkG5LoE5qrvW6btnhyTb43vIVnfgVwKp3pw+QGCgO/lefwdf22lbYaY2BElB41fz6y0DcMCA==","signature_status":"signed_v1","signed_at":"2026-07-05T03:46:22.411657Z","signed_message":"canonical_sha256_bytes"},"source_id":"2109.08457","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7de7dd24d749a847af206100b998fbaaf19c7eec0e969e18ea6635f58a92bd02","sha256:3bd0e08542fda322f9a6c4d855938f2159a0de0e7ea9079e830528a6bf5575b9"],"state_sha256":"02ebe5b90f0ed8fd86649752399740c7fa5976c175abeee0c0c6b8233894350d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iNIYNQBUiBxE8CGo4mBRF805k8haSrBgwaFrJq8eT9ij0TqgQlBBe8NSnhZFZU7g2XDNmTOsD05rG++TPg00Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-23T22:54:50.289123Z","bundle_sha256":"30c7d6981e54fbe25ff0d379ca83c42852acd8114e5a494efbbbdc8a3624314b"}}