{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:KD762XCIRJLWPL55E3JWMCOPKS","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":"be7c87c030b40d14bc1d8b67792874402537c3e4b8d38165bde2cf4bbcaaf828","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-11-18T14:58:29Z","title_canon_sha256":"c4e49192086431b523353eba2069387356ee13bfb35469d9739c4017139c1a3e"},"schema_version":"1.0","source":{"id":"1311.4415","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.4415","created_at":"2026-05-18T03:06:52Z"},{"alias_kind":"arxiv_version","alias_value":"1311.4415v1","created_at":"2026-05-18T03:06:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.4415","created_at":"2026-05-18T03:06:52Z"},{"alias_kind":"pith_short_12","alias_value":"KD762XCIRJLW","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"KD762XCIRJLWPL55","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"KD762XCI","created_at":"2026-05-18T12:27:49Z"}],"graph_snapshots":[{"event_id":"sha256:33b267b7290e5d41395b5168a7c200c43e1fae8527600b60ea3b08d48c634bac","target":"graph","created_at":"2026-05-18T03:06:52Z","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":"We study the time optimal control problem with a general target $\\mathcal S$ for a class of differential inclusions that satisfy mild smoothness and controllability assumptions. In particular, we do not require Petrov's condition at the boundary of $\\mathcal S$. Consequently, the minimum time function $T(\\cdot)$ fails to be locally Lipschitz---never mind semiconcave---near $\\mathcal S$. Instead of such a regularity, we use an exterior sphere condition for the hypograph of $T(\\cdot)$ to develop the analysis. In this way, we obtain dual arc inclusions which we apply to show the constancy of the ","authors_text":"Antonio Marigonda, Khai T. Nguyen, Piermarco Cannarsa","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-11-18T14:58:29Z","title":"Optimality conditions and regularity results for time optimal control problems with differential inclusions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.4415","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:ab87a5795d0eb266bda2ae752021fae58bafff74424282b1c2f184ff8e597f7b","target":"record","created_at":"2026-05-18T03:06:52Z","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":"be7c87c030b40d14bc1d8b67792874402537c3e4b8d38165bde2cf4bbcaaf828","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-11-18T14:58:29Z","title_canon_sha256":"c4e49192086431b523353eba2069387356ee13bfb35469d9739c4017139c1a3e"},"schema_version":"1.0","source":{"id":"1311.4415","kind":"arxiv","version":1}},"canonical_sha256":"50ffed5c488a5767afbd26d36609cf54a84c2c8b8e13f787660d64856fb13413","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"50ffed5c488a5767afbd26d36609cf54a84c2c8b8e13f787660d64856fb13413","first_computed_at":"2026-05-18T03:06:52.764495Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:06:52.764495Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/XCmUm2X0NrvvOY/xoHF6WdKsDsr5v5Zl2+9z+AQWXRWYyicGCiEPXPN3SiRhXTj0m+2RjGys61+j/LHok1kDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:06:52.765155Z","signed_message":"canonical_sha256_bytes"},"source_id":"1311.4415","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ab87a5795d0eb266bda2ae752021fae58bafff74424282b1c2f184ff8e597f7b","sha256:33b267b7290e5d41395b5168a7c200c43e1fae8527600b60ea3b08d48c634bac"],"state_sha256":"ec9f8a77d7b14fa8582c2bad0602102f833fa8d375602f8310b3e4b5545e96a3"}