{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:MTLDXTDN2EUBOQNZS4HGTNRXVK","short_pith_number":"pith:MTLDXTDN","canonical_record":{"source":{"id":"1605.05232","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-05-17T16:46:26Z","cross_cats_sorted":[],"title_canon_sha256":"09de5b41091783e95de2f6506ac141a14569ccecd8a6f7ee524e3128b45b2bca","abstract_canon_sha256":"c2b653d968161ea55d9fea6fc2c8516bd4436654a9ae2b8dcc3d1b8b34363eb0"},"schema_version":"1.0"},"canonical_sha256":"64d63bcc6dd1281741b9970e69b637aa96e966bf6dbb9fc7e0fc8003ad92feef","source":{"kind":"arxiv","id":"1605.05232","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.05232","created_at":"2026-05-18T01:14:12Z"},{"alias_kind":"arxiv_version","alias_value":"1605.05232v2","created_at":"2026-05-18T01:14:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.05232","created_at":"2026-05-18T01:14:12Z"},{"alias_kind":"pith_short_12","alias_value":"MTLDXTDN2EUB","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_16","alias_value":"MTLDXTDN2EUBOQNZ","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_8","alias_value":"MTLDXTDN","created_at":"2026-05-18T12:30:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:MTLDXTDN2EUBOQNZS4HGTNRXVK","target":"record","payload":{"canonical_record":{"source":{"id":"1605.05232","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-05-17T16:46:26Z","cross_cats_sorted":[],"title_canon_sha256":"09de5b41091783e95de2f6506ac141a14569ccecd8a6f7ee524e3128b45b2bca","abstract_canon_sha256":"c2b653d968161ea55d9fea6fc2c8516bd4436654a9ae2b8dcc3d1b8b34363eb0"},"schema_version":"1.0"},"canonical_sha256":"64d63bcc6dd1281741b9970e69b637aa96e966bf6dbb9fc7e0fc8003ad92feef","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:14:12.072353Z","signature_b64":"5SzrPBM/1KoeOWDfzZq8Uq15/q/VwxeNLwVc7Ht2wllp6f6pNu0DQM5LuIDgFaTBnWc3hNwj9gryjJ1ibzmGDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"64d63bcc6dd1281741b9970e69b637aa96e966bf6dbb9fc7e0fc8003ad92feef","last_reissued_at":"2026-05-18T01:14:12.071735Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:14:12.071735Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1605.05232","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":"2026-05-18T01:14:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5h4c/iknDExIOSNQnRDK6FhGcgUmg8g4rQEtHwj4cChEOzVaQgrrwZU6sgG2Y8qbsaIJjT/3Gqc2QQL2oGBADw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T12:22:00.332224Z"},"content_sha256":"c151f350c6a4db138aec45e8391c844fee20f8078d8c9e7b29b972df97e01425","schema_version":"1.0","event_id":"sha256:c151f350c6a4db138aec45e8391c844fee20f8078d8c9e7b29b972df97e01425"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:MTLDXTDN2EUBOQNZS4HGTNRXVK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Switching in time-optimal problem. The 3-D case with 2-D control","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Andrei A. Agrachev, Carolina Biolo","submitted_at":"2016-05-17T16:46:26Z","abstract_excerpt":"We study local structure of time-optimal controls and trajectories for a 3-dimensional control-affine system with a 2-dimensional control parameter with values in the disk. In particular, we give sufficient conditions, in terms of Lie bracket relations, for optimal controls to be smooth or to have only isolated jump discontinuities."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.05232","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":"2026-05-18T01:14:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tTlz65XXNiIH+pOMDlCJnJNhaQlC4LgRk1LwIEWLwGaSOzfMpj+WJTo9qfJ9AIOFfV+nc9egeeqlbJFB60E3Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T12:22:00.332714Z"},"content_sha256":"8f81352bdadd6812969fcca7d76e85ca9fd35f999ea16163e8fa12b48930e327","schema_version":"1.0","event_id":"sha256:8f81352bdadd6812969fcca7d76e85ca9fd35f999ea16163e8fa12b48930e327"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MTLDXTDN2EUBOQNZS4HGTNRXVK/bundle.json","state_url":"https://pith.science/pith/MTLDXTDN2EUBOQNZS4HGTNRXVK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MTLDXTDN2EUBOQNZS4HGTNRXVK/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":"2026-06-26T12:22:00Z","links":{"resolver":"https://pith.science/pith/MTLDXTDN2EUBOQNZS4HGTNRXVK","bundle":"https://pith.science/pith/MTLDXTDN2EUBOQNZS4HGTNRXVK/bundle.json","state":"https://pith.science/pith/MTLDXTDN2EUBOQNZS4HGTNRXVK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MTLDXTDN2EUBOQNZS4HGTNRXVK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:MTLDXTDN2EUBOQNZS4HGTNRXVK","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":"c2b653d968161ea55d9fea6fc2c8516bd4436654a9ae2b8dcc3d1b8b34363eb0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-05-17T16:46:26Z","title_canon_sha256":"09de5b41091783e95de2f6506ac141a14569ccecd8a6f7ee524e3128b45b2bca"},"schema_version":"1.0","source":{"id":"1605.05232","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.05232","created_at":"2026-05-18T01:14:12Z"},{"alias_kind":"arxiv_version","alias_value":"1605.05232v2","created_at":"2026-05-18T01:14:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.05232","created_at":"2026-05-18T01:14:12Z"},{"alias_kind":"pith_short_12","alias_value":"MTLDXTDN2EUB","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_16","alias_value":"MTLDXTDN2EUBOQNZ","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_8","alias_value":"MTLDXTDN","created_at":"2026-05-18T12:30:32Z"}],"graph_snapshots":[{"event_id":"sha256:8f81352bdadd6812969fcca7d76e85ca9fd35f999ea16163e8fa12b48930e327","target":"graph","created_at":"2026-05-18T01:14:12Z","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 local structure of time-optimal controls and trajectories for a 3-dimensional control-affine system with a 2-dimensional control parameter with values in the disk. In particular, we give sufficient conditions, in terms of Lie bracket relations, for optimal controls to be smooth or to have only isolated jump discontinuities.","authors_text":"Andrei A. Agrachev, Carolina Biolo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-05-17T16:46:26Z","title":"Switching in time-optimal problem. The 3-D case with 2-D control"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.05232","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:c151f350c6a4db138aec45e8391c844fee20f8078d8c9e7b29b972df97e01425","target":"record","created_at":"2026-05-18T01:14:12Z","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":"c2b653d968161ea55d9fea6fc2c8516bd4436654a9ae2b8dcc3d1b8b34363eb0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-05-17T16:46:26Z","title_canon_sha256":"09de5b41091783e95de2f6506ac141a14569ccecd8a6f7ee524e3128b45b2bca"},"schema_version":"1.0","source":{"id":"1605.05232","kind":"arxiv","version":2}},"canonical_sha256":"64d63bcc6dd1281741b9970e69b637aa96e966bf6dbb9fc7e0fc8003ad92feef","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"64d63bcc6dd1281741b9970e69b637aa96e966bf6dbb9fc7e0fc8003ad92feef","first_computed_at":"2026-05-18T01:14:12.071735Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:14:12.071735Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5SzrPBM/1KoeOWDfzZq8Uq15/q/VwxeNLwVc7Ht2wllp6f6pNu0DQM5LuIDgFaTBnWc3hNwj9gryjJ1ibzmGDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:14:12.072353Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.05232","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c151f350c6a4db138aec45e8391c844fee20f8078d8c9e7b29b972df97e01425","sha256:8f81352bdadd6812969fcca7d76e85ca9fd35f999ea16163e8fa12b48930e327"],"state_sha256":"cc8a8b87ee1940bcfaffafb81029f4e1f66d4ff1acd5734da0ccea4a668da539"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CsJjHhOZvnc/CwC851LlSnl56eSwZLyMcO2WiFVUIQChhD0RoXpxIV6lil+TjlXfDHuYEcV6yWwRyQB9PW9/Dg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T12:22:00.336086Z","bundle_sha256":"c37e835f4e4bf922936bd48c578a2283b84ac9192463ac3feed384737455a6f1"}}