{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:3YPSK5ETWY5AHHFNKQQX6AFPS5","short_pith_number":"pith:3YPSK5ET","canonical_record":{"source":{"id":"1504.06219","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-04-23T15:24:23Z","cross_cats_sorted":[],"title_canon_sha256":"7ac981b3ea11afbed8b495414f6471455a091615466f70991e9ff46fb38f3691","abstract_canon_sha256":"a385b5a0dca25a104b828cd8868f04c748dd63c5d708422b2a8c035035ab8c7f"},"schema_version":"1.0"},"canonical_sha256":"de1f257493b63a039cad54217f00af975a5ce7fc9e8a9f298b12b522297fc066","source":{"kind":"arxiv","id":"1504.06219","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.06219","created_at":"2026-05-18T02:18:02Z"},{"alias_kind":"arxiv_version","alias_value":"1504.06219v1","created_at":"2026-05-18T02:18:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.06219","created_at":"2026-05-18T02:18:02Z"},{"alias_kind":"pith_short_12","alias_value":"3YPSK5ETWY5A","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"3YPSK5ETWY5AHHFN","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"3YPSK5ET","created_at":"2026-05-18T12:29:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:3YPSK5ETWY5AHHFNKQQX6AFPS5","target":"record","payload":{"canonical_record":{"source":{"id":"1504.06219","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-04-23T15:24:23Z","cross_cats_sorted":[],"title_canon_sha256":"7ac981b3ea11afbed8b495414f6471455a091615466f70991e9ff46fb38f3691","abstract_canon_sha256":"a385b5a0dca25a104b828cd8868f04c748dd63c5d708422b2a8c035035ab8c7f"},"schema_version":"1.0"},"canonical_sha256":"de1f257493b63a039cad54217f00af975a5ce7fc9e8a9f298b12b522297fc066","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:18:02.233542Z","signature_b64":"YL1wW0HomOoja2bgEBlGQ4fRl/Fpitc7cZhYWGXYENo1/GUg+r7QYKnp5V9ikDgjf2yc/OQvbU17vUokAhSzAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"de1f257493b63a039cad54217f00af975a5ce7fc9e8a9f298b12b522297fc066","last_reissued_at":"2026-05-18T02:18:02.232765Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:18:02.232765Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1504.06219","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":"2026-05-18T02:18:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"A+waNuVM2mEQoeXqtpU8Ug6/3E3mnPW6klbs11hrGnuQqIYSvWz4nsH4ONle/Nc+ODVDRzeXlFGbiIgu/QTpBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T09:22:57.883030Z"},"content_sha256":"69bb32d6af0a463db37ee7f519f54766e32c0d214539be24187364d78b84f87c","schema_version":"1.0","event_id":"sha256:69bb32d6af0a463db37ee7f519f54766e32c0d214539be24187364d78b84f87c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:3YPSK5ETWY5AHHFNKQQX6AFPS5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Planar tilting maneuver of a spacecraft: singular arcs in the minimum time problem and chattering","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Emmanuel Tr\\'elat, Jiamin Zhu, Max Cerf","submitted_at":"2015-04-23T15:24:23Z","abstract_excerpt":"In this paper, we study the minimum time planar tilting maneuver of a spacecraft, from the theoretical as well as from the numerical point of view, with a particular focus on the chattering phenomenon. We prove that there exist optimal chattering arcs when a singular junction occurs. Our study is based on the Pontryagin Maximum Principle and on results by M.I. Zelikin and V.F. Borisov. We give sufficient conditions on the initial values under which the optimal solutions do not contain any singular arc, and are bang-bang with a finite number of switchings. Moreover, we implement sub-optimal str"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.06219","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":"2026-05-18T02:18:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YikvqYYiDjoFiNwIEd8y9MXToSfSsthAjPSFzEXC2XfjzKEqDlACBoDD7F9h7QxV6lVM+itcxk3937UZD5NzDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T09:22:57.883393Z"},"content_sha256":"9ff16d08d1b11149f3f40224f2cd1ef7291bf12cd2ba8aea0e5430d0231edf11","schema_version":"1.0","event_id":"sha256:9ff16d08d1b11149f3f40224f2cd1ef7291bf12cd2ba8aea0e5430d0231edf11"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3YPSK5ETWY5AHHFNKQQX6AFPS5/bundle.json","state_url":"https://pith.science/pith/3YPSK5ETWY5AHHFNKQQX6AFPS5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3YPSK5ETWY5AHHFNKQQX6AFPS5/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":"2026-06-27T09:22:57Z","links":{"resolver":"https://pith.science/pith/3YPSK5ETWY5AHHFNKQQX6AFPS5","bundle":"https://pith.science/pith/3YPSK5ETWY5AHHFNKQQX6AFPS5/bundle.json","state":"https://pith.science/pith/3YPSK5ETWY5AHHFNKQQX6AFPS5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3YPSK5ETWY5AHHFNKQQX6AFPS5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:3YPSK5ETWY5AHHFNKQQX6AFPS5","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":"a385b5a0dca25a104b828cd8868f04c748dd63c5d708422b2a8c035035ab8c7f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-04-23T15:24:23Z","title_canon_sha256":"7ac981b3ea11afbed8b495414f6471455a091615466f70991e9ff46fb38f3691"},"schema_version":"1.0","source":{"id":"1504.06219","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.06219","created_at":"2026-05-18T02:18:02Z"},{"alias_kind":"arxiv_version","alias_value":"1504.06219v1","created_at":"2026-05-18T02:18:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.06219","created_at":"2026-05-18T02:18:02Z"},{"alias_kind":"pith_short_12","alias_value":"3YPSK5ETWY5A","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"3YPSK5ETWY5AHHFN","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"3YPSK5ET","created_at":"2026-05-18T12:29:02Z"}],"graph_snapshots":[{"event_id":"sha256:9ff16d08d1b11149f3f40224f2cd1ef7291bf12cd2ba8aea0e5430d0231edf11","target":"graph","created_at":"2026-05-18T02:18:02Z","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, we study the minimum time planar tilting maneuver of a spacecraft, from the theoretical as well as from the numerical point of view, with a particular focus on the chattering phenomenon. We prove that there exist optimal chattering arcs when a singular junction occurs. Our study is based on the Pontryagin Maximum Principle and on results by M.I. Zelikin and V.F. Borisov. We give sufficient conditions on the initial values under which the optimal solutions do not contain any singular arc, and are bang-bang with a finite number of switchings. Moreover, we implement sub-optimal str","authors_text":"Emmanuel Tr\\'elat, Jiamin Zhu, Max Cerf","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-04-23T15:24:23Z","title":"Planar tilting maneuver of a spacecraft: singular arcs in the minimum time problem and chattering"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.06219","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":"sha256:69bb32d6af0a463db37ee7f519f54766e32c0d214539be24187364d78b84f87c","target":"record","created_at":"2026-05-18T02:18:02Z","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":"a385b5a0dca25a104b828cd8868f04c748dd63c5d708422b2a8c035035ab8c7f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-04-23T15:24:23Z","title_canon_sha256":"7ac981b3ea11afbed8b495414f6471455a091615466f70991e9ff46fb38f3691"},"schema_version":"1.0","source":{"id":"1504.06219","kind":"arxiv","version":1}},"canonical_sha256":"de1f257493b63a039cad54217f00af975a5ce7fc9e8a9f298b12b522297fc066","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"de1f257493b63a039cad54217f00af975a5ce7fc9e8a9f298b12b522297fc066","first_computed_at":"2026-05-18T02:18:02.232765Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:18:02.232765Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YL1wW0HomOoja2bgEBlGQ4fRl/Fpitc7cZhYWGXYENo1/GUg+r7QYKnp5V9ikDgjf2yc/OQvbU17vUokAhSzAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:18:02.233542Z","signed_message":"canonical_sha256_bytes"},"source_id":"1504.06219","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:69bb32d6af0a463db37ee7f519f54766e32c0d214539be24187364d78b84f87c","sha256:9ff16d08d1b11149f3f40224f2cd1ef7291bf12cd2ba8aea0e5430d0231edf11"],"state_sha256":"40f7c914aba19b352ae804ca31a3ed01689db486278bdad00f3455bf79f17f8c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qMgy3XaRojipfvsM4Ru41tJGn01cU2gJjwICMF6ZWie4rClN6qyx2ex05JN8Z0687LwwwwauyzFmEvXtaoN5Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T09:22:57.888894Z","bundle_sha256":"d24756c451985292c53f1bab5989d376d263d192582f2eeae58b7fcf208f5334"}}