{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:LFLLETWA45AQ5U7LSOQJPDMU56","short_pith_number":"pith:LFLLETWA","canonical_record":{"source":{"id":"2403.06167","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"eess.SY","submitted_at":"2024-03-10T10:36:39Z","cross_cats_sorted":["cs.SY"],"title_canon_sha256":"698d2b1d45c3b2034e5d0a3c49b1683f65b51cc768248b2f10daeaa323a5ad9c","abstract_canon_sha256":"efd056e8da0394acac8f703e8d3386af1d2a56af4bd4c2bbb2efdb079a6364a2"},"schema_version":"1.0"},"canonical_sha256":"5956b24ec0e7410ed3eb93a0978d94ef8e85abbdff4e773f0363e4b5683bdb7a","source":{"kind":"arxiv","id":"2403.06167","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2403.06167","created_at":"2026-07-05T07:54:19Z"},{"alias_kind":"arxiv_version","alias_value":"2403.06167v1","created_at":"2026-07-05T07:54:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2403.06167","created_at":"2026-07-05T07:54:19Z"},{"alias_kind":"pith_short_12","alias_value":"LFLLETWA45AQ","created_at":"2026-07-05T07:54:19Z"},{"alias_kind":"pith_short_16","alias_value":"LFLLETWA45AQ5U7L","created_at":"2026-07-05T07:54:19Z"},{"alias_kind":"pith_short_8","alias_value":"LFLLETWA","created_at":"2026-07-05T07:54:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:LFLLETWA45AQ5U7LSOQJPDMU56","target":"record","payload":{"canonical_record":{"source":{"id":"2403.06167","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"eess.SY","submitted_at":"2024-03-10T10:36:39Z","cross_cats_sorted":["cs.SY"],"title_canon_sha256":"698d2b1d45c3b2034e5d0a3c49b1683f65b51cc768248b2f10daeaa323a5ad9c","abstract_canon_sha256":"efd056e8da0394acac8f703e8d3386af1d2a56af4bd4c2bbb2efdb079a6364a2"},"schema_version":"1.0"},"canonical_sha256":"5956b24ec0e7410ed3eb93a0978d94ef8e85abbdff4e773f0363e4b5683bdb7a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:54:19.329740Z","signature_b64":"mxvolxEGQ3ySuDj1CKnMeLNkla0NE1c/tY4vNYY4qL4RWXmOm/ge9MNxyykZjjcw0MR3yh1nY0QikLmlNLfyBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5956b24ec0e7410ed3eb93a0978d94ef8e85abbdff4e773f0363e4b5683bdb7a","last_reissued_at":"2026-07-05T07:54:19.329277Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:54:19.329277Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2403.06167","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":"2026-07-05T07:54:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"10aWmmAO4fBSBox2n9w5L4NTet3ITy8+uU9M9n4dz4pbXiU3VKUteh5WOIF1+n2M+Qa9+JAiwP7lz5K5Y2KYBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T19:55:35.653810Z"},"content_sha256":"05b5f9c7cb58f60be18a4aa96382cbeadbe31b8d5ae9e7554faabaacbb00f1d8","schema_version":"1.0","event_id":"sha256:05b5f9c7cb58f60be18a4aa96382cbeadbe31b8d5ae9e7554faabaacbb00f1d8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:LFLLETWA45AQ5U7LSOQJPDMU56","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Direct Shooting Method for Numerical Optimal Control: A Modified Transcription Approach","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.SY"],"primary_cat":"eess.SY","authors_text":"Jiawei Tang, Ling Shi, Pengyu Wang, Shuang Wu, Xingzhou Chen, Yuxing Zhong","submitted_at":"2024-03-10T10:36:39Z","abstract_excerpt":"Direct shooting is an efficient method to solve numerical optimal control. It utilizes the Runge-Kutta scheme to discretize a continuous-time optimal control problem making the problem solvable by nonlinear programming solvers. However, conventional direct shooting raises a contradictory dynamics issue when using an augmented state to handle {high-order} systems. This paper fills the research gap by considering the direct shooting method for {high-order} systems. We derive the modified Euler and Runge-Kutta-4 methods to transcribe the system dynamics constraint directly. Additionally, we provi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2403.06167","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2403.06167/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":"2026-07-05T07:54:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gN38+2Wwr+0muf/HE9MgC4D9L41FP/5gEmdgWe5eJuhZDmnIAQZFOdoOvzoGAjhx3q5kF2tSGxrtzeh40d9ADw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T19:55:35.654407Z"},"content_sha256":"f5a7a204716c9c63a49ab0ab2814011b26346509fe36138fa90072a2d900969b","schema_version":"1.0","event_id":"sha256:f5a7a204716c9c63a49ab0ab2814011b26346509fe36138fa90072a2d900969b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LFLLETWA45AQ5U7LSOQJPDMU56/bundle.json","state_url":"https://pith.science/pith/LFLLETWA45AQ5U7LSOQJPDMU56/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LFLLETWA45AQ5U7LSOQJPDMU56/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":"2026-08-10T19:55:35Z","links":{"resolver":"https://pith.science/pith/LFLLETWA45AQ5U7LSOQJPDMU56","bundle":"https://pith.science/pith/LFLLETWA45AQ5U7LSOQJPDMU56/bundle.json","state":"https://pith.science/pith/LFLLETWA45AQ5U7LSOQJPDMU56/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LFLLETWA45AQ5U7LSOQJPDMU56/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:LFLLETWA45AQ5U7LSOQJPDMU56","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":"efd056e8da0394acac8f703e8d3386af1d2a56af4bd4c2bbb2efdb079a6364a2","cross_cats_sorted":["cs.SY"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"eess.SY","submitted_at":"2024-03-10T10:36:39Z","title_canon_sha256":"698d2b1d45c3b2034e5d0a3c49b1683f65b51cc768248b2f10daeaa323a5ad9c"},"schema_version":"1.0","source":{"id":"2403.06167","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2403.06167","created_at":"2026-07-05T07:54:19Z"},{"alias_kind":"arxiv_version","alias_value":"2403.06167v1","created_at":"2026-07-05T07:54:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2403.06167","created_at":"2026-07-05T07:54:19Z"},{"alias_kind":"pith_short_12","alias_value":"LFLLETWA45AQ","created_at":"2026-07-05T07:54:19Z"},{"alias_kind":"pith_short_16","alias_value":"LFLLETWA45AQ5U7L","created_at":"2026-07-05T07:54:19Z"},{"alias_kind":"pith_short_8","alias_value":"LFLLETWA","created_at":"2026-07-05T07:54:19Z"}],"graph_snapshots":[{"event_id":"sha256:f5a7a204716c9c63a49ab0ab2814011b26346509fe36138fa90072a2d900969b","target":"graph","created_at":"2026-07-05T07:54:19Z","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/2403.06167/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Direct shooting is an efficient method to solve numerical optimal control. It utilizes the Runge-Kutta scheme to discretize a continuous-time optimal control problem making the problem solvable by nonlinear programming solvers. However, conventional direct shooting raises a contradictory dynamics issue when using an augmented state to handle {high-order} systems. This paper fills the research gap by considering the direct shooting method for {high-order} systems. We derive the modified Euler and Runge-Kutta-4 methods to transcribe the system dynamics constraint directly. Additionally, we provi","authors_text":"Jiawei Tang, Ling Shi, Pengyu Wang, Shuang Wu, Xingzhou Chen, Yuxing Zhong","cross_cats":["cs.SY"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"eess.SY","submitted_at":"2024-03-10T10:36:39Z","title":"Direct Shooting Method for Numerical Optimal Control: A Modified Transcription Approach"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2403.06167","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":"sha256:05b5f9c7cb58f60be18a4aa96382cbeadbe31b8d5ae9e7554faabaacbb00f1d8","target":"record","created_at":"2026-07-05T07:54:19Z","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":"efd056e8da0394acac8f703e8d3386af1d2a56af4bd4c2bbb2efdb079a6364a2","cross_cats_sorted":["cs.SY"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"eess.SY","submitted_at":"2024-03-10T10:36:39Z","title_canon_sha256":"698d2b1d45c3b2034e5d0a3c49b1683f65b51cc768248b2f10daeaa323a5ad9c"},"schema_version":"1.0","source":{"id":"2403.06167","kind":"arxiv","version":1}},"canonical_sha256":"5956b24ec0e7410ed3eb93a0978d94ef8e85abbdff4e773f0363e4b5683bdb7a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5956b24ec0e7410ed3eb93a0978d94ef8e85abbdff4e773f0363e4b5683bdb7a","first_computed_at":"2026-07-05T07:54:19.329277Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:54:19.329277Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mxvolxEGQ3ySuDj1CKnMeLNkla0NE1c/tY4vNYY4qL4RWXmOm/ge9MNxyykZjjcw0MR3yh1nY0QikLmlNLfyBA==","signature_status":"signed_v1","signed_at":"2026-07-05T07:54:19.329740Z","signed_message":"canonical_sha256_bytes"},"source_id":"2403.06167","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:05b5f9c7cb58f60be18a4aa96382cbeadbe31b8d5ae9e7554faabaacbb00f1d8","sha256:f5a7a204716c9c63a49ab0ab2814011b26346509fe36138fa90072a2d900969b"],"state_sha256":"37fb7871a88d6447270e92173666f99f6a37b4f3e238236d966c5d974032074f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LWXfn55MCJX8jiIbGwtqHjrKR5QB1+YxRAC+7JjWZ70ulwEqbUjofOJSjnkVBPuwpcaCgXDjGNTVwUFOuV7kCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-10T19:55:35.658197Z","bundle_sha256":"b5333df67b048cb51553118c3fddf313e7c0fc38e8de63df588f2a773c27e140"}}