{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:DTU54FAKVJUMZWBH7WBBDU6OFG","short_pith_number":"pith:DTU54FAK","canonical_record":{"source":{"id":"2505.19454","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2025-05-26T03:20:01Z","cross_cats_sorted":["cs.SY","eess.SY"],"title_canon_sha256":"3a7107774fd1d36a9630690094f54cd40eda9e5cb973a5457282e25d150ec53b","abstract_canon_sha256":"7d658fc60cf03d22c0226133193906f20412a8cd35d4722382136e5f4c2080b1"},"schema_version":"1.0"},"canonical_sha256":"1ce9de140aaa68ccd827fd8211d3ce29839f541c53a59e4fa4d81a38655c82d7","source":{"kind":"arxiv","id":"2505.19454","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.19454","created_at":"2026-07-05T12:06:13Z"},{"alias_kind":"arxiv_version","alias_value":"2505.19454v2","created_at":"2026-07-05T12:06:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.19454","created_at":"2026-07-05T12:06:13Z"},{"alias_kind":"pith_short_12","alias_value":"DTU54FAKVJUM","created_at":"2026-07-05T12:06:13Z"},{"alias_kind":"pith_short_16","alias_value":"DTU54FAKVJUMZWBH","created_at":"2026-07-05T12:06:13Z"},{"alias_kind":"pith_short_8","alias_value":"DTU54FAK","created_at":"2026-07-05T12:06:13Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:DTU54FAKVJUMZWBH7WBBDU6OFG","target":"record","payload":{"canonical_record":{"source":{"id":"2505.19454","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2025-05-26T03:20:01Z","cross_cats_sorted":["cs.SY","eess.SY"],"title_canon_sha256":"3a7107774fd1d36a9630690094f54cd40eda9e5cb973a5457282e25d150ec53b","abstract_canon_sha256":"7d658fc60cf03d22c0226133193906f20412a8cd35d4722382136e5f4c2080b1"},"schema_version":"1.0"},"canonical_sha256":"1ce9de140aaa68ccd827fd8211d3ce29839f541c53a59e4fa4d81a38655c82d7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T12:06:13.124721Z","signature_b64":"oBzFhdd6NQOuTHf7lW3Epr69j/XoTA0m1PAfpP90T9uKS/N4H/jsLAckNP3gvdLoaKvu9XMxOeVExBHqELS0Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1ce9de140aaa68ccd827fd8211d3ce29839f541c53a59e4fa4d81a38655c82d7","last_reissued_at":"2026-07-05T12:06:13.124212Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T12:06:13.124212Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2505.19454","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":"2026-07-05T12:06:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WqhnAZwN9/PukZE9bQnToFvJ23DO1FNx4tKHOZK7OQ6FKr26XYz1zdEVUqZ7972oTuW05PNE/sSRrotwzE/RDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T17:56:01.727891Z"},"content_sha256":"08473d40da04c38820773a7ceb02826b54e97e945ca4ce071598eb65e2b56701","schema_version":"1.0","event_id":"sha256:08473d40da04c38820773a7ceb02826b54e97e945ca4ce071598eb65e2b56701"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:DTU54FAKVJUMZWBH7WBBDU6OFG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Direct Pseudospectral Optimal Control by Orthogonal Polynomial Integral Collocation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SY","eess.SY"],"primary_cat":"math.OC","authors_text":"Ian M. Down, Manoranjan Majji, Thomas L. Ahrens","submitted_at":"2025-05-26T03:20:01Z","abstract_excerpt":"This paper details a methodology to transcribe an optimal control problem into a nonlinear program for generation of the trajectories that optimize a given functional by approximating only the highest order derivatives of a given system's dynamics. The underlying method uses orthogonal polynomial integral collocation by which successive integrals are taken to approximate all lower order states. Hence, one set of polynomial coefficients can represent an entire coordinate's degree of freedom. Specifically, Chebyshev polynomials of the first and second kind and Legendre polynomials are used over "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.19454","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/2505.19454/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":"2026-07-05T12:06:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dN432jtgFXOaoYeYHzUbSWn0YU2hlOlK3COIA85lVCl8YTnnwxehlUdjJwFpJqOJhRDoepRd00aiEUsra1E6BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T17:56:01.728872Z"},"content_sha256":"209198b5a4c8159e8f3b822caf43f5d23b0721f3275e4af610df7bf36e1fbb6a","schema_version":"1.0","event_id":"sha256:209198b5a4c8159e8f3b822caf43f5d23b0721f3275e4af610df7bf36e1fbb6a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DTU54FAKVJUMZWBH7WBBDU6OFG/bundle.json","state_url":"https://pith.science/pith/DTU54FAKVJUMZWBH7WBBDU6OFG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DTU54FAKVJUMZWBH7WBBDU6OFG/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":"2026-08-12T17:56:01Z","links":{"resolver":"https://pith.science/pith/DTU54FAKVJUMZWBH7WBBDU6OFG","bundle":"https://pith.science/pith/DTU54FAKVJUMZWBH7WBBDU6OFG/bundle.json","state":"https://pith.science/pith/DTU54FAKVJUMZWBH7WBBDU6OFG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DTU54FAKVJUMZWBH7WBBDU6OFG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:DTU54FAKVJUMZWBH7WBBDU6OFG","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":"7d658fc60cf03d22c0226133193906f20412a8cd35d4722382136e5f4c2080b1","cross_cats_sorted":["cs.SY","eess.SY"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2025-05-26T03:20:01Z","title_canon_sha256":"3a7107774fd1d36a9630690094f54cd40eda9e5cb973a5457282e25d150ec53b"},"schema_version":"1.0","source":{"id":"2505.19454","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.19454","created_at":"2026-07-05T12:06:13Z"},{"alias_kind":"arxiv_version","alias_value":"2505.19454v2","created_at":"2026-07-05T12:06:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.19454","created_at":"2026-07-05T12:06:13Z"},{"alias_kind":"pith_short_12","alias_value":"DTU54FAKVJUM","created_at":"2026-07-05T12:06:13Z"},{"alias_kind":"pith_short_16","alias_value":"DTU54FAKVJUMZWBH","created_at":"2026-07-05T12:06:13Z"},{"alias_kind":"pith_short_8","alias_value":"DTU54FAK","created_at":"2026-07-05T12:06:13Z"}],"graph_snapshots":[{"event_id":"sha256:209198b5a4c8159e8f3b822caf43f5d23b0721f3275e4af610df7bf36e1fbb6a","target":"graph","created_at":"2026-07-05T12:06:13Z","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/2505.19454/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper details a methodology to transcribe an optimal control problem into a nonlinear program for generation of the trajectories that optimize a given functional by approximating only the highest order derivatives of a given system's dynamics. The underlying method uses orthogonal polynomial integral collocation by which successive integrals are taken to approximate all lower order states. Hence, one set of polynomial coefficients can represent an entire coordinate's degree of freedom. Specifically, Chebyshev polynomials of the first and second kind and Legendre polynomials are used over ","authors_text":"Ian M. Down, Manoranjan Majji, Thomas L. Ahrens","cross_cats":["cs.SY","eess.SY"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2025-05-26T03:20:01Z","title":"Direct Pseudospectral Optimal Control by Orthogonal Polynomial Integral Collocation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.19454","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":"sha256:08473d40da04c38820773a7ceb02826b54e97e945ca4ce071598eb65e2b56701","target":"record","created_at":"2026-07-05T12:06:13Z","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":"7d658fc60cf03d22c0226133193906f20412a8cd35d4722382136e5f4c2080b1","cross_cats_sorted":["cs.SY","eess.SY"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2025-05-26T03:20:01Z","title_canon_sha256":"3a7107774fd1d36a9630690094f54cd40eda9e5cb973a5457282e25d150ec53b"},"schema_version":"1.0","source":{"id":"2505.19454","kind":"arxiv","version":2}},"canonical_sha256":"1ce9de140aaa68ccd827fd8211d3ce29839f541c53a59e4fa4d81a38655c82d7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1ce9de140aaa68ccd827fd8211d3ce29839f541c53a59e4fa4d81a38655c82d7","first_computed_at":"2026-07-05T12:06:13.124212Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T12:06:13.124212Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oBzFhdd6NQOuTHf7lW3Epr69j/XoTA0m1PAfpP90T9uKS/N4H/jsLAckNP3gvdLoaKvu9XMxOeVExBHqELS0Bg==","signature_status":"signed_v1","signed_at":"2026-07-05T12:06:13.124721Z","signed_message":"canonical_sha256_bytes"},"source_id":"2505.19454","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:08473d40da04c38820773a7ceb02826b54e97e945ca4ce071598eb65e2b56701","sha256:209198b5a4c8159e8f3b822caf43f5d23b0721f3275e4af610df7bf36e1fbb6a"],"state_sha256":"40dd585bd6e7a1545d0ce36a96413db2b00ac9e000c55548379023fde7966623"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sco3QIlIQDPHp6NxYejW6x7O2rMJI8NKgp/NPuoQTXsBpag0dW1uQHBRbAxNISPpOGtbaSDbNugGHofxNtBUCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-12T17:56:01.734586Z","bundle_sha256":"3d1e51b290dbda3bf9aa3949922ca1a873a94d7e563c4ffb8fc4cebd119c81c2"}}