{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:WUX77AMOR2GDECBVW5XFZZ5PDL","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":"ba5a4967391d740d2de28df7606294a2688d365418e129e2a5012476388d962f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-07-11T00:09:30Z","title_canon_sha256":"1fed0f09aff1c96d66f32e1b6aa99637fce5214e519d244db4e800959177cbb3"},"schema_version":"1.0","source":{"id":"1607.02798","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.02798","created_at":"2026-05-18T00:05:46Z"},{"alias_kind":"arxiv_version","alias_value":"1607.02798v4","created_at":"2026-05-18T00:05:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.02798","created_at":"2026-05-18T00:05:46Z"},{"alias_kind":"pith_short_12","alias_value":"WUX77AMOR2GD","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_16","alias_value":"WUX77AMOR2GDECBV","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_8","alias_value":"WUX77AMO","created_at":"2026-05-18T12:30:51Z"}],"graph_snapshots":[{"event_id":"sha256:b75b6e0bd7098f5e51b2907960778f362580d4cc321bf998c203950a9390fa79","target":"graph","created_at":"2026-05-18T00:05:46Z","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":"A local convergence rate is established for a Gauss orthogonal collocation method applied to optimal control problems with control constraints. If the Hamiltonian possesses a strong convexity property, then the theory yields convergence for problems whose optimal state and costate possess two square integrable derivatives. The convergence theory is based on a stability result for the sup-norm change in the solution of a variational inequality relative to a 2-norm perturbation, and on a Sobolev space bound for the error in interpolation at the Gauss quadrature points and the additional point -1","authors_text":"Anil V. Rao, Jun Liu, Subhashree Mohapatra, William W. Hager, Xiang-Sheng Wang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-07-11T00:09:30Z","title":"Convergence rate for a Gauss collocation method applied to constrained optimal control"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.02798","kind":"arxiv","version":4},"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:fdc2fc61c4cdd50264f8a554368f3ec6f4bfcead38dc859f9c039fe9daacb246","target":"record","created_at":"2026-05-18T00:05:46Z","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":"ba5a4967391d740d2de28df7606294a2688d365418e129e2a5012476388d962f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-07-11T00:09:30Z","title_canon_sha256":"1fed0f09aff1c96d66f32e1b6aa99637fce5214e519d244db4e800959177cbb3"},"schema_version":"1.0","source":{"id":"1607.02798","kind":"arxiv","version":4}},"canonical_sha256":"b52fff818e8e8c320835b76e5ce7af1ae6d3c00157d81945c46fb28b6951dafc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b52fff818e8e8c320835b76e5ce7af1ae6d3c00157d81945c46fb28b6951dafc","first_computed_at":"2026-05-18T00:05:46.430872Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:05:46.430872Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/wxnf40o2bFw5MJWfqPXomnqShjHuhGY8S76PF3AlHG0gEtdyle/L2adNT7ftMZT0xgcLiZTSwhUJe/i2fcLCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:05:46.431480Z","signed_message":"canonical_sha256_bytes"},"source_id":"1607.02798","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fdc2fc61c4cdd50264f8a554368f3ec6f4bfcead38dc859f9c039fe9daacb246","sha256:b75b6e0bd7098f5e51b2907960778f362580d4cc321bf998c203950a9390fa79"],"state_sha256":"deb4b487aae195c532f70d54486518fb19defe3cbd9516f1c50371764230fefa"}