{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:RIKNFKO7CGRBRYTD4XTIWF4NYZ","short_pith_number":"pith:RIKNFKO7","canonical_record":{"source":{"id":"1610.00394","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-10-03T02:55:11Z","cross_cats_sorted":[],"title_canon_sha256":"28e3374b494a94dca8e1399eb66523f9d60b676d02b06b03d8d532f7e43c81cf","abstract_canon_sha256":"95b5b5f8d169555ad3b49a5320d387fcb75c350deb55338bfea249688bedd182"},"schema_version":"1.0"},"canonical_sha256":"8a14d2a9df11a218e263e5e68b178dc67c088c562880dad8ec40736156c1f91c","source":{"kind":"arxiv","id":"1610.00394","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.00394","created_at":"2026-05-18T00:49:42Z"},{"alias_kind":"arxiv_version","alias_value":"1610.00394v2","created_at":"2026-05-18T00:49:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.00394","created_at":"2026-05-18T00:49:42Z"},{"alias_kind":"pith_short_12","alias_value":"RIKNFKO7CGRB","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_16","alias_value":"RIKNFKO7CGRBRYTD","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_8","alias_value":"RIKNFKO7","created_at":"2026-05-18T12:30:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:RIKNFKO7CGRBRYTD4XTIWF4NYZ","target":"record","payload":{"canonical_record":{"source":{"id":"1610.00394","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-10-03T02:55:11Z","cross_cats_sorted":[],"title_canon_sha256":"28e3374b494a94dca8e1399eb66523f9d60b676d02b06b03d8d532f7e43c81cf","abstract_canon_sha256":"95b5b5f8d169555ad3b49a5320d387fcb75c350deb55338bfea249688bedd182"},"schema_version":"1.0"},"canonical_sha256":"8a14d2a9df11a218e263e5e68b178dc67c088c562880dad8ec40736156c1f91c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:49:42.050322Z","signature_b64":"eplfUjnli5mUB02++IpklSSGNJR6j7jtcN5wI5ow6g+76QJOzU29sZ0LdX24K97Rm7+uoxA9tMFs+eTqyRI4CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8a14d2a9df11a218e263e5e68b178dc67c088c562880dad8ec40736156c1f91c","last_reissued_at":"2026-05-18T00:49:42.049871Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:49:42.049871Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1610.00394","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":"2026-05-18T00:49:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ho6W7SoWxear+oQNWtfoHnkaJC+P9jjbPT9C5p6LEssKpbzC2LaL3AM1RNRjZ/Z8dHgx4ImJUX5eOTk3FT0BDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T06:35:09.783463Z"},"content_sha256":"f093ed6ef85d9edcfd8d294893d0ab65f69758f9bcbd1ad0a752b2e69a03c930","schema_version":"1.0","event_id":"sha256:f093ed6ef85d9edcfd8d294893d0ab65f69758f9bcbd1ad0a752b2e69a03c930"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:RIKNFKO7CGRBRYTD4XTIWF4NYZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Control Synthesis for Nonlinear Optimal Control via Convex Relaxations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Pengcheng Zhao, Ram Vasudevan, Shankar Mohan","submitted_at":"2016-10-03T02:55:11Z","abstract_excerpt":"This paper addresses the problem of control synthesis for nonlinear optimal control problems in the presence of state and input constraints. The presented approach relies upon transforming the given problem into an infinite-dimensional linear program over the space of measures. To generate approximations to this infinite-dimensional program, a sequence of Semi-Definite Programs (SDP)s is formulated in the instance of polynomial cost and dynamics with semi-algebraic state and bounded input constraints. A method to extract a polynomial control function from each SDP is also given. This paper pro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.00394","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":"2026-05-18T00:49:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zqCLTpsDroV9uwpWfueKLIoaBDXy+GLPh7sSyQKTOFCATva3kHh5e3UVESo/qFjGoZqU/fCXNQrcfk5oOYpMBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T06:35:09.784231Z"},"content_sha256":"99d15cedfdce1fae82350dfe44905e6ab7700b4ae232176495319759456c06d1","schema_version":"1.0","event_id":"sha256:99d15cedfdce1fae82350dfe44905e6ab7700b4ae232176495319759456c06d1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RIKNFKO7CGRBRYTD4XTIWF4NYZ/bundle.json","state_url":"https://pith.science/pith/RIKNFKO7CGRBRYTD4XTIWF4NYZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RIKNFKO7CGRBRYTD4XTIWF4NYZ/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":"2026-05-30T06:35:09Z","links":{"resolver":"https://pith.science/pith/RIKNFKO7CGRBRYTD4XTIWF4NYZ","bundle":"https://pith.science/pith/RIKNFKO7CGRBRYTD4XTIWF4NYZ/bundle.json","state":"https://pith.science/pith/RIKNFKO7CGRBRYTD4XTIWF4NYZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RIKNFKO7CGRBRYTD4XTIWF4NYZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:RIKNFKO7CGRBRYTD4XTIWF4NYZ","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":"95b5b5f8d169555ad3b49a5320d387fcb75c350deb55338bfea249688bedd182","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-10-03T02:55:11Z","title_canon_sha256":"28e3374b494a94dca8e1399eb66523f9d60b676d02b06b03d8d532f7e43c81cf"},"schema_version":"1.0","source":{"id":"1610.00394","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.00394","created_at":"2026-05-18T00:49:42Z"},{"alias_kind":"arxiv_version","alias_value":"1610.00394v2","created_at":"2026-05-18T00:49:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.00394","created_at":"2026-05-18T00:49:42Z"},{"alias_kind":"pith_short_12","alias_value":"RIKNFKO7CGRB","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_16","alias_value":"RIKNFKO7CGRBRYTD","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_8","alias_value":"RIKNFKO7","created_at":"2026-05-18T12:30:41Z"}],"graph_snapshots":[{"event_id":"sha256:99d15cedfdce1fae82350dfe44905e6ab7700b4ae232176495319759456c06d1","target":"graph","created_at":"2026-05-18T00:49:42Z","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":"This paper addresses the problem of control synthesis for nonlinear optimal control problems in the presence of state and input constraints. The presented approach relies upon transforming the given problem into an infinite-dimensional linear program over the space of measures. To generate approximations to this infinite-dimensional program, a sequence of Semi-Definite Programs (SDP)s is formulated in the instance of polynomial cost and dynamics with semi-algebraic state and bounded input constraints. A method to extract a polynomial control function from each SDP is also given. This paper pro","authors_text":"Pengcheng Zhao, Ram Vasudevan, Shankar Mohan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-10-03T02:55:11Z","title":"Control Synthesis for Nonlinear Optimal Control via Convex Relaxations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.00394","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:f093ed6ef85d9edcfd8d294893d0ab65f69758f9bcbd1ad0a752b2e69a03c930","target":"record","created_at":"2026-05-18T00:49:42Z","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":"95b5b5f8d169555ad3b49a5320d387fcb75c350deb55338bfea249688bedd182","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-10-03T02:55:11Z","title_canon_sha256":"28e3374b494a94dca8e1399eb66523f9d60b676d02b06b03d8d532f7e43c81cf"},"schema_version":"1.0","source":{"id":"1610.00394","kind":"arxiv","version":2}},"canonical_sha256":"8a14d2a9df11a218e263e5e68b178dc67c088c562880dad8ec40736156c1f91c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8a14d2a9df11a218e263e5e68b178dc67c088c562880dad8ec40736156c1f91c","first_computed_at":"2026-05-18T00:49:42.049871Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:49:42.049871Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eplfUjnli5mUB02++IpklSSGNJR6j7jtcN5wI5ow6g+76QJOzU29sZ0LdX24K97Rm7+uoxA9tMFs+eTqyRI4CA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:49:42.050322Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.00394","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f093ed6ef85d9edcfd8d294893d0ab65f69758f9bcbd1ad0a752b2e69a03c930","sha256:99d15cedfdce1fae82350dfe44905e6ab7700b4ae232176495319759456c06d1"],"state_sha256":"3fd2b55b3dda09155eca9815950ab90eca19f78664e2b0fdc55e9b1e70ce5cc0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JXTc0S8In1NOS9EWF/gZjISK6N/AR3bX5+HGxqSFioWjrvW96/RmWvT4zBDhm70OUUcbe4QuIHXJUDv3MzBTBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T06:35:09.788450Z","bundle_sha256":"836a7410055b48a84224b6831a9d7f210c0ee1ea0fce7cc412224918152365aa"}}