{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:MEDS4B3QCUZVINEOO76KGNNC4R","short_pith_number":"pith:MEDS4B3Q","canonical_record":{"source":{"id":"1609.03183","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-09-11T16:54:20Z","cross_cats_sorted":[],"title_canon_sha256":"a11c6603f94ac2934d4c5215844c436ce1f6ea79a8c73a18c9ece178bd93bd44","abstract_canon_sha256":"7f3a8eb6c8fa6d0b372dc8af54670b53a6184dc7e74c1c768802fb04b66d5976"},"schema_version":"1.0"},"canonical_sha256":"61072e0770153354348e77fca335a2e4529383ec4f3ab76242ceb45842a179e4","source":{"kind":"arxiv","id":"1609.03183","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.03183","created_at":"2026-05-18T01:04:47Z"},{"alias_kind":"arxiv_version","alias_value":"1609.03183v1","created_at":"2026-05-18T01:04:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.03183","created_at":"2026-05-18T01:04:47Z"},{"alias_kind":"pith_short_12","alias_value":"MEDS4B3QCUZV","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_16","alias_value":"MEDS4B3QCUZVINEO","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_8","alias_value":"MEDS4B3Q","created_at":"2026-05-18T12:30:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:MEDS4B3QCUZVINEOO76KGNNC4R","target":"record","payload":{"canonical_record":{"source":{"id":"1609.03183","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-09-11T16:54:20Z","cross_cats_sorted":[],"title_canon_sha256":"a11c6603f94ac2934d4c5215844c436ce1f6ea79a8c73a18c9ece178bd93bd44","abstract_canon_sha256":"7f3a8eb6c8fa6d0b372dc8af54670b53a6184dc7e74c1c768802fb04b66d5976"},"schema_version":"1.0"},"canonical_sha256":"61072e0770153354348e77fca335a2e4529383ec4f3ab76242ceb45842a179e4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:04:47.598874Z","signature_b64":"cOnLho/RlNTwh5Hsrz1XmNi4JlqlvVAwzKY9xoshjq+u5iTKIkilsMaErIIGZ+rqvQKLlNQSyoGLJSLu15rHBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"61072e0770153354348e77fca335a2e4529383ec4f3ab76242ceb45842a179e4","last_reissued_at":"2026-05-18T01:04:47.598387Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:04:47.598387Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1609.03183","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":"2026-05-18T01:04:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dWxd3HI3tafT1QaR4/LSDXIIElsk1a6aRsp7YxjRBqWtsy6+n8+Ck0nnU3M5oMdg/zvFzUcsDpLWI41xAiojDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T20:28:16.235691Z"},"content_sha256":"493cd3cc0ba6b45242adfe0bd69f420eb0975eca90b273da5a4474e635ba1127","schema_version":"1.0","event_id":"sha256:493cd3cc0ba6b45242adfe0bd69f420eb0975eca90b273da5a4474e635ba1127"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:MEDS4B3QCUZVINEOO76KGNNC4R","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Hamiltonian-based Algorithm for Relaxed Optimal Control","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Magnus Egerstedt, Muhammad Umer Qureshi, Yorai Wardi","submitted_at":"2016-09-11T16:54:20Z","abstract_excerpt":"This paper concerns a first-order algorithmic technique for a class of optimal control problems defined on switched-mode hybrid systems. The salient feature of the algorithm is that it avoids the computation of Fr\\'echet or G\\^ateaux derivatives of the cost functional, which can be time consuming, but rather moves in a projected-gradient direction that is easily computable (for a class of problems) and does not require any explicit derivatives. The algorithm is applicable to a class of problems where a pointwise minimizer of the Hamiltonian is computable by a simple formula, and this includes "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.03183","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":"2026-05-18T01:04:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NJr+sVRM6qy8UKcwllX10otLDXySgHkvzokOIDgFJqbchewI1ExhOFoWfzha/TkSR2LetIkqk7vKpxGTQ7fKDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T20:28:16.236190Z"},"content_sha256":"ee7cf47b70340d53e8aa952aec97e9ce279e8e2bae6a53990bef3eb88e128ee2","schema_version":"1.0","event_id":"sha256:ee7cf47b70340d53e8aa952aec97e9ce279e8e2bae6a53990bef3eb88e128ee2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MEDS4B3QCUZVINEOO76KGNNC4R/bundle.json","state_url":"https://pith.science/pith/MEDS4B3QCUZVINEOO76KGNNC4R/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MEDS4B3QCUZVINEOO76KGNNC4R/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":"2026-06-05T20:28:16Z","links":{"resolver":"https://pith.science/pith/MEDS4B3QCUZVINEOO76KGNNC4R","bundle":"https://pith.science/pith/MEDS4B3QCUZVINEOO76KGNNC4R/bundle.json","state":"https://pith.science/pith/MEDS4B3QCUZVINEOO76KGNNC4R/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MEDS4B3QCUZVINEOO76KGNNC4R/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:MEDS4B3QCUZVINEOO76KGNNC4R","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":"7f3a8eb6c8fa6d0b372dc8af54670b53a6184dc7e74c1c768802fb04b66d5976","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-09-11T16:54:20Z","title_canon_sha256":"a11c6603f94ac2934d4c5215844c436ce1f6ea79a8c73a18c9ece178bd93bd44"},"schema_version":"1.0","source":{"id":"1609.03183","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.03183","created_at":"2026-05-18T01:04:47Z"},{"alias_kind":"arxiv_version","alias_value":"1609.03183v1","created_at":"2026-05-18T01:04:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.03183","created_at":"2026-05-18T01:04:47Z"},{"alias_kind":"pith_short_12","alias_value":"MEDS4B3QCUZV","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_16","alias_value":"MEDS4B3QCUZVINEO","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_8","alias_value":"MEDS4B3Q","created_at":"2026-05-18T12:30:32Z"}],"graph_snapshots":[{"event_id":"sha256:ee7cf47b70340d53e8aa952aec97e9ce279e8e2bae6a53990bef3eb88e128ee2","target":"graph","created_at":"2026-05-18T01:04:47Z","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 concerns a first-order algorithmic technique for a class of optimal control problems defined on switched-mode hybrid systems. The salient feature of the algorithm is that it avoids the computation of Fr\\'echet or G\\^ateaux derivatives of the cost functional, which can be time consuming, but rather moves in a projected-gradient direction that is easily computable (for a class of problems) and does not require any explicit derivatives. The algorithm is applicable to a class of problems where a pointwise minimizer of the Hamiltonian is computable by a simple formula, and this includes ","authors_text":"Magnus Egerstedt, Muhammad Umer Qureshi, Yorai Wardi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-09-11T16:54:20Z","title":"Hamiltonian-based Algorithm for Relaxed Optimal Control"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.03183","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":"sha256:493cd3cc0ba6b45242adfe0bd69f420eb0975eca90b273da5a4474e635ba1127","target":"record","created_at":"2026-05-18T01:04:47Z","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":"7f3a8eb6c8fa6d0b372dc8af54670b53a6184dc7e74c1c768802fb04b66d5976","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-09-11T16:54:20Z","title_canon_sha256":"a11c6603f94ac2934d4c5215844c436ce1f6ea79a8c73a18c9ece178bd93bd44"},"schema_version":"1.0","source":{"id":"1609.03183","kind":"arxiv","version":1}},"canonical_sha256":"61072e0770153354348e77fca335a2e4529383ec4f3ab76242ceb45842a179e4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"61072e0770153354348e77fca335a2e4529383ec4f3ab76242ceb45842a179e4","first_computed_at":"2026-05-18T01:04:47.598387Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:04:47.598387Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cOnLho/RlNTwh5Hsrz1XmNi4JlqlvVAwzKY9xoshjq+u5iTKIkilsMaErIIGZ+rqvQKLlNQSyoGLJSLu15rHBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:04:47.598874Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.03183","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:493cd3cc0ba6b45242adfe0bd69f420eb0975eca90b273da5a4474e635ba1127","sha256:ee7cf47b70340d53e8aa952aec97e9ce279e8e2bae6a53990bef3eb88e128ee2"],"state_sha256":"adb482f07729699bd454045160a40646e067b425a93e127bc63f600aea817445"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3JrIVikh4OfJJbJ2sEN607DsVPvYVeOdXc5g4z7p/A/HXYGj3ocl5c53G3U1a9o9X1g0Cdb7WXAo4Yn2LYPhDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T20:28:16.239510Z","bundle_sha256":"8b6d3951422a3b5ba7cc52b2b3bbee3617d378b945cd563a408c4750f27a8017"}}