{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:BQ2Y2CWPNNBLK6K44NJAR42MJ6","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":"38efa9f9a6adc1c3ede77e63217bfba8d8ce7f151642a4d4f4e0bc226cea867d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2026-06-17T08:36:11Z","title_canon_sha256":"19aa162b63c71703c85e7e0b16ff1ec3048521c734cb6ae82852d82ea4765e12"},"schema_version":"1.0","source":{"id":"2606.18818","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.18818","created_at":"2026-06-19T16:11:48Z"},{"alias_kind":"arxiv_version","alias_value":"2606.18818v1","created_at":"2026-06-19T16:11:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.18818","created_at":"2026-06-19T16:11:48Z"},{"alias_kind":"pith_short_12","alias_value":"BQ2Y2CWPNNBL","created_at":"2026-06-19T16:11:48Z"},{"alias_kind":"pith_short_16","alias_value":"BQ2Y2CWPNNBLK6K4","created_at":"2026-06-19T16:11:48Z"},{"alias_kind":"pith_short_8","alias_value":"BQ2Y2CWP","created_at":"2026-06-19T16:11:48Z"}],"graph_snapshots":[{"event_id":"sha256:c36eed343eb1a91916e480d33c3c84f510f6fbe2fb4b03a8458cad3175127be0","target":"graph","created_at":"2026-06-19T16:11:48Z","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/2606.18818/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This note generalizes the port-Hamiltonian formulation of the continuous time primal-dual gradient algorithm for static constrained convex optimization to the convex optimal control problem.The resulting dynamics is shown to be a port-Hamiltonian system of partial differential equations, involving ordinary physical time as well 'algorithmic' time. Convergence to the optimal control solution is indicated, and it is argued that sub-optimal control strategies could be derived starting from the partial differential equation formulation.","authors_text":"Arjan van der Schaft","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2026-06-17T08:36:11Z","title":"Sub-optimal control by primal-dual gradient dynamics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.18818","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":"sha256:6380cfc15998321ea7f3c60f480a9b0eb6a24022c7b26385680b9facba14fd19","target":"record","created_at":"2026-06-19T16:11:48Z","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":"38efa9f9a6adc1c3ede77e63217bfba8d8ce7f151642a4d4f4e0bc226cea867d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2026-06-17T08:36:11Z","title_canon_sha256":"19aa162b63c71703c85e7e0b16ff1ec3048521c734cb6ae82852d82ea4765e12"},"schema_version":"1.0","source":{"id":"2606.18818","kind":"arxiv","version":1}},"canonical_sha256":"0c358d0acf6b42b5795ce35208f34c4f8956c961f195c5faf0c3f88c79af0859","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0c358d0acf6b42b5795ce35208f34c4f8956c961f195c5faf0c3f88c79af0859","first_computed_at":"2026-06-19T16:11:48.326669Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-19T16:11:48.326669Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BcODFZUzxLyA96cTUoVpzHm9Lt0kckQGOhoOE8ALv9+tEsLqE9BsQe+0QoF5ByoZRACUocpeeuxDzR999r2ZCw==","signature_status":"signed_v1","signed_at":"2026-06-19T16:11:48.327048Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.18818","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6380cfc15998321ea7f3c60f480a9b0eb6a24022c7b26385680b9facba14fd19","sha256:c36eed343eb1a91916e480d33c3c84f510f6fbe2fb4b03a8458cad3175127be0"],"state_sha256":"6af5a9d05e60a65adb733a3bae551d6d33d926e54c9eef186c507d072b1d9beb"}