{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:7L2VLMUDV27F4IO6ZS7RMRFLCR","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":"49577aefc9a8b2a81623151b472b9689bd15bf50ebc2c864565b25c8a29a0d7a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-05-28T10:08:32Z","title_canon_sha256":"174e309626e194ed998fb01aba985c1d7d9ac92562086b555d6b3e56507dc39f"},"schema_version":"1.0","source":{"id":"1905.11717","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.11717","created_at":"2026-07-05T04:51:50Z"},{"alias_kind":"arxiv_version","alias_value":"1905.11717v4","created_at":"2026-07-05T04:51:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.11717","created_at":"2026-07-05T04:51:50Z"},{"alias_kind":"pith_short_12","alias_value":"7L2VLMUDV27F","created_at":"2026-07-05T04:51:50Z"},{"alias_kind":"pith_short_16","alias_value":"7L2VLMUDV27F4IO6","created_at":"2026-07-05T04:51:50Z"},{"alias_kind":"pith_short_8","alias_value":"7L2VLMUD","created_at":"2026-07-05T04:51:50Z"}],"graph_snapshots":[{"event_id":"sha256:aa2f87ad5c1955b53bbaad22e6e2e39e7f3d60b8ea3121b0c1da91fbd61c5da1","target":"graph","created_at":"2026-07-05T04:51:50Z","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/1905.11717/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We present a framework of sequential action control (SAC) for stabilization of systems of partial differential equations which can be posed as abstract semilinear control problems in Hilbert spaces. We follow a late-lumping approach and show that the control action can be explicitly obtained from variational principles using adjoint information. Moreover, we analyze the closed-loop system obtained from the SAC feedback for the linear problem with quadratic stage costs. We apply this theory to a prototypical example of an unstable heat equation and provide numerical results as the verification ","authors_text":"Arno Seidel, Falk M. Hante, Yan Brodskyi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-05-28T10:08:32Z","title":"Stabilization of Partial Differential Equations by Sequential Action Control"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.11717","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":"sha256:7cae286616ba993182b29fd74311dd91079aa3565fa9eb672dab2ffaec1863b5","target":"record","created_at":"2026-07-05T04:51:50Z","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":"49577aefc9a8b2a81623151b472b9689bd15bf50ebc2c864565b25c8a29a0d7a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-05-28T10:08:32Z","title_canon_sha256":"174e309626e194ed998fb01aba985c1d7d9ac92562086b555d6b3e56507dc39f"},"schema_version":"1.0","source":{"id":"1905.11717","kind":"arxiv","version":4}},"canonical_sha256":"faf555b283aebe5e21deccbf1644ab14499ad0e867784ae3959d79b441f62e41","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"faf555b283aebe5e21deccbf1644ab14499ad0e867784ae3959d79b441f62e41","first_computed_at":"2026-07-05T04:51:50.879576Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:51:50.879576Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ou35vTRYJjxE0L2f1WlU+lr5rMdIp39yeOLsj9M15j0YdMMyXnWWIn8otqAuOPVoem5aIlQNZbi7ZTPPeD9LBw==","signature_status":"signed_v1","signed_at":"2026-07-05T04:51:50.879987Z","signed_message":"canonical_sha256_bytes"},"source_id":"1905.11717","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7cae286616ba993182b29fd74311dd91079aa3565fa9eb672dab2ffaec1863b5","sha256:aa2f87ad5c1955b53bbaad22e6e2e39e7f3d60b8ea3121b0c1da91fbd61c5da1"],"state_sha256":"d276c2d0f2ff2e15860a4b5906de75144984f7e424391b94042e2be67ae67a83"}