{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:SQB66URVJSVKB2J3HKRWPVLMIW","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":"b4c672fb47c3adac2f783609767604842588bb7a2c90bce99bac81dcae22c401","cross_cats_sorted":["math.AP","math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-08-22T11:27:17Z","title_canon_sha256":"aff8d39ebc145fb787d7ee33bb90381cb23e36bb0fbdb80e2c60fab57e8466ee"},"schema_version":"1.0","source":{"id":"1908.08317","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.08317","created_at":"2026-07-05T04:02:50Z"},{"alias_kind":"arxiv_version","alias_value":"1908.08317v1","created_at":"2026-07-05T04:02:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.08317","created_at":"2026-07-05T04:02:50Z"},{"alias_kind":"pith_short_12","alias_value":"SQB66URVJSVK","created_at":"2026-07-05T04:02:50Z"},{"alias_kind":"pith_short_16","alias_value":"SQB66URVJSVKB2J3","created_at":"2026-07-05T04:02:50Z"},{"alias_kind":"pith_short_8","alias_value":"SQB66URV","created_at":"2026-07-05T04:02:50Z"}],"graph_snapshots":[{"event_id":"sha256:f155a5803e954610bad0adc11bf28b187b1e7802a38e32c870ae0629f5413997","target":"graph","created_at":"2026-07-05T04:02:50Z","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/1908.08317/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Input-to-state stability (ISS) for systems described by partial differential equations has seen intensified research activity recently, and in particular the class of boundary control systems, for which truly infinite-dimensional effects enter the situation. This note reviews input-to-state stability for parabolic equations with respect to general $L^{p}$-input-norms in the linear case and includes extensions of recent results on semilinear equations.","authors_text":"Felix Schwenninger","cross_cats":["math.AP","math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-08-22T11:27:17Z","title":"Input-to-state stability for parabolic boundary control: Linear and semi-linear systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.08317","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":"sha256:3f3788e58096c3f4b1fdd4632fc5a023a504d1f925b0cdc11a147c3c6835193d","target":"record","created_at":"2026-07-05T04:02:50Z","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":"b4c672fb47c3adac2f783609767604842588bb7a2c90bce99bac81dcae22c401","cross_cats_sorted":["math.AP","math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-08-22T11:27:17Z","title_canon_sha256":"aff8d39ebc145fb787d7ee33bb90381cb23e36bb0fbdb80e2c60fab57e8466ee"},"schema_version":"1.0","source":{"id":"1908.08317","kind":"arxiv","version":1}},"canonical_sha256":"9403ef52354caaa0e93b3aa367d56c45b95c71d4001ba8dd0847b0911bdf3d54","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9403ef52354caaa0e93b3aa367d56c45b95c71d4001ba8dd0847b0911bdf3d54","first_computed_at":"2026-07-05T04:02:50.692701Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:02:50.692701Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Lp4tXXEUW5h7c6ufF2ZKcRjDqXb5MAYmedLB4QLEaY5069FUaRIjIl55jVvzheXAsOpeGsqPgsVcX5syULLmDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T04:02:50.693411Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.08317","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3f3788e58096c3f4b1fdd4632fc5a023a504d1f925b0cdc11a147c3c6835193d","sha256:f155a5803e954610bad0adc11bf28b187b1e7802a38e32c870ae0629f5413997"],"state_sha256":"8f8182cf496549d878108872e6344f46b027a6c7222f31173d92203ae97f13e0"}