{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:2P2VVIFNNZA3VVCLN2IDIYOMKJ","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":"480e037c9b21ab3a4dad4db4999163359302246fb17a59b3fc8f7bcedbd515ef","cross_cats_sorted":["cs.SY","math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2011-08-30T07:59:32Z","title_canon_sha256":"93b95a185484f9d0ffd9accaed5265f9fd595ec653dc601590f9796a5c9a144f"},"schema_version":"1.0","source":{"id":"1108.5860","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.5860","created_at":"2026-05-18T03:37:41Z"},{"alias_kind":"arxiv_version","alias_value":"1108.5860v2","created_at":"2026-05-18T03:37:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.5860","created_at":"2026-05-18T03:37:41Z"},{"alias_kind":"pith_short_12","alias_value":"2P2VVIFNNZA3","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_16","alias_value":"2P2VVIFNNZA3VVCL","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_8","alias_value":"2P2VVIFN","created_at":"2026-05-18T12:26:18Z"}],"graph_snapshots":[{"event_id":"sha256:6dafe4df0ca1cdad3cf2cd1ba5f85d4e7f7d6a78f3f51b1fb7897ae049a0762b","target":"graph","created_at":"2026-05-18T03:37:41Z","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":"We consider linear systems on a separable Hilbert space $H$, which are null controllable at some time $T_0>0$ under the action of a point or boundary control. Parabolic and hyperbolic control systems usually studied in applications are special cases. To every initial state $ y_0 \\in H$ we associate the minimal \"energy\" needed to transfer $ y_0 $ to $ 0 $ in a time $ T \\ge T_0$ (\"energy\" of a control being the square of its $ L^2 $ norm). We give both necessary and sufficient conditions under which the minimal energy converges to $ 0 $ for $ T\\to+\\infty $. This extends to boundary control syste","authors_text":"Enrico Priola, Jerzy Zabczyk, Luciano Pandolfi","cross_cats":["cs.SY","math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2011-08-30T07:59:32Z","title":"Linear Operator Inequality and Null Controllability with Vanishing Energy for unbounded control systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.5860","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:ebe0765f9c24fcf9ed0250f4239dd749206ce2142427973a4d31320754bed3d2","target":"record","created_at":"2026-05-18T03:37:41Z","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":"480e037c9b21ab3a4dad4db4999163359302246fb17a59b3fc8f7bcedbd515ef","cross_cats_sorted":["cs.SY","math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2011-08-30T07:59:32Z","title_canon_sha256":"93b95a185484f9d0ffd9accaed5265f9fd595ec653dc601590f9796a5c9a144f"},"schema_version":"1.0","source":{"id":"1108.5860","kind":"arxiv","version":2}},"canonical_sha256":"d3f55aa0ad6e41bad44b6e903461cc52793d97e3f0b397ec48ba1a476cbe165d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d3f55aa0ad6e41bad44b6e903461cc52793d97e3f0b397ec48ba1a476cbe165d","first_computed_at":"2026-05-18T03:37:41.744444Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:37:41.744444Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Nea47GzAHkZB2PvEnZ3FD6yLrueCJFjMez48wtii6+clC4VPH5jiaVtgOjFotaXyyFRDQB+45py6izUwtS3HCA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:37:41.745285Z","signed_message":"canonical_sha256_bytes"},"source_id":"1108.5860","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ebe0765f9c24fcf9ed0250f4239dd749206ce2142427973a4d31320754bed3d2","sha256:6dafe4df0ca1cdad3cf2cd1ba5f85d4e7f7d6a78f3f51b1fb7897ae049a0762b"],"state_sha256":"d863b4c8f4807c286612e8eab7539b16969363f94c387814fb1568568bf8d6d1"}