{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:UNC6LQ7UXEVS66IAGSESG7YZ57","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":"75acb1fa42bb2d5dece24e34987d5f354068eeb12ee98b826eded8645b55a2a0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-01-20T08:02:00Z","title_canon_sha256":"7cb5849f8dea10126311f2f4c5f015462379edebd0c129cd5f66f0d7fbe46d17"},"schema_version":"1.0","source":{"id":"1701.05717","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.05717","created_at":"2026-05-18T00:52:28Z"},{"alias_kind":"arxiv_version","alias_value":"1701.05717v1","created_at":"2026-05-18T00:52:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.05717","created_at":"2026-05-18T00:52:28Z"},{"alias_kind":"pith_short_12","alias_value":"UNC6LQ7UXEVS","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_16","alias_value":"UNC6LQ7UXEVS66IA","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_8","alias_value":"UNC6LQ7U","created_at":"2026-05-18T12:31:46Z"}],"graph_snapshots":[{"event_id":"sha256:6ac4b60c21e15d7491d0e84d2599b8d8ae66f27c21526ea1c5b797e5e9cd7734","target":"graph","created_at":"2026-05-18T00:52:28Z","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 studies the approximate and null controllability for impulse controlled systems of heat equations coupled by a pair (A,B) of constant matrices. We present a necessary and sufficient condition for the approximate controllability, which is exactly Kalman's controllability rank condition of (A,B). We prove that when such a system is approximately controllable, the approximate controllability over an interval [0,T] can be realized by adding controls at arbitrary n different control instants 0<\\tau_1<\\tau_2<\\cdots<\\tau_n<T, provided that \\tau_n-\\tau_1<d_A, where d_A=\\min\\{\\pi/|Im \\lambda","authors_text":"Gengsheng Wang, Shulin Qin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-01-20T08:02:00Z","title":"Controllability of impulse controlled systems of heat equations coupled by constant matrices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.05717","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":"sha256:6bf06e163c1f408ede930524e5383576d66e0a9c4ace5c29f7b62684ccdf135e","target":"record","created_at":"2026-05-18T00:52:28Z","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":"75acb1fa42bb2d5dece24e34987d5f354068eeb12ee98b826eded8645b55a2a0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-01-20T08:02:00Z","title_canon_sha256":"7cb5849f8dea10126311f2f4c5f015462379edebd0c129cd5f66f0d7fbe46d17"},"schema_version":"1.0","source":{"id":"1701.05717","kind":"arxiv","version":1}},"canonical_sha256":"a345e5c3f4b92b2f79003489237f19effd4d96799869d689c8f5fdd687e54337","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a345e5c3f4b92b2f79003489237f19effd4d96799869d689c8f5fdd687e54337","first_computed_at":"2026-05-18T00:52:28.704022Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:52:28.704022Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"n3NY/oIO4ZxlyPwtwi5OvRiCtCsgpGnBMB8EAXjuh1dL+PHOkRgaSkwG7RamwAH/G5RnCwD7QwVw2mziKd/YAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:52:28.704650Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.05717","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6bf06e163c1f408ede930524e5383576d66e0a9c4ace5c29f7b62684ccdf135e","sha256:6ac4b60c21e15d7491d0e84d2599b8d8ae66f27c21526ea1c5b797e5e9cd7734"],"state_sha256":"9cd807d93e756a291d085d8b6e47e6cd7045c93dd40c4207248490d26d92d19c"}