{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:YAIUVUGZPES6TD3I3FQZBVC34B","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":"8270abf6682cbde37612f86cba10a159f1935adb04f5da2b5a1884dd6cbb0fab","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-04-19T14:21:00Z","title_canon_sha256":"46a256c4f07c7c95005080811672ba712a497b5e8092591b81fabaf80d23ced3"},"schema_version":"1.0","source":{"id":"1304.5426","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.5426","created_at":"2026-05-18T03:27:33Z"},{"alias_kind":"arxiv_version","alias_value":"1304.5426v1","created_at":"2026-05-18T03:27:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.5426","created_at":"2026-05-18T03:27:33Z"},{"alias_kind":"pith_short_12","alias_value":"YAIUVUGZPES6","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"YAIUVUGZPES6TD3I","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"YAIUVUGZ","created_at":"2026-05-18T12:28:06Z"}],"graph_snapshots":[{"event_id":"sha256:b0c2c3199767502bb0545b2af460bd335b32cbc3645367093a0e718796b6c33e","target":"graph","created_at":"2026-05-18T03:27:33Z","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 derive in a direct and rather straightforward way the null controllability of a 2-D heat equation with boundary control. We use the so-called flatness approach, which consists in parameterizing the solution and the control by the derivatives of a \"flat output\". This provides an explicit control law achieving the exact steering to zero. Numerical experiments demonstrate the relevance of the approach.","authors_text":"Lionel Rosier, Philippe Martin, Pierre Rouchon","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-04-19T14:21:00Z","title":"Null Controllability of the 2D Heat Equation Using Flatness"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.5426","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":"sha256:6c1ef88cb550a00db2d6abdc8c8de06af6bf1a5f22c5437fcbba49aee7e1a1f8","target":"record","created_at":"2026-05-18T03:27:33Z","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":"8270abf6682cbde37612f86cba10a159f1935adb04f5da2b5a1884dd6cbb0fab","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-04-19T14:21:00Z","title_canon_sha256":"46a256c4f07c7c95005080811672ba712a497b5e8092591b81fabaf80d23ced3"},"schema_version":"1.0","source":{"id":"1304.5426","kind":"arxiv","version":1}},"canonical_sha256":"c0114ad0d97925e98f68d96190d45be04cebd73465da55fb240ea5272b688935","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c0114ad0d97925e98f68d96190d45be04cebd73465da55fb240ea5272b688935","first_computed_at":"2026-05-18T03:27:33.539577Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:27:33.539577Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DC83qovcpkY8PDnjupbDbxpBRUymVjZuhLBU4w1FOA6WJNykqH9GhYqQw704dYy2Si696ZviWD5gaBqk5M59Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:27:33.540169Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.5426","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6c1ef88cb550a00db2d6abdc8c8de06af6bf1a5f22c5437fcbba49aee7e1a1f8","sha256:b0c2c3199767502bb0545b2af460bd335b32cbc3645367093a0e718796b6c33e"],"state_sha256":"db448aa83bc89b97bbe262e81e2cf51e0116ce9b588776db99652d57b19c9d83"}