{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:FOXNITAQSLFSSBLAMQPY2SCMQZ","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":"12894c32935035997f6f88a8921cc27caf536b655d8aa292526351aa3cba6421","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-04-15T13:39:36Z","title_canon_sha256":"6e3521ec40356b065e70ca88a28557847e78127332957918bc7f6e27e4b9e933"},"schema_version":"1.0","source":{"id":"1904.07038","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.07038","created_at":"2026-05-17T23:48:35Z"},{"alias_kind":"arxiv_version","alias_value":"1904.07038v1","created_at":"2026-05-17T23:48:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.07038","created_at":"2026-05-17T23:48:35Z"},{"alias_kind":"pith_short_12","alias_value":"FOXNITAQSLFS","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_16","alias_value":"FOXNITAQSLFSSBLA","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_8","alias_value":"FOXNITAQ","created_at":"2026-05-18T12:33:15Z"}],"graph_snapshots":[{"event_id":"sha256:77f98d30332b0166ed8e59cb96626a05c18b7cba82af21da7d58e51245f8e019","target":"graph","created_at":"2026-05-17T23:48:35Z","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":"In this article we consider a control problem of a linear Euler-Bernoulli damped beam equation with potential in dimension one with periodic boundary conditions. We derive a new Carleman estimate for an adjoint of the equation under consideration. Then using a well known duality argument we obtain explicitly the control function which can be used to drive the solution trajectory of the control problem to zero state.","authors_text":"Sourav Mitra","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-04-15T13:39:36Z","title":"Carleman estimate for an adjoint of a damped beam equation and an application to null controllability"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.07038","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:f7fd246b120b46bd24d2450409b0ce6b1c5569a77186423630f6e9e9c3b3befc","target":"record","created_at":"2026-05-17T23:48:35Z","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":"12894c32935035997f6f88a8921cc27caf536b655d8aa292526351aa3cba6421","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-04-15T13:39:36Z","title_canon_sha256":"6e3521ec40356b065e70ca88a28557847e78127332957918bc7f6e27e4b9e933"},"schema_version":"1.0","source":{"id":"1904.07038","kind":"arxiv","version":1}},"canonical_sha256":"2baed44c1092cb290560641f8d484c8678b297dd95bd908f7ef078cb8dcd4aab","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2baed44c1092cb290560641f8d484c8678b297dd95bd908f7ef078cb8dcd4aab","first_computed_at":"2026-05-17T23:48:35.429463Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:48:35.429463Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DcR3RxQC6XIkF6NuZ8hBBO1JkVHNiV1sFeeNSM07/Q2vW/cQrF68bsKJhznNcM7aCm9b3qHd/GXnNd04iOyuDg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:48:35.429865Z","signed_message":"canonical_sha256_bytes"},"source_id":"1904.07038","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f7fd246b120b46bd24d2450409b0ce6b1c5569a77186423630f6e9e9c3b3befc","sha256:77f98d30332b0166ed8e59cb96626a05c18b7cba82af21da7d58e51245f8e019"],"state_sha256":"9c414771dba01799e20e53de9212343cced1693f92054819c37e7cf0808b6801"}