{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:JESHZSLSKQKIHKKSKWQ3NF7WQC","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":"385da18503ba5de14bdfe5a4ba3e4861586005dc814f845da0a6d94d0071431c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-09-08T09:46:58Z","title_canon_sha256":"572a9f6bb56ec4d7d6f4882240e0b0040f583de209cabe216d9e5fed5199acb9"},"schema_version":"1.0","source":{"id":"1309.1943","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.1943","created_at":"2026-05-18T03:13:56Z"},{"alias_kind":"arxiv_version","alias_value":"1309.1943v1","created_at":"2026-05-18T03:13:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.1943","created_at":"2026-05-18T03:13:56Z"},{"alias_kind":"pith_short_12","alias_value":"JESHZSLSKQKI","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"JESHZSLSKQKIHKKS","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"JESHZSLS","created_at":"2026-05-18T12:27:49Z"}],"graph_snapshots":[{"event_id":"sha256:8f07248adc67409eed99ff2067afbe2b994a6b6f4bc3d2c8df0714002e782a02","target":"graph","created_at":"2026-05-18T03:13:56Z","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 paper, we consider the cost of null controllability for a large class of linear equations of parabolic or dispersive type in one space dimension in small time. By extending the work of Tenenbaum and Tucsnak in \"New blow-up rates for fast controls of Schr\\\"odinger and heat equations`\", we are able to give precise upper bounds on the time-dependance of the cost of fast controls when the time of control T tends to 0. We also give a lower bound of the cost of fast controls for the same class of equations, which proves the optimality of the power of T involved in the cost of the control. Th","authors_text":"Pierre Lissy","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-09-08T09:46:58Z","title":"On the cost of fast controls for some families of dispersive or parabolic equations in one space dimension"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.1943","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:a7831f5f56dfc13d151306f9d07fcd85f63c0b319c7553be5b72c4b75e54d024","target":"record","created_at":"2026-05-18T03:13:56Z","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":"385da18503ba5de14bdfe5a4ba3e4861586005dc814f845da0a6d94d0071431c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-09-08T09:46:58Z","title_canon_sha256":"572a9f6bb56ec4d7d6f4882240e0b0040f583de209cabe216d9e5fed5199acb9"},"schema_version":"1.0","source":{"id":"1309.1943","kind":"arxiv","version":1}},"canonical_sha256":"49247cc972541483a95255a1b697f680a9ea45bcc230ed7958328fb6b13ba68b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"49247cc972541483a95255a1b697f680a9ea45bcc230ed7958328fb6b13ba68b","first_computed_at":"2026-05-18T03:13:56.933150Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:13:56.933150Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PN5ek6g/TkvEYeQW7A2+JqhT7vcalX4u9hnS8AfcXPW6iVRSQuHiK3ccfovR9D52G+BKQK/Raj8B6edCas6tDw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:13:56.933869Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.1943","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a7831f5f56dfc13d151306f9d07fcd85f63c0b319c7553be5b72c4b75e54d024","sha256:8f07248adc67409eed99ff2067afbe2b994a6b6f4bc3d2c8df0714002e782a02"],"state_sha256":"e387fdbc7986806e7502803176e05739c3c32d691780e07ac0bb1e1da937d86b"}