{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:RFQEXI2CCPPCKRLO745PCLL3I2","short_pith_number":"pith:RFQEXI2C","schema_version":"1.0","canonical_sha256":"89604ba34213de25456eff3af12d7b4695583da3502cc7d529b303a6c0da3136","source":{"kind":"arxiv","id":"1401.6828","version":1},"attestation_state":"computed","paper":{"title":"Minimal time for the bilinear control of Schr\\\"odinger equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Holger Teismann, Jean-Michel Coron (LJLL), Karine Beauchard (CMLS-EcolePolytechnique)","submitted_at":"2014-01-27T12:53:26Z","abstract_excerpt":"We consider a quantum particle in a potential V (x) (x in R^N) subject to a (spatially homogeneous) time-dependent electric field E(t), which plays the role of the control. Under generic assumptions on V, this system is approximately controllable on the L2(R^N;C)-sphere, in su ffiently large times T, as proved by Boscain, Caponigro, Chambrion and Sigalotti. In the present article, we show that this approximate controllability result is false in small time. As a consequence, the result by Boscain et al. is, in some sense, optimal with respect to the control time T."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1401.6828","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-01-27T12:53:26Z","cross_cats_sorted":[],"title_canon_sha256":"4f8b4f92b2f1cbf2d8815189bc5de2a65ec014eb0ae0f74e6bde1b1d404f04f0","abstract_canon_sha256":"6ca17b783b1c96dbc7f32a9546ad9fef456b687c2a2514d00f12ad551ba97010"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:01:00.546949Z","signature_b64":"d4tv/BGefUXo1KgCJ33ody2xpu6nqe8sEILkOzfiq1gV3co7LGehYTO2eQxJXhOAELF6aGBGelBtl46qm3mQAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"89604ba34213de25456eff3af12d7b4695583da3502cc7d529b303a6c0da3136","last_reissued_at":"2026-05-18T03:01:00.546204Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:01:00.546204Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Minimal time for the bilinear control of Schr\\\"odinger equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Holger Teismann, Jean-Michel Coron (LJLL), Karine Beauchard (CMLS-EcolePolytechnique)","submitted_at":"2014-01-27T12:53:26Z","abstract_excerpt":"We consider a quantum particle in a potential V (x) (x in R^N) subject to a (spatially homogeneous) time-dependent electric field E(t), which plays the role of the control. Under generic assumptions on V, this system is approximately controllable on the L2(R^N;C)-sphere, in su ffiently large times T, as proved by Boscain, Caponigro, Chambrion and Sigalotti. In the present article, we show that this approximate controllability result is false in small time. As a consequence, the result by Boscain et al. is, in some sense, optimal with respect to the control time T."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.6828","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1401.6828","created_at":"2026-05-18T03:01:00.546313+00:00"},{"alias_kind":"arxiv_version","alias_value":"1401.6828v1","created_at":"2026-05-18T03:01:00.546313+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.6828","created_at":"2026-05-18T03:01:00.546313+00:00"},{"alias_kind":"pith_short_12","alias_value":"RFQEXI2CCPPC","created_at":"2026-05-18T12:28:46.137349+00:00"},{"alias_kind":"pith_short_16","alias_value":"RFQEXI2CCPPCKRLO","created_at":"2026-05-18T12:28:46.137349+00:00"},{"alias_kind":"pith_short_8","alias_value":"RFQEXI2C","created_at":"2026-05-18T12:28:46.137349+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/RFQEXI2CCPPCKRLO745PCLL3I2","json":"https://pith.science/pith/RFQEXI2CCPPCKRLO745PCLL3I2.json","graph_json":"https://pith.science/api/pith-number/RFQEXI2CCPPCKRLO745PCLL3I2/graph.json","events_json":"https://pith.science/api/pith-number/RFQEXI2CCPPCKRLO745PCLL3I2/events.json","paper":"https://pith.science/paper/RFQEXI2C"},"agent_actions":{"view_html":"https://pith.science/pith/RFQEXI2CCPPCKRLO745PCLL3I2","download_json":"https://pith.science/pith/RFQEXI2CCPPCKRLO745PCLL3I2.json","view_paper":"https://pith.science/paper/RFQEXI2C","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1401.6828&json=true","fetch_graph":"https://pith.science/api/pith-number/RFQEXI2CCPPCKRLO745PCLL3I2/graph.json","fetch_events":"https://pith.science/api/pith-number/RFQEXI2CCPPCKRLO745PCLL3I2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RFQEXI2CCPPCKRLO745PCLL3I2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RFQEXI2CCPPCKRLO745PCLL3I2/action/storage_attestation","attest_author":"https://pith.science/pith/RFQEXI2CCPPCKRLO745PCLL3I2/action/author_attestation","sign_citation":"https://pith.science/pith/RFQEXI2CCPPCKRLO745PCLL3I2/action/citation_signature","submit_replication":"https://pith.science/pith/RFQEXI2CCPPCKRLO745PCLL3I2/action/replication_record"}},"created_at":"2026-05-18T03:01:00.546313+00:00","updated_at":"2026-05-18T03:01:00.546313+00:00"}