{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:2EUTYVSM52MCVVWONIVMEXENA2","short_pith_number":"pith:2EUTYVSM","schema_version":"1.0","canonical_sha256":"d1293c564cee982ad6ce6a2ac25c8d0687205358b2cd90d6192779946e81c91d","source":{"kind":"arxiv","id":"1004.5594","version":2},"attestation_state":"computed","paper":{"title":"Bilinear control of discrete spectrum Schr\\\"odinger operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Kais Ammari, Zied Ammari","submitted_at":"2010-04-30T19:15:47Z","abstract_excerpt":"The bilinear control problem of  the Schr\\\"odinger equation $i\\frac{\\partial}{\\partial t}\\psi(t)$ $=(A+u(t) B)\\psi(t)$, where $u(t)$ is the control function,  is investigated through topological irreducibility of the set  $\\mathfrak{M}=\\{e^{-it (A+u B)}, u\\in \\mathbb{R}, t>0\\}$ of bounded operators. This allows to prove the approximate controllability of such systems when the uncontrolled Hamiltonian $A$ has a simple discrete spectrum and under an appropriate assumption on $B$."},"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":"1004.5594","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-04-30T19:15:47Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"6de3b56a708e2ec3c734d48b27ed2ebd562ce1937c0f6f27e51dd9b05cb3c900","abstract_canon_sha256":"408f40cebce5508dfe4837167b3f7f7814863496caa3add21a3cf45e9c28a704"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:24:09.733352Z","signature_b64":"038ILYVY3ftveYsygxGKL19euEZOE7nCXTsLbocvuu/9s/UvnHkND1EgylyCsNocnLn4v+BLCxI31aRz7gO0Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d1293c564cee982ad6ce6a2ac25c8d0687205358b2cd90d6192779946e81c91d","last_reissued_at":"2026-05-18T02:24:09.732701Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:24:09.732701Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Bilinear control of discrete spectrum Schr\\\"odinger operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Kais Ammari, Zied Ammari","submitted_at":"2010-04-30T19:15:47Z","abstract_excerpt":"The bilinear control problem of  the Schr\\\"odinger equation $i\\frac{\\partial}{\\partial t}\\psi(t)$ $=(A+u(t) B)\\psi(t)$, where $u(t)$ is the control function,  is investigated through topological irreducibility of the set  $\\mathfrak{M}=\\{e^{-it (A+u B)}, u\\in \\mathbb{R}, t>0\\}$ of bounded operators. This allows to prove the approximate controllability of such systems when the uncontrolled Hamiltonian $A$ has a simple discrete spectrum and under an appropriate assumption on $B$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.5594","kind":"arxiv","version":2},"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":"1004.5594","created_at":"2026-05-18T02:24:09.732808+00:00"},{"alias_kind":"arxiv_version","alias_value":"1004.5594v2","created_at":"2026-05-18T02:24:09.732808+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1004.5594","created_at":"2026-05-18T02:24:09.732808+00:00"},{"alias_kind":"pith_short_12","alias_value":"2EUTYVSM52MC","created_at":"2026-05-18T12:26:03.138858+00:00"},{"alias_kind":"pith_short_16","alias_value":"2EUTYVSM52MCVVWO","created_at":"2026-05-18T12:26:03.138858+00:00"},{"alias_kind":"pith_short_8","alias_value":"2EUTYVSM","created_at":"2026-05-18T12:26:03.138858+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/2EUTYVSM52MCVVWONIVMEXENA2","json":"https://pith.science/pith/2EUTYVSM52MCVVWONIVMEXENA2.json","graph_json":"https://pith.science/api/pith-number/2EUTYVSM52MCVVWONIVMEXENA2/graph.json","events_json":"https://pith.science/api/pith-number/2EUTYVSM52MCVVWONIVMEXENA2/events.json","paper":"https://pith.science/paper/2EUTYVSM"},"agent_actions":{"view_html":"https://pith.science/pith/2EUTYVSM52MCVVWONIVMEXENA2","download_json":"https://pith.science/pith/2EUTYVSM52MCVVWONIVMEXENA2.json","view_paper":"https://pith.science/paper/2EUTYVSM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1004.5594&json=true","fetch_graph":"https://pith.science/api/pith-number/2EUTYVSM52MCVVWONIVMEXENA2/graph.json","fetch_events":"https://pith.science/api/pith-number/2EUTYVSM52MCVVWONIVMEXENA2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2EUTYVSM52MCVVWONIVMEXENA2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2EUTYVSM52MCVVWONIVMEXENA2/action/storage_attestation","attest_author":"https://pith.science/pith/2EUTYVSM52MCVVWONIVMEXENA2/action/author_attestation","sign_citation":"https://pith.science/pith/2EUTYVSM52MCVVWONIVMEXENA2/action/citation_signature","submit_replication":"https://pith.science/pith/2EUTYVSM52MCVVWONIVMEXENA2/action/replication_record"}},"created_at":"2026-05-18T02:24:09.732808+00:00","updated_at":"2026-05-18T02:24:09.732808+00:00"}