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Resonances are defined using analytic scattering theory. The main result is that if $\\zeta_n$, ${\\rm Im}\\zeta_n<0$, are resonances of $H^{\\varepsilon_n}$ for a sequence $\\varepsilon_n\\downarrow0$ as $n\\to\\infty$ and $\\zeta_n\\to\\zeta_0$ as $n\\to\\infty$, ${\\rm Im}\\zeta_0<0$, then $\\zeta_0$ is \\emph{not} a resonance of $H^0$."},"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":"1804.05620","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-04-16T11:45:45Z","cross_cats_sorted":["math.MP","math.SP"],"title_canon_sha256":"cf547322b95d8b0c6340f50021df57feda2af559aa5984c3596e0ca0dba7888b","abstract_canon_sha256":"afcb7d923085f659deda6854a2b008fdfa4b57a4b3aca797ce26c5ca2d14be08"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:53:31.244600Z","signature_b64":"QZazAaKSZ1BlTFq6DmRoQu7T36B1PkHY/Wj9eonyA0UC2hOZjgHA6yEjK86ZOgTOK/aVT22G/FbB5QniVrLSBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"04076201e343fe9af2bcae1229dbd0c9d19d36aae4067ba715fcc2e775d57a82","last_reissued_at":"2026-05-17T23:53:31.243981Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:53:31.243981Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Instability of resonances under Stark perturbations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","math.SP"],"primary_cat":"math-ph","authors_text":"Arne Jensen, Kenji Yajima","submitted_at":"2018-04-16T11:45:45Z","abstract_excerpt":"Let $H^{\\varepsilon}=-\\frac{d^2}{dx^2}+\\varepsilon x +V$, $\\varepsilon\\geq0$, on $L^2(\\mathbf{R})$. Let $V=\\sum_{k=1}^Nc_k|\\psi_k\\rangle\\langle\\psi_k|$ be a rank $N$ operator, where the $\\psi_k\\in L^2(\\mathbf{R})$ are real, compactly supported, and even. Resonances are defined using analytic scattering theory. The main result is that if $\\zeta_n$, ${\\rm Im}\\zeta_n<0$, are resonances of $H^{\\varepsilon_n}$ for a sequence $\\varepsilon_n\\downarrow0$ as $n\\to\\infty$ and $\\zeta_n\\to\\zeta_0$ as $n\\to\\infty$, ${\\rm Im}\\zeta_0<0$, then $\\zeta_0$ is \\emph{not} a resonance of $H^0$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.05620","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":"1804.05620","created_at":"2026-05-17T23:53:31.244062+00:00"},{"alias_kind":"arxiv_version","alias_value":"1804.05620v1","created_at":"2026-05-17T23:53:31.244062+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.05620","created_at":"2026-05-17T23:53:31.244062+00:00"},{"alias_kind":"pith_short_12","alias_value":"AQDWEAPDIP7J","created_at":"2026-05-18T12:32:13.499390+00:00"},{"alias_kind":"pith_short_16","alias_value":"AQDWEAPDIP7JV4V4","created_at":"2026-05-18T12:32:13.499390+00:00"},{"alias_kind":"pith_short_8","alias_value":"AQDWEAPD","created_at":"2026-05-18T12:32:13.499390+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"1907.03333","citing_title":"Resonances in the one dimensional Stark effect in the limit of small field","ref_index":4,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/AQDWEAPDIP7JV4V4VYJCTW6QZH","json":"https://pith.science/pith/AQDWEAPDIP7JV4V4VYJCTW6QZH.json","graph_json":"https://pith.science/api/pith-number/AQDWEAPDIP7JV4V4VYJCTW6QZH/graph.json","events_json":"https://pith.science/api/pith-number/AQDWEAPDIP7JV4V4VYJCTW6QZH/events.json","paper":"https://pith.science/paper/AQDWEAPD"},"agent_actions":{"view_html":"https://pith.science/pith/AQDWEAPDIP7JV4V4VYJCTW6QZH","download_json":"https://pith.science/pith/AQDWEAPDIP7JV4V4VYJCTW6QZH.json","view_paper":"https://pith.science/paper/AQDWEAPD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1804.05620&json=true","fetch_graph":"https://pith.science/api/pith-number/AQDWEAPDIP7JV4V4VYJCTW6QZH/graph.json","fetch_events":"https://pith.science/api/pith-number/AQDWEAPDIP7JV4V4VYJCTW6QZH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AQDWEAPDIP7JV4V4VYJCTW6QZH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AQDWEAPDIP7JV4V4VYJCTW6QZH/action/storage_attestation","attest_author":"https://pith.science/pith/AQDWEAPDIP7JV4V4VYJCTW6QZH/action/author_attestation","sign_citation":"https://pith.science/pith/AQDWEAPDIP7JV4V4VYJCTW6QZH/action/citation_signature","submit_replication":"https://pith.science/pith/AQDWEAPDIP7JV4V4VYJCTW6QZH/action/replication_record"}},"created_at":"2026-05-17T23:53:31.244062+00:00","updated_at":"2026-05-17T23:53:31.244062+00:00"}