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We establish a limiting absorption principle for $H(B, \\epsilon)$ and an estimate ${\\mathcal O}(\\epsilon^{n-2})$ for $\\xi'(\\lambda; B, \\epsilon)$, provided $\\lambda \\notin \\sigma(Q)$, where $Q = (D_x - By)^2 + D_y^2 + V(x,y).$"},"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":"0907.2164","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2009-07-13T13:46:29Z","cross_cats_sorted":["math.MP","math.SP"],"title_canon_sha256":"33a640bd9e5bdacd71d51fe12b74be55e283036203419994780859d53fdfd3f6","abstract_canon_sha256":"88f1ba0d2fc8a79ca70fd4122b6b25cfbac9dcf778f2b86a9d93bfafe324269b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:13:03.515885Z","signature_b64":"2hM/rHYO4R6cKAURegy7HVInjFIuY8T/Ve2Ps5azFSDycJWVayZvIY6rjFi06hhm5w/LQTQc1Q6ja41d31ZRBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e25b6e0e608e5f6444c80c7753b0e65af31607b1d09143ec7cbb7b6ae24f14c6","last_reissued_at":"2026-05-18T02:13:03.515039Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:13:03.515039Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Spectral shift function for operators with crossed magnetic and electric fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","math.SP"],"primary_cat":"math-ph","authors_text":"Mouez Dimassi, Vesselin Petkov","submitted_at":"2009-07-13T13:46:29Z","abstract_excerpt":"We obtain a representation formula for the derivative of the spectral shift function $\\xi(\\lambda; B, \\epsilon)$ related to the operators $H_0(B,\\epsilon) = (D_x - By)^2 + D_y^2 + \\epsilon x$ and $H(B, \\epsilon) = H_0(B, \\epsilon) + V(x,y), \\: B > 0, \\epsilon > 0$. We establish a limiting absorption principle for $H(B, \\epsilon)$ and an estimate ${\\mathcal O}(\\epsilon^{n-2})$ for $\\xi'(\\lambda; B, \\epsilon)$, provided $\\lambda \\notin \\sigma(Q)$, where $Q = (D_x - By)^2 + D_y^2 + V(x,y).$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0907.2164","kind":"arxiv","version":4},"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":"0907.2164","created_at":"2026-05-18T02:13:03.515190+00:00"},{"alias_kind":"arxiv_version","alias_value":"0907.2164v4","created_at":"2026-05-18T02:13:03.515190+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0907.2164","created_at":"2026-05-18T02:13:03.515190+00:00"},{"alias_kind":"pith_short_12","alias_value":"4JNW4DTARZPW","created_at":"2026-05-18T12:25:58.837520+00:00"},{"alias_kind":"pith_short_16","alias_value":"4JNW4DTARZPWIRGI","created_at":"2026-05-18T12:25:58.837520+00:00"},{"alias_kind":"pith_short_8","alias_value":"4JNW4DTA","created_at":"2026-05-18T12:25:58.837520+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/4JNW4DTARZPWIRGIBR3VHMHGLL","json":"https://pith.science/pith/4JNW4DTARZPWIRGIBR3VHMHGLL.json","graph_json":"https://pith.science/api/pith-number/4JNW4DTARZPWIRGIBR3VHMHGLL/graph.json","events_json":"https://pith.science/api/pith-number/4JNW4DTARZPWIRGIBR3VHMHGLL/events.json","paper":"https://pith.science/paper/4JNW4DTA"},"agent_actions":{"view_html":"https://pith.science/pith/4JNW4DTARZPWIRGIBR3VHMHGLL","download_json":"https://pith.science/pith/4JNW4DTARZPWIRGIBR3VHMHGLL.json","view_paper":"https://pith.science/paper/4JNW4DTA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0907.2164&json=true","fetch_graph":"https://pith.science/api/pith-number/4JNW4DTARZPWIRGIBR3VHMHGLL/graph.json","fetch_events":"https://pith.science/api/pith-number/4JNW4DTARZPWIRGIBR3VHMHGLL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4JNW4DTARZPWIRGIBR3VHMHGLL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4JNW4DTARZPWIRGIBR3VHMHGLL/action/storage_attestation","attest_author":"https://pith.science/pith/4JNW4DTARZPWIRGIBR3VHMHGLL/action/author_attestation","sign_citation":"https://pith.science/pith/4JNW4DTARZPWIRGIBR3VHMHGLL/action/citation_signature","submit_replication":"https://pith.science/pith/4JNW4DTARZPWIRGIBR3VHMHGLL/action/replication_record"}},"created_at":"2026-05-18T02:13:03.515190+00:00","updated_at":"2026-05-18T02:13:03.515190+00:00"}