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We compare the distribution of the eigenvalues of $H_D$ and $H_N$ below the respective infima of the essential spectra. To this end, we construct effective Hamiltonians which govern the asymptotic behaviour of the discrete spectrum of $H_\\ell$ near $\\inf \\sigma_{ess}(H_\\ell) = "},"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":"1212.1727","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2012-12-07T21:33:10Z","cross_cats_sorted":["math-ph","math.AP","math.MP"],"title_canon_sha256":"1abc773554a49c7de57b1b0a6434735a414f4b55f692fc5669401090fe21a5be","abstract_canon_sha256":"fa78d96e975594842019c3b948a01fed73f404d261b071dd46aec6315aa56e8e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:38:55.278139Z","signature_b64":"4/nGB3H2pb6VEA8n3lK9EFt96ZiJKCrk251tZsTFoltg/tVMAbIgCPNc4yQFVfgbLcPm2To5TBcSzDW+4YNRCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d5bb6c5ccca39fd8ab328b96b21caea421067252d5dd83cbb73105fd6a8e6271","last_reissued_at":"2026-05-18T03:38:55.277666Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:38:55.277666Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Dirichlet and Neumann Eigenvalues for Half-Plane Magnetic Hamiltonians","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.AP","math.MP"],"primary_cat":"math.SP","authors_text":"Georgi Raikov, Pablo Miranda, Vincent Bruneau","submitted_at":"2012-12-07T21:33:10Z","abstract_excerpt":"Let $H_{0, D}$ (resp., $H_{0,N}$) be the Schroedinger operator in constant magnetic field on the half-plane with Dirichlet (resp., Neumann) boundary conditions, and let $H_\\ell : = H_{0, \\ell} - V$, $\\ell =D,N$, where the scalar potential $V$ is non negative, bounded, does not vanish identically, and decays at infinity. We compare the distribution of the eigenvalues of $H_D$ and $H_N$ below the respective infima of the essential spectra. To this end, we construct effective Hamiltonians which govern the asymptotic behaviour of the discrete spectrum of $H_\\ell$ near $\\inf \\sigma_{ess}(H_\\ell) = "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.1727","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":"1212.1727","created_at":"2026-05-18T03:38:55.277725+00:00"},{"alias_kind":"arxiv_version","alias_value":"1212.1727v1","created_at":"2026-05-18T03:38:55.277725+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.1727","created_at":"2026-05-18T03:38:55.277725+00:00"},{"alias_kind":"pith_short_12","alias_value":"2W5WYXGMUOP5","created_at":"2026-05-18T12:26:50.516681+00:00"},{"alias_kind":"pith_short_16","alias_value":"2W5WYXGMUOP5RKZS","created_at":"2026-05-18T12:26:50.516681+00:00"},{"alias_kind":"pith_short_8","alias_value":"2W5WYXGM","created_at":"2026-05-18T12:26:50.516681+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/2W5WYXGMUOP5RKZSROLLEHFOUQ","json":"https://pith.science/pith/2W5WYXGMUOP5RKZSROLLEHFOUQ.json","graph_json":"https://pith.science/api/pith-number/2W5WYXGMUOP5RKZSROLLEHFOUQ/graph.json","events_json":"https://pith.science/api/pith-number/2W5WYXGMUOP5RKZSROLLEHFOUQ/events.json","paper":"https://pith.science/paper/2W5WYXGM"},"agent_actions":{"view_html":"https://pith.science/pith/2W5WYXGMUOP5RKZSROLLEHFOUQ","download_json":"https://pith.science/pith/2W5WYXGMUOP5RKZSROLLEHFOUQ.json","view_paper":"https://pith.science/paper/2W5WYXGM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1212.1727&json=true","fetch_graph":"https://pith.science/api/pith-number/2W5WYXGMUOP5RKZSROLLEHFOUQ/graph.json","fetch_events":"https://pith.science/api/pith-number/2W5WYXGMUOP5RKZSROLLEHFOUQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2W5WYXGMUOP5RKZSROLLEHFOUQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2W5WYXGMUOP5RKZSROLLEHFOUQ/action/storage_attestation","attest_author":"https://pith.science/pith/2W5WYXGMUOP5RKZSROLLEHFOUQ/action/author_attestation","sign_citation":"https://pith.science/pith/2W5WYXGMUOP5RKZSROLLEHFOUQ/action/citation_signature","submit_replication":"https://pith.science/pith/2W5WYXGMUOP5RKZSROLLEHFOUQ/action/replication_record"}},"created_at":"2026-05-18T03:38:55.277725+00:00","updated_at":"2026-05-18T03:38:55.277725+00:00"}