{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:YUYB7I4IL6X2EICIR6OFDQUZU6","short_pith_number":"pith:YUYB7I4I","schema_version":"1.0","canonical_sha256":"c5301fa3885fafa220488f9c51c299a7b4b05c8b58ebbc40ead8d3958f280802","source":{"kind":"arxiv","id":"1812.09145","version":1},"attestation_state":"computed","paper":{"title":"The Landau Hamiltonian with $\\delta$-potentials supported on curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.AP","math.FA","math.MP"],"primary_cat":"math.SP","authors_text":"Jussi Behrndt, Markus Holzmann, Pavel Exner, Vladimir Lotoreichik","submitted_at":"2018-12-21T14:30:05Z","abstract_excerpt":"The spectral properties of the singularly perturbed self-adjoint Landau Hamiltonian $A_\\alpha =(i \\nabla + A)^2 + \\alpha\\delta$ in $L^2(R^2)$ with a $\\delta$-potential supported on a finite $C^{1,1}$-smooth curve $\\Sigma$ are studied. Here $A = \\frac{1}{2} B (-x_2, x_1)^\\top$ is the vector potential, $B>0$ is the strength of the homogeneous magnetic field, and $\\alpha\\in L^\\infty(\\Sigma)$ is a position-dependent real coefficient modeling the strength of the singular interaction on the curve $\\Sigma$. After a general discussion of the qualitative spectral properties of $A_\\alpha$ and its resolv"},"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":"1812.09145","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2018-12-21T14:30:05Z","cross_cats_sorted":["math-ph","math.AP","math.FA","math.MP"],"title_canon_sha256":"2bc4c9f26684fc60852f0f6d2f6155622aa8da6e73b0b525056b9b602c373f04","abstract_canon_sha256":"e95249e9b220509c7b52c364551c38ea1b25dabd433112c77f0bccdfb195a4ec"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:57:45.235386Z","signature_b64":"mM7xfT5V7l5flri0Kb60HP0g4mwPJZCZDiyKU0jQB1ulZ0OoVhSoDvh/HCXSUhgY9lldQBR70IjFZmC3OSLuDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c5301fa3885fafa220488f9c51c299a7b4b05c8b58ebbc40ead8d3958f280802","last_reissued_at":"2026-05-17T23:57:45.234755Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:57:45.234755Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Landau Hamiltonian with $\\delta$-potentials supported on curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.AP","math.FA","math.MP"],"primary_cat":"math.SP","authors_text":"Jussi Behrndt, Markus Holzmann, Pavel Exner, Vladimir Lotoreichik","submitted_at":"2018-12-21T14:30:05Z","abstract_excerpt":"The spectral properties of the singularly perturbed self-adjoint Landau Hamiltonian $A_\\alpha =(i \\nabla + A)^2 + \\alpha\\delta$ in $L^2(R^2)$ with a $\\delta$-potential supported on a finite $C^{1,1}$-smooth curve $\\Sigma$ are studied. Here $A = \\frac{1}{2} B (-x_2, x_1)^\\top$ is the vector potential, $B>0$ is the strength of the homogeneous magnetic field, and $\\alpha\\in L^\\infty(\\Sigma)$ is a position-dependent real coefficient modeling the strength of the singular interaction on the curve $\\Sigma$. After a general discussion of the qualitative spectral properties of $A_\\alpha$ and its resolv"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.09145","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":"1812.09145","created_at":"2026-05-17T23:57:45.234858+00:00"},{"alias_kind":"arxiv_version","alias_value":"1812.09145v1","created_at":"2026-05-17T23:57:45.234858+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.09145","created_at":"2026-05-17T23:57:45.234858+00:00"},{"alias_kind":"pith_short_12","alias_value":"YUYB7I4IL6X2","created_at":"2026-05-18T12:33:04.347982+00:00"},{"alias_kind":"pith_short_16","alias_value":"YUYB7I4IL6X2EICI","created_at":"2026-05-18T12:33:04.347982+00:00"},{"alias_kind":"pith_short_8","alias_value":"YUYB7I4I","created_at":"2026-05-18T12:33:04.347982+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"1907.04282","citing_title":"Boundary integral formulations of eigenvalue problems for elliptic differential operators with singular interactions and their numerical approximation by boundary element methods","ref_index":4,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/YUYB7I4IL6X2EICIR6OFDQUZU6","json":"https://pith.science/pith/YUYB7I4IL6X2EICIR6OFDQUZU6.json","graph_json":"https://pith.science/api/pith-number/YUYB7I4IL6X2EICIR6OFDQUZU6/graph.json","events_json":"https://pith.science/api/pith-number/YUYB7I4IL6X2EICIR6OFDQUZU6/events.json","paper":"https://pith.science/paper/YUYB7I4I"},"agent_actions":{"view_html":"https://pith.science/pith/YUYB7I4IL6X2EICIR6OFDQUZU6","download_json":"https://pith.science/pith/YUYB7I4IL6X2EICIR6OFDQUZU6.json","view_paper":"https://pith.science/paper/YUYB7I4I","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1812.09145&json=true","fetch_graph":"https://pith.science/api/pith-number/YUYB7I4IL6X2EICIR6OFDQUZU6/graph.json","fetch_events":"https://pith.science/api/pith-number/YUYB7I4IL6X2EICIR6OFDQUZU6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YUYB7I4IL6X2EICIR6OFDQUZU6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YUYB7I4IL6X2EICIR6OFDQUZU6/action/storage_attestation","attest_author":"https://pith.science/pith/YUYB7I4IL6X2EICIR6OFDQUZU6/action/author_attestation","sign_citation":"https://pith.science/pith/YUYB7I4IL6X2EICIR6OFDQUZU6/action/citation_signature","submit_replication":"https://pith.science/pith/YUYB7I4IL6X2EICIR6OFDQUZU6/action/replication_record"}},"created_at":"2026-05-17T23:57:45.234858+00:00","updated_at":"2026-05-17T23:57:45.234858+00:00"}