{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:TBC436SZEXNXDXAQVOVYWF7DNT","short_pith_number":"pith:TBC436SZ","schema_version":"1.0","canonical_sha256":"9845cdfa5925db71dc10abab8b17e36ccfad431bd25e7b0b17c8afddc6d60942","source":{"kind":"arxiv","id":"1710.00899","version":3},"attestation_state":"computed","paper":{"title":"Wegner estimate and disorder dependence for alloy-type Hamiltonians with bounded magnetic potential","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.MP"],"primary_cat":"math-ph","authors_text":"Martin Tautenhahn, Matthias T\\\"aufer","submitted_at":"2017-10-02T20:37:44Z","abstract_excerpt":"We consider non-ergodic magnetic random Sch\\\"odinger operators with a bounded magnetic vector potential. We prove an optimal Wegner estimate valid at all energies. The proof is an adaptation of the arguments from [Kle13], combined with a recent quantitative unique continuation estimate for eigenfunctions of elliptic operators from [BTV15]. This generalizes Klein's result to operators with a bounded magnetic vector potential. Moreover, we study the dependence of the Wegner-constant on the disorder parameter. In particular, we show that above the model-dependent threshold $E_0(\\infty) \\in (0, \\i"},"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":"1710.00899","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-10-02T20:37:44Z","cross_cats_sorted":["math.AP","math.MP"],"title_canon_sha256":"287cb8e3b8855c1cf5008d07c634b30a7eb134450d549ecfec0e75ddad8fefa4","abstract_canon_sha256":"5ae3e826e6b66a6375b98dc732ce1e044416d1d3533723c86ab2aa794a0b90af"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:28:29.615355Z","signature_b64":"KnP6Lrh1toe57ximjTOSh9r3xxnCPqUuhJuc/GtXS9LkMruSQbxuTGKv4ze/JOgoR87drztrVhmNcCYjVhgUDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9845cdfa5925db71dc10abab8b17e36ccfad431bd25e7b0b17c8afddc6d60942","last_reissued_at":"2026-05-18T00:28:29.614626Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:28:29.614626Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Wegner estimate and disorder dependence for alloy-type Hamiltonians with bounded magnetic potential","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.MP"],"primary_cat":"math-ph","authors_text":"Martin Tautenhahn, Matthias T\\\"aufer","submitted_at":"2017-10-02T20:37:44Z","abstract_excerpt":"We consider non-ergodic magnetic random Sch\\\"odinger operators with a bounded magnetic vector potential. We prove an optimal Wegner estimate valid at all energies. The proof is an adaptation of the arguments from [Kle13], combined with a recent quantitative unique continuation estimate for eigenfunctions of elliptic operators from [BTV15]. This generalizes Klein's result to operators with a bounded magnetic vector potential. Moreover, we study the dependence of the Wegner-constant on the disorder parameter. In particular, we show that above the model-dependent threshold $E_0(\\infty) \\in (0, \\i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.00899","kind":"arxiv","version":3},"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":"1710.00899","created_at":"2026-05-18T00:28:29.614735+00:00"},{"alias_kind":"arxiv_version","alias_value":"1710.00899v3","created_at":"2026-05-18T00:28:29.614735+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.00899","created_at":"2026-05-18T00:28:29.614735+00:00"},{"alias_kind":"pith_short_12","alias_value":"TBC436SZEXNX","created_at":"2026-05-18T12:31:43.269735+00:00"},{"alias_kind":"pith_short_16","alias_value":"TBC436SZEXNXDXAQ","created_at":"2026-05-18T12:31:43.269735+00:00"},{"alias_kind":"pith_short_8","alias_value":"TBC436SZ","created_at":"2026-05-18T12:31:43.269735+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/TBC436SZEXNXDXAQVOVYWF7DNT","json":"https://pith.science/pith/TBC436SZEXNXDXAQVOVYWF7DNT.json","graph_json":"https://pith.science/api/pith-number/TBC436SZEXNXDXAQVOVYWF7DNT/graph.json","events_json":"https://pith.science/api/pith-number/TBC436SZEXNXDXAQVOVYWF7DNT/events.json","paper":"https://pith.science/paper/TBC436SZ"},"agent_actions":{"view_html":"https://pith.science/pith/TBC436SZEXNXDXAQVOVYWF7DNT","download_json":"https://pith.science/pith/TBC436SZEXNXDXAQVOVYWF7DNT.json","view_paper":"https://pith.science/paper/TBC436SZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1710.00899&json=true","fetch_graph":"https://pith.science/api/pith-number/TBC436SZEXNXDXAQVOVYWF7DNT/graph.json","fetch_events":"https://pith.science/api/pith-number/TBC436SZEXNXDXAQVOVYWF7DNT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TBC436SZEXNXDXAQVOVYWF7DNT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TBC436SZEXNXDXAQVOVYWF7DNT/action/storage_attestation","attest_author":"https://pith.science/pith/TBC436SZEXNXDXAQVOVYWF7DNT/action/author_attestation","sign_citation":"https://pith.science/pith/TBC436SZEXNXDXAQVOVYWF7DNT/action/citation_signature","submit_replication":"https://pith.science/pith/TBC436SZEXNXDXAQVOVYWF7DNT/action/replication_record"}},"created_at":"2026-05-18T00:28:29.614735+00:00","updated_at":"2026-05-18T00:28:29.614735+00:00"}