{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:OU5DKLBNA3LRSXFUTBOCLLPEXS","short_pith_number":"pith:OU5DKLBN","schema_version":"1.0","canonical_sha256":"753a352c2d06d7195cb4985c25ade4bc95bc4c66cfa1cd6b8c405e0ef19a4fb3","source":{"kind":"arxiv","id":"1606.01579","version":1},"attestation_state":"computed","paper":{"title":"A bound on the averaged spectral shift function and a lower bound on the density of states for random Schr\\\"odinger operators on $\\mathbb{R}^d$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Abel Klein, Adrian Dietlein, Martin Gebert, Peter D. Hislop, Peter M\\\"uller","submitted_at":"2016-06-05T23:12:59Z","abstract_excerpt":"We obtain a bound on the expectation of the spectral shift function for alloy-type random Schr\\\"odinger operators on $\\mathbb{R}^d$ in the region of localisation, corresponding to a change from Dirichlet to Neumann boundary conditions along the boundary of a finite volume. The bound scales with the area of the surface where the boundary conditions are changed. As an application of our bound on the spectral shift function, we prove a reverse Wegner inequality for finite-volume Schr\\\"odinger operators in the region of localisation with a constant locally uniform in the energy. The application re"},"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":"1606.01579","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-06-05T23:12:59Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"1cac7d306cc9bfb9c3885c99273cd5bb6560377f0f4e7504b5cd454677bcb9c6","abstract_canon_sha256":"a5442e5de830f32e15ef86b1f52a1a9e8b79405ab4d1ad6ba423a9a4371de9d6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:55:30.153763Z","signature_b64":"PYS+j8bz999uEJ6jLO7+zrHk7sDRRN0cTantEm2kMEXDT/9DliIeZGcvD55hTdePvD/ASUriW5JOARD1eNV4AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"753a352c2d06d7195cb4985c25ade4bc95bc4c66cfa1cd6b8c405e0ef19a4fb3","last_reissued_at":"2026-05-17T23:55:30.153209Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:55:30.153209Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A bound on the averaged spectral shift function and a lower bound on the density of states for random Schr\\\"odinger operators on $\\mathbb{R}^d$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Abel Klein, Adrian Dietlein, Martin Gebert, Peter D. Hislop, Peter M\\\"uller","submitted_at":"2016-06-05T23:12:59Z","abstract_excerpt":"We obtain a bound on the expectation of the spectral shift function for alloy-type random Schr\\\"odinger operators on $\\mathbb{R}^d$ in the region of localisation, corresponding to a change from Dirichlet to Neumann boundary conditions along the boundary of a finite volume. The bound scales with the area of the surface where the boundary conditions are changed. As an application of our bound on the spectral shift function, we prove a reverse Wegner inequality for finite-volume Schr\\\"odinger operators in the region of localisation with a constant locally uniform in the energy. The application re"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.01579","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":"1606.01579","created_at":"2026-05-17T23:55:30.153300+00:00"},{"alias_kind":"arxiv_version","alias_value":"1606.01579v1","created_at":"2026-05-17T23:55:30.153300+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.01579","created_at":"2026-05-17T23:55:30.153300+00:00"},{"alias_kind":"pith_short_12","alias_value":"OU5DKLBNA3LR","created_at":"2026-05-18T12:30:36.002864+00:00"},{"alias_kind":"pith_short_16","alias_value":"OU5DKLBNA3LRSXFU","created_at":"2026-05-18T12:30:36.002864+00:00"},{"alias_kind":"pith_short_8","alias_value":"OU5DKLBN","created_at":"2026-05-18T12:30:36.002864+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/OU5DKLBNA3LRSXFUTBOCLLPEXS","json":"https://pith.science/pith/OU5DKLBNA3LRSXFUTBOCLLPEXS.json","graph_json":"https://pith.science/api/pith-number/OU5DKLBNA3LRSXFUTBOCLLPEXS/graph.json","events_json":"https://pith.science/api/pith-number/OU5DKLBNA3LRSXFUTBOCLLPEXS/events.json","paper":"https://pith.science/paper/OU5DKLBN"},"agent_actions":{"view_html":"https://pith.science/pith/OU5DKLBNA3LRSXFUTBOCLLPEXS","download_json":"https://pith.science/pith/OU5DKLBNA3LRSXFUTBOCLLPEXS.json","view_paper":"https://pith.science/paper/OU5DKLBN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1606.01579&json=true","fetch_graph":"https://pith.science/api/pith-number/OU5DKLBNA3LRSXFUTBOCLLPEXS/graph.json","fetch_events":"https://pith.science/api/pith-number/OU5DKLBNA3LRSXFUTBOCLLPEXS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OU5DKLBNA3LRSXFUTBOCLLPEXS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OU5DKLBNA3LRSXFUTBOCLLPEXS/action/storage_attestation","attest_author":"https://pith.science/pith/OU5DKLBNA3LRSXFUTBOCLLPEXS/action/author_attestation","sign_citation":"https://pith.science/pith/OU5DKLBNA3LRSXFUTBOCLLPEXS/action/citation_signature","submit_replication":"https://pith.science/pith/OU5DKLBNA3LRSXFUTBOCLLPEXS/action/replication_record"}},"created_at":"2026-05-17T23:55:30.153300+00:00","updated_at":"2026-05-17T23:55:30.153300+00:00"}