{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:YIHBBLU7YSPSL73T63RFGQZRCH","short_pith_number":"pith:YIHBBLU7","schema_version":"1.0","canonical_sha256":"c20e10ae9fc49f25ff73f6e253433111f9c527e60c1a3589a390d53b9f67e746","source":{"kind":"arxiv","id":"0907.4465","version":1},"attestation_state":"computed","paper":{"title":"Lower bound on the density of states for periodic Schr\\\"odinger operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Irina Pchelintseva, Leonid Parnovski, Sergey Morozov","submitted_at":"2009-07-26T09:00:23Z","abstract_excerpt":"We consider Schr\\\"odinger operators with smooth periodic potentials in Euclidean spaces of dimension bigger than 1 and prove a uniform lower bound on the density of states for large values of the spectral parameter."},"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":"0907.4465","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2009-07-26T09:00:23Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"86c90fffe0f4dc750918dca021d96ae36ac1c23427aca95f9d1e084a63258909","abstract_canon_sha256":"b57340dcf7aa70a7255e4a2ddc9945a4d2c8df183e5ef82d4eb6359a350cb551"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:58:37.078129Z","signature_b64":"Y+tmnZf2V8cCTCuDXy+M2y8AK7DK+EFLEnoOFyHpZCk6wc6vaMN0pYI3UpiTwBVLvJmsVh9L1n1ZyZOh/rcPBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c20e10ae9fc49f25ff73f6e253433111f9c527e60c1a3589a390d53b9f67e746","last_reissued_at":"2026-05-18T03:58:37.077655Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:58:37.077655Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Lower bound on the density of states for periodic Schr\\\"odinger operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Irina Pchelintseva, Leonid Parnovski, Sergey Morozov","submitted_at":"2009-07-26T09:00:23Z","abstract_excerpt":"We consider Schr\\\"odinger operators with smooth periodic potentials in Euclidean spaces of dimension bigger than 1 and prove a uniform lower bound on the density of states for large values of the spectral parameter."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0907.4465","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":"0907.4465","created_at":"2026-05-18T03:58:37.077721+00:00"},{"alias_kind":"arxiv_version","alias_value":"0907.4465v1","created_at":"2026-05-18T03:58:37.077721+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0907.4465","created_at":"2026-05-18T03:58:37.077721+00:00"},{"alias_kind":"pith_short_12","alias_value":"YIHBBLU7YSPS","created_at":"2026-05-18T12:26:02.257875+00:00"},{"alias_kind":"pith_short_16","alias_value":"YIHBBLU7YSPSL73T","created_at":"2026-05-18T12:26:02.257875+00:00"},{"alias_kind":"pith_short_8","alias_value":"YIHBBLU7","created_at":"2026-05-18T12:26:02.257875+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/YIHBBLU7YSPSL73T63RFGQZRCH","json":"https://pith.science/pith/YIHBBLU7YSPSL73T63RFGQZRCH.json","graph_json":"https://pith.science/api/pith-number/YIHBBLU7YSPSL73T63RFGQZRCH/graph.json","events_json":"https://pith.science/api/pith-number/YIHBBLU7YSPSL73T63RFGQZRCH/events.json","paper":"https://pith.science/paper/YIHBBLU7"},"agent_actions":{"view_html":"https://pith.science/pith/YIHBBLU7YSPSL73T63RFGQZRCH","download_json":"https://pith.science/pith/YIHBBLU7YSPSL73T63RFGQZRCH.json","view_paper":"https://pith.science/paper/YIHBBLU7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0907.4465&json=true","fetch_graph":"https://pith.science/api/pith-number/YIHBBLU7YSPSL73T63RFGQZRCH/graph.json","fetch_events":"https://pith.science/api/pith-number/YIHBBLU7YSPSL73T63RFGQZRCH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YIHBBLU7YSPSL73T63RFGQZRCH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YIHBBLU7YSPSL73T63RFGQZRCH/action/storage_attestation","attest_author":"https://pith.science/pith/YIHBBLU7YSPSL73T63RFGQZRCH/action/author_attestation","sign_citation":"https://pith.science/pith/YIHBBLU7YSPSL73T63RFGQZRCH/action/citation_signature","submit_replication":"https://pith.science/pith/YIHBBLU7YSPSL73T63RFGQZRCH/action/replication_record"}},"created_at":"2026-05-18T03:58:37.077721+00:00","updated_at":"2026-05-18T03:58:37.077721+00:00"}