{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:OCFGDZIWBHIDIMLOZRREZYKK7C","short_pith_number":"pith:OCFGDZIW","schema_version":"1.0","canonical_sha256":"708a61e51609d034316ecc624ce14af89f219dafcc0b81e52c02a615c7134dd6","source":{"kind":"arxiv","id":"1011.1832","version":3},"attestation_state":"computed","paper":{"title":"Spectral statistics for random Schr\\\"odinger operators in the localized regime","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.SP","authors_text":"Fran\\c{c}ois Germinet (AGM), Fr\\'ed\\'eric Klopp (LAGA)","submitted_at":"2010-11-08T15:43:51Z","abstract_excerpt":"We study various statistics related to the eigenvalues and eigenfunctions of random Hamiltonians in the localized regime. Consider a random Hamiltonian at an energy $E$ in the localized phase. Assume the density of states function is not too flat near $E$. Restrict it to some large cube $\\Lambda$. Consider now $I_\\Lambda$, a small energy interval centered at $E$ that asymptotically contains infintely many eigenvalues when the volume of the cube $\\Lambda$ grows to infinity. We prove that, with probability one in the large volume limit, the eigenvalues of the random Hamiltonian restricted to the"},"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":"1011.1832","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2010-11-08T15:43:51Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"99554943d779f18746c43857c1813c1ae738bfe08d64ae2440ae174b5b5b232e","abstract_canon_sha256":"1d1b6313c18a03ef1477ceb1f0cc33e954f1893e86d2938c6b17aea70507a52f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:43:40.644858Z","signature_b64":"uVAEgzwBCNy4EHO8d6fTdFjt+bau1biaVwsGsqOhd67ncwsISAGHSslN4TAY8f7JV7/MNLO6r0MxxLdN2azNDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"708a61e51609d034316ecc624ce14af89f219dafcc0b81e52c02a615c7134dd6","last_reissued_at":"2026-05-18T03:43:40.644029Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:43:40.644029Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Spectral statistics for random Schr\\\"odinger operators in the localized regime","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.SP","authors_text":"Fran\\c{c}ois Germinet (AGM), Fr\\'ed\\'eric Klopp (LAGA)","submitted_at":"2010-11-08T15:43:51Z","abstract_excerpt":"We study various statistics related to the eigenvalues and eigenfunctions of random Hamiltonians in the localized regime. Consider a random Hamiltonian at an energy $E$ in the localized phase. Assume the density of states function is not too flat near $E$. Restrict it to some large cube $\\Lambda$. Consider now $I_\\Lambda$, a small energy interval centered at $E$ that asymptotically contains infintely many eigenvalues when the volume of the cube $\\Lambda$ grows to infinity. We prove that, with probability one in the large volume limit, the eigenvalues of the random Hamiltonian restricted to the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.1832","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":"1011.1832","created_at":"2026-05-18T03:43:40.644176+00:00"},{"alias_kind":"arxiv_version","alias_value":"1011.1832v3","created_at":"2026-05-18T03:43:40.644176+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.1832","created_at":"2026-05-18T03:43:40.644176+00:00"},{"alias_kind":"pith_short_12","alias_value":"OCFGDZIWBHID","created_at":"2026-05-18T12:26:12.377268+00:00"},{"alias_kind":"pith_short_16","alias_value":"OCFGDZIWBHIDIMLO","created_at":"2026-05-18T12:26:12.377268+00:00"},{"alias_kind":"pith_short_8","alias_value":"OCFGDZIW","created_at":"2026-05-18T12:26:12.377268+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/OCFGDZIWBHIDIMLOZRREZYKK7C","json":"https://pith.science/pith/OCFGDZIWBHIDIMLOZRREZYKK7C.json","graph_json":"https://pith.science/api/pith-number/OCFGDZIWBHIDIMLOZRREZYKK7C/graph.json","events_json":"https://pith.science/api/pith-number/OCFGDZIWBHIDIMLOZRREZYKK7C/events.json","paper":"https://pith.science/paper/OCFGDZIW"},"agent_actions":{"view_html":"https://pith.science/pith/OCFGDZIWBHIDIMLOZRREZYKK7C","download_json":"https://pith.science/pith/OCFGDZIWBHIDIMLOZRREZYKK7C.json","view_paper":"https://pith.science/paper/OCFGDZIW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1011.1832&json=true","fetch_graph":"https://pith.science/api/pith-number/OCFGDZIWBHIDIMLOZRREZYKK7C/graph.json","fetch_events":"https://pith.science/api/pith-number/OCFGDZIWBHIDIMLOZRREZYKK7C/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OCFGDZIWBHIDIMLOZRREZYKK7C/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OCFGDZIWBHIDIMLOZRREZYKK7C/action/storage_attestation","attest_author":"https://pith.science/pith/OCFGDZIWBHIDIMLOZRREZYKK7C/action/author_attestation","sign_citation":"https://pith.science/pith/OCFGDZIWBHIDIMLOZRREZYKK7C/action/citation_signature","submit_replication":"https://pith.science/pith/OCFGDZIWBHIDIMLOZRREZYKK7C/action/replication_record"}},"created_at":"2026-05-18T03:43:40.644176+00:00","updated_at":"2026-05-18T03:43:40.644176+00:00"}