{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:A2DRDR4FX3W7ELPCBUSBEW6TDY","short_pith_number":"pith:A2DRDR4F","schema_version":"1.0","canonical_sha256":"068711c785beedf22de20d24125bd31e2551012db17af67e5c31420f01d6c198","source":{"kind":"arxiv","id":"1206.1449","version":3},"attestation_state":"computed","paper":{"title":"Local Circular Law for Random Matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Horng-Tzer Yau, Jun Yin, Paul Bourgade","submitted_at":"2012-06-07T11:01:56Z","abstract_excerpt":"The circular law asserts that the spectral measure of eigenvalues of rescaled random matrices without symmetry assumption converges to the uniform measure on the unit disk. We prove a local version of this law at any point $z$ away from the unit circle. More precisely, if $ | |z| - 1 | \\ge \\tau$ for arbitrarily small $\\tau> 0$, the circular law is valid around $z$ up to scale $N^{-1/2+ \\e}$ for any $\\e > 0$ under the assumption that the distributions of the matrix entries satisfy a uniform subexponential decay condition."},"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":"1206.1449","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-06-07T11:01:56Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"db6838dd985fdaf2cd92cb6cb8b12557ae425dedf223442c28383f01c7b31797","abstract_canon_sha256":"1d7b60911219a134dd728d3e193e3156922f1d67c9af960b1433412fddb585d2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:05:35.846867Z","signature_b64":"4mlxfxWkP/l36AkNgHdTs0VHzHfbuopy35Eni59n/mdmNtXdg0iJ6ofbLNXPAPmPft+SYbGnWtXu8fJl+QPwDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"068711c785beedf22de20d24125bd31e2551012db17af67e5c31420f01d6c198","last_reissued_at":"2026-05-18T03:05:35.846187Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:05:35.846187Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Local Circular Law for Random Matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Horng-Tzer Yau, Jun Yin, Paul Bourgade","submitted_at":"2012-06-07T11:01:56Z","abstract_excerpt":"The circular law asserts that the spectral measure of eigenvalues of rescaled random matrices without symmetry assumption converges to the uniform measure on the unit disk. We prove a local version of this law at any point $z$ away from the unit circle. More precisely, if $ | |z| - 1 | \\ge \\tau$ for arbitrarily small $\\tau> 0$, the circular law is valid around $z$ up to scale $N^{-1/2+ \\e}$ for any $\\e > 0$ under the assumption that the distributions of the matrix entries satisfy a uniform subexponential decay condition."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.1449","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":"1206.1449","created_at":"2026-05-18T03:05:35.846288+00:00"},{"alias_kind":"arxiv_version","alias_value":"1206.1449v3","created_at":"2026-05-18T03:05:35.846288+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.1449","created_at":"2026-05-18T03:05:35.846288+00:00"},{"alias_kind":"pith_short_12","alias_value":"A2DRDR4FX3W7","created_at":"2026-05-18T12:26:58.693483+00:00"},{"alias_kind":"pith_short_16","alias_value":"A2DRDR4FX3W7ELPC","created_at":"2026-05-18T12:26:58.693483+00:00"},{"alias_kind":"pith_short_8","alias_value":"A2DRDR4F","created_at":"2026-05-18T12:26:58.693483+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/A2DRDR4FX3W7ELPCBUSBEW6TDY","json":"https://pith.science/pith/A2DRDR4FX3W7ELPCBUSBEW6TDY.json","graph_json":"https://pith.science/api/pith-number/A2DRDR4FX3W7ELPCBUSBEW6TDY/graph.json","events_json":"https://pith.science/api/pith-number/A2DRDR4FX3W7ELPCBUSBEW6TDY/events.json","paper":"https://pith.science/paper/A2DRDR4F"},"agent_actions":{"view_html":"https://pith.science/pith/A2DRDR4FX3W7ELPCBUSBEW6TDY","download_json":"https://pith.science/pith/A2DRDR4FX3W7ELPCBUSBEW6TDY.json","view_paper":"https://pith.science/paper/A2DRDR4F","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1206.1449&json=true","fetch_graph":"https://pith.science/api/pith-number/A2DRDR4FX3W7ELPCBUSBEW6TDY/graph.json","fetch_events":"https://pith.science/api/pith-number/A2DRDR4FX3W7ELPCBUSBEW6TDY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/A2DRDR4FX3W7ELPCBUSBEW6TDY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/A2DRDR4FX3W7ELPCBUSBEW6TDY/action/storage_attestation","attest_author":"https://pith.science/pith/A2DRDR4FX3W7ELPCBUSBEW6TDY/action/author_attestation","sign_citation":"https://pith.science/pith/A2DRDR4FX3W7ELPCBUSBEW6TDY/action/citation_signature","submit_replication":"https://pith.science/pith/A2DRDR4FX3W7ELPCBUSBEW6TDY/action/replication_record"}},"created_at":"2026-05-18T03:05:35.846288+00:00","updated_at":"2026-05-18T03:05:35.846288+00:00"}