{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:WXLO2TYJKW33MX5DJGVD2CWWD6","short_pith_number":"pith:WXLO2TYJ","schema_version":"1.0","canonical_sha256":"b5d6ed4f0955b7b65fa349aa3d0ad61f9e69f95234fa3bcc9fa121e4c956d20a","source":{"kind":"arxiv","id":"1809.02205","version":2},"attestation_state":"computed","paper":{"title":"Two short pieces around the Wigner problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.dis-nn","math.MP"],"primary_cat":"math-ph","authors_text":"J. P. Bouchaud, M. Potters","submitted_at":"2018-09-06T20:14:38Z","abstract_excerpt":"We revisit the classic Wigner semi-circle from two different angles. One consists in studying the Stieltjes transform directly on the real axis, which does not converge to a fixed value but follows a Cauchy distribution that depends on the local eigenvalue density. This result was recently proven by Aizenman \\& Warzel for a wide class of eigenvalue distributions. We shed new light onto their result using a Coulomb gas method. The second angle is to derive a Langevin equation for the full (matrix) resolvent, extending Dyson's Brownian motion framework. The full matrix structure of this equation"},"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":"1809.02205","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-09-06T20:14:38Z","cross_cats_sorted":["cond-mat.dis-nn","math.MP"],"title_canon_sha256":"2f99a191789c69cb953132b3374d8fdb92eb6c4d13457ef1f5f0717b91b41a29","abstract_canon_sha256":"d89aa24fd45711b436937277167592040bbca2ba22d20cabb3eaecd4ead7800b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:57:40.087764Z","signature_b64":"qdvcm0+yqZhRM34k0wPSoQyshD1A74JERT9u2w8rwaWd3ivhCRzf+ndj5Pc7/PJGljoQ9tBGbTqrgc6sxSRDBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b5d6ed4f0955b7b65fa349aa3d0ad61f9e69f95234fa3bcc9fa121e4c956d20a","last_reissued_at":"2026-05-17T23:57:40.087107Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:57:40.087107Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Two short pieces around the Wigner problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.dis-nn","math.MP"],"primary_cat":"math-ph","authors_text":"J. P. Bouchaud, M. Potters","submitted_at":"2018-09-06T20:14:38Z","abstract_excerpt":"We revisit the classic Wigner semi-circle from two different angles. One consists in studying the Stieltjes transform directly on the real axis, which does not converge to a fixed value but follows a Cauchy distribution that depends on the local eigenvalue density. This result was recently proven by Aizenman \\& Warzel for a wide class of eigenvalue distributions. We shed new light onto their result using a Coulomb gas method. The second angle is to derive a Langevin equation for the full (matrix) resolvent, extending Dyson's Brownian motion framework. The full matrix structure of this equation"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.02205","kind":"arxiv","version":2},"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":"1809.02205","created_at":"2026-05-17T23:57:40.087201+00:00"},{"alias_kind":"arxiv_version","alias_value":"1809.02205v2","created_at":"2026-05-17T23:57:40.087201+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.02205","created_at":"2026-05-17T23:57:40.087201+00:00"},{"alias_kind":"pith_short_12","alias_value":"WXLO2TYJKW33","created_at":"2026-05-18T12:33:01.666342+00:00"},{"alias_kind":"pith_short_16","alias_value":"WXLO2TYJKW33MX5D","created_at":"2026-05-18T12:33:01.666342+00:00"},{"alias_kind":"pith_short_8","alias_value":"WXLO2TYJ","created_at":"2026-05-18T12:33:01.666342+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/WXLO2TYJKW33MX5DJGVD2CWWD6","json":"https://pith.science/pith/WXLO2TYJKW33MX5DJGVD2CWWD6.json","graph_json":"https://pith.science/api/pith-number/WXLO2TYJKW33MX5DJGVD2CWWD6/graph.json","events_json":"https://pith.science/api/pith-number/WXLO2TYJKW33MX5DJGVD2CWWD6/events.json","paper":"https://pith.science/paper/WXLO2TYJ"},"agent_actions":{"view_html":"https://pith.science/pith/WXLO2TYJKW33MX5DJGVD2CWWD6","download_json":"https://pith.science/pith/WXLO2TYJKW33MX5DJGVD2CWWD6.json","view_paper":"https://pith.science/paper/WXLO2TYJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1809.02205&json=true","fetch_graph":"https://pith.science/api/pith-number/WXLO2TYJKW33MX5DJGVD2CWWD6/graph.json","fetch_events":"https://pith.science/api/pith-number/WXLO2TYJKW33MX5DJGVD2CWWD6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WXLO2TYJKW33MX5DJGVD2CWWD6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WXLO2TYJKW33MX5DJGVD2CWWD6/action/storage_attestation","attest_author":"https://pith.science/pith/WXLO2TYJKW33MX5DJGVD2CWWD6/action/author_attestation","sign_citation":"https://pith.science/pith/WXLO2TYJKW33MX5DJGVD2CWWD6/action/citation_signature","submit_replication":"https://pith.science/pith/WXLO2TYJKW33MX5DJGVD2CWWD6/action/replication_record"}},"created_at":"2026-05-17T23:57:40.087201+00:00","updated_at":"2026-05-17T23:57:40.087201+00:00"}