{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:GTXFRW7LIZROFVINN54O2RCJCK","short_pith_number":"pith:GTXFRW7L","schema_version":"1.0","canonical_sha256":"34ee58dbeb4662e2d50d6f78ed4449129396cdb1c5adae91cd9ab61ec26bfcc1","source":{"kind":"arxiv","id":"1601.02898","version":1},"attestation_state":"computed","paper":{"title":"The Tracy-Widom distribution is not infinitely divisible","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"J. Armando Dom\\'inguez-Molina","submitted_at":"2016-01-12T15:10:20Z","abstract_excerpt":"The classical infinite divisibility of distributions related to eigenvalues of some random matrix ensembles is investigated. It is proved that the $\\beta$-Tracy-Widom distribution, which is the limiting distribution of the largest eigenvalue of a $\\beta$-Hermite ensemble, is not infinitely divisible. Furthermore, for each fixed $N \\ge 2$ it is proved that the largest eigenvalue of a GOE/GUE random matrix is not infinitely divisible."},"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":"1601.02898","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-01-12T15:10:20Z","cross_cats_sorted":[],"title_canon_sha256":"b4a1f8dcd05b98bbf9113ddaf21e84433490a7c790cba32f182a572a908456ee","abstract_canon_sha256":"a155fd79c715448b1bb89c619b3ca9ef8b3482cda8c67afe09f8466640e12761"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:22:59.384145Z","signature_b64":"oXTNv7rIRi2Kvn6FdvunctDG+faD+AH8QYnMo07Rqu22rDvGZJAtg3tcelodOg3rMuK2pf4aTzttVEgLxw3bBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"34ee58dbeb4662e2d50d6f78ed4449129396cdb1c5adae91cd9ab61ec26bfcc1","last_reissued_at":"2026-05-18T01:22:59.383703Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:22:59.383703Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Tracy-Widom distribution is not infinitely divisible","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"J. Armando Dom\\'inguez-Molina","submitted_at":"2016-01-12T15:10:20Z","abstract_excerpt":"The classical infinite divisibility of distributions related to eigenvalues of some random matrix ensembles is investigated. It is proved that the $\\beta$-Tracy-Widom distribution, which is the limiting distribution of the largest eigenvalue of a $\\beta$-Hermite ensemble, is not infinitely divisible. Furthermore, for each fixed $N \\ge 2$ it is proved that the largest eigenvalue of a GOE/GUE random matrix is not infinitely divisible."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.02898","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":"1601.02898","created_at":"2026-05-18T01:22:59.383774+00:00"},{"alias_kind":"arxiv_version","alias_value":"1601.02898v1","created_at":"2026-05-18T01:22:59.383774+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.02898","created_at":"2026-05-18T01:22:59.383774+00:00"},{"alias_kind":"pith_short_12","alias_value":"GTXFRW7LIZRO","created_at":"2026-05-18T12:30:19.053100+00:00"},{"alias_kind":"pith_short_16","alias_value":"GTXFRW7LIZROFVIN","created_at":"2026-05-18T12:30:19.053100+00:00"},{"alias_kind":"pith_short_8","alias_value":"GTXFRW7L","created_at":"2026-05-18T12:30:19.053100+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/GTXFRW7LIZROFVINN54O2RCJCK","json":"https://pith.science/pith/GTXFRW7LIZROFVINN54O2RCJCK.json","graph_json":"https://pith.science/api/pith-number/GTXFRW7LIZROFVINN54O2RCJCK/graph.json","events_json":"https://pith.science/api/pith-number/GTXFRW7LIZROFVINN54O2RCJCK/events.json","paper":"https://pith.science/paper/GTXFRW7L"},"agent_actions":{"view_html":"https://pith.science/pith/GTXFRW7LIZROFVINN54O2RCJCK","download_json":"https://pith.science/pith/GTXFRW7LIZROFVINN54O2RCJCK.json","view_paper":"https://pith.science/paper/GTXFRW7L","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1601.02898&json=true","fetch_graph":"https://pith.science/api/pith-number/GTXFRW7LIZROFVINN54O2RCJCK/graph.json","fetch_events":"https://pith.science/api/pith-number/GTXFRW7LIZROFVINN54O2RCJCK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GTXFRW7LIZROFVINN54O2RCJCK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GTXFRW7LIZROFVINN54O2RCJCK/action/storage_attestation","attest_author":"https://pith.science/pith/GTXFRW7LIZROFVINN54O2RCJCK/action/author_attestation","sign_citation":"https://pith.science/pith/GTXFRW7LIZROFVINN54O2RCJCK/action/citation_signature","submit_replication":"https://pith.science/pith/GTXFRW7LIZROFVINN54O2RCJCK/action/replication_record"}},"created_at":"2026-05-18T01:22:59.383774+00:00","updated_at":"2026-05-18T01:22:59.383774+00:00"}