{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:WHWXXHHI6AGULPDUDWAJTNDQFX","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"13390728df9ca91e19d09d3d0fd1080c98eb4e70921000b682a28c8aeeee525e","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-08-20T19:41:06Z","title_canon_sha256":"d30981ec422c0d9455441e1579705a1e80bc86fbd22196a4634b70ec4adc181f"},"schema_version":"1.0","source":{"id":"1008.3560","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1008.3560","created_at":"2026-05-18T04:41:55Z"},{"alias_kind":"arxiv_version","alias_value":"1008.3560v2","created_at":"2026-05-18T04:41:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.3560","created_at":"2026-05-18T04:41:55Z"},{"alias_kind":"pith_short_12","alias_value":"WHWXXHHI6AGU","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_16","alias_value":"WHWXXHHI6AGULPDU","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_8","alias_value":"WHWXXHHI","created_at":"2026-05-18T12:26:15Z"}],"graph_snapshots":[{"event_id":"sha256:f382339871585aa623c6017809ec2ee681173154c3a777ac391004cdaa84c239","target":"graph","created_at":"2026-05-18T04:41:55Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Tracy-Widom (TW) equations for one-matrix unitary ensembles (UE) (equivalent to a particular case of Schlesinger equations for isomonodromic deformations) are rewritten in a general form which allows one to derive all the lowest order equations (PDE) for spectral gap probabilities of UE without intermediate higher-order PDE. This is demonstrated on the example of Gaussian ensemble (GUE) for which all the third order PDE for gap probabilities are obtained explicitly. Moreover, there is a {\\it second order} PDE for GUE probabilities in the case of more than one spectral endpoint.\n  This approach","authors_text":"Igor Rumanov","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-08-20T19:41:06Z","title":"All the lowest order PDE for spectral gaps of Gaussian matrices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.3560","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:32e937bdb0bf0c7d1158ef2cc128c4dd8b63c9c643d10db9f072848a12ca4ba3","target":"record","created_at":"2026-05-18T04:41:55Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"13390728df9ca91e19d09d3d0fd1080c98eb4e70921000b682a28c8aeeee525e","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-08-20T19:41:06Z","title_canon_sha256":"d30981ec422c0d9455441e1579705a1e80bc86fbd22196a4634b70ec4adc181f"},"schema_version":"1.0","source":{"id":"1008.3560","kind":"arxiv","version":2}},"canonical_sha256":"b1ed7b9ce8f00d45bc741d8099b4702dd988166f9a069a8fa3a7673b1955503b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b1ed7b9ce8f00d45bc741d8099b4702dd988166f9a069a8fa3a7673b1955503b","first_computed_at":"2026-05-18T04:41:55.625967Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:41:55.625967Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SeSTh1xKRlZ36xoAubt2De8Lbv0M93E7a4O2LlfcfxIRTOkrqItEoUgQmjifNgjDGUWc5AmYxLCaxY4PtNSjBA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:41:55.626432Z","signed_message":"canonical_sha256_bytes"},"source_id":"1008.3560","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:32e937bdb0bf0c7d1158ef2cc128c4dd8b63c9c643d10db9f072848a12ca4ba3","sha256:f382339871585aa623c6017809ec2ee681173154c3a777ac391004cdaa84c239"],"state_sha256":"0ceb2fb53b78e04609dd1cb120f10fc3e3bed1cec051bf56663f7e3ba1d14025"}