{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:WQUF67TVGFERWFJ5TEWY7C3VYJ","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":"03bf9a6148015352babf6415783f009dbdbe063b1b1f66889345cc0422cfecb4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-09-18T15:44:17Z","title_canon_sha256":"f0fcd9f3c297da61a41d70ad7d4be7b6e061ea653ce86c12eb98c798ce66e9d9"},"schema_version":"1.0","source":{"id":"1809.06804","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.06804","created_at":"2026-05-17T23:55:19Z"},{"alias_kind":"arxiv_version","alias_value":"1809.06804v3","created_at":"2026-05-17T23:55:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.06804","created_at":"2026-05-17T23:55:19Z"},{"alias_kind":"pith_short_12","alias_value":"WQUF67TVGFER","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_16","alias_value":"WQUF67TVGFERWFJ5","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_8","alias_value":"WQUF67TV","created_at":"2026-05-18T12:33:01Z"}],"graph_snapshots":[{"event_id":"sha256:11925904007c19d61b822cd38793e50ba06ba64e54510dee4fc063d7b2705f1a","target":"graph","created_at":"2026-05-17T23:55:19Z","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":"We consider the asymptotics of the difference between the empirical measures of the $\\beta$-Hermite tridiagonal matrix and its minor. We prove that this difference has a deterministic limit and Gaussian fluctuations. Through a correspondence between measures and continual Young diagrams, this deterministic limit is identified with the Vershik-Kerov-Logan-Shepp curve. Moreover, the Gaussian fluctuations are identified with a sectional derivative of the Gaussian free field.","authors_text":"Andrew Ahn, Gopal Goel","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-09-18T15:44:17Z","title":"Discrete Derivative Asymptotics of the $\\beta$-Hermite Eigenvalues"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.06804","kind":"arxiv","version":3},"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":"sha256:2badc9d655c014556f6e778782a6f7e2f7a1d286d48964653ea58b3d7f25f638","target":"record","created_at":"2026-05-17T23:55:19Z","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":"03bf9a6148015352babf6415783f009dbdbe063b1b1f66889345cc0422cfecb4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-09-18T15:44:17Z","title_canon_sha256":"f0fcd9f3c297da61a41d70ad7d4be7b6e061ea653ce86c12eb98c798ce66e9d9"},"schema_version":"1.0","source":{"id":"1809.06804","kind":"arxiv","version":3}},"canonical_sha256":"b4285f7e7531491b153d992d8f8b75c2404e1eaf3f2b033f4ba25590dfe93fe5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b4285f7e7531491b153d992d8f8b75c2404e1eaf3f2b033f4ba25590dfe93fe5","first_computed_at":"2026-05-17T23:55:19.749958Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:55:19.749958Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/5DC7aLXrsfGFfQ7j9Og8v2RIEJebaFj8v7WrWks0BhJcofXp1xYdHufOPbRbYl8MBHe0mDqOkNwJdS3/5e+Bg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:55:19.750518Z","signed_message":"canonical_sha256_bytes"},"source_id":"1809.06804","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2badc9d655c014556f6e778782a6f7e2f7a1d286d48964653ea58b3d7f25f638","sha256:11925904007c19d61b822cd38793e50ba06ba64e54510dee4fc063d7b2705f1a"],"state_sha256":"341723eef2adce8eb74df0140c1db5293c72df378e207d6b34bde8ae07cdb0a6"}