{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:6JW6LOZF55ZRHBKL5CEJJHQNLF","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":"b2dd685a8a8dff6847373225b4e7e2a51d0f5cf2f3dd2b3fc7ba8cd641c7f042","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-01-24T13:14:59Z","title_canon_sha256":"020995490a3c715511302ad383b4797240c0d4dfeecd0ccffb73bd950d6202a1"},"schema_version":"1.0","source":{"id":"1201.4972","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.4972","created_at":"2026-05-18T02:56:12Z"},{"alias_kind":"arxiv_version","alias_value":"1201.4972v4","created_at":"2026-05-18T02:56:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.4972","created_at":"2026-05-18T02:56:12Z"},{"alias_kind":"pith_short_12","alias_value":"6JW6LOZF55ZR","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"6JW6LOZF55ZRHBKL","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"6JW6LOZF","created_at":"2026-05-18T12:26:56Z"}],"graph_snapshots":[{"event_id":"sha256:2e265f211ac9d213c65dd1375f83e2d797793dde2af50d5c5134ae36cc6c7193","target":"graph","created_at":"2026-05-18T02:56:12Z","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 relate the distribution of eigenvalues of a random symmetric matrix in the Gaussian Orthogonal Ensemble to the distribution of critical values of a random linear combination of eigenfunctions of the Laplacian on a compact Riemann manifold. We then prove a central limit theorem describing what happens when the dimension of the manifold is very large.","authors_text":"Liviu I. Nicolaescu","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-01-24T13:14:59Z","title":"Complexity of random smooth functions on compact manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.4972","kind":"arxiv","version":4},"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:f108ecc2ca66135ecbdbeb5e19397b78db7b8b894c60190b3517693bc00e5fb5","target":"record","created_at":"2026-05-18T02:56:12Z","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":"b2dd685a8a8dff6847373225b4e7e2a51d0f5cf2f3dd2b3fc7ba8cd641c7f042","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-01-24T13:14:59Z","title_canon_sha256":"020995490a3c715511302ad383b4797240c0d4dfeecd0ccffb73bd950d6202a1"},"schema_version":"1.0","source":{"id":"1201.4972","kind":"arxiv","version":4}},"canonical_sha256":"f26de5bb25ef7313854be888949e0d5947d397bd0b27d32464bb27544f86f6d9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f26de5bb25ef7313854be888949e0d5947d397bd0b27d32464bb27544f86f6d9","first_computed_at":"2026-05-18T02:56:12.863643Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:56:12.863643Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"e187QP7kzfKjUgLlk2tTJwhyAv9tATWHG4ImIDxinlieyl6DeLJx7VGDE/zzv6x2EDB/pxqtJZmlDLuprRm8DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:56:12.864054Z","signed_message":"canonical_sha256_bytes"},"source_id":"1201.4972","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f108ecc2ca66135ecbdbeb5e19397b78db7b8b894c60190b3517693bc00e5fb5","sha256:2e265f211ac9d213c65dd1375f83e2d797793dde2af50d5c5134ae36cc6c7193"],"state_sha256":"6487b133ebd72f2c379b5ec64494fe7e3d12bdd771b3c47ba67ef0e1456d959f"}