{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:3SLYWJZLXO5MYKEL6JDCARF7OK","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":"ce0fd50ca4e4251eb7138b332cea244b60e87f0a76521a7ff989771d3d61a863","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-07-22T20:03:25Z","title_canon_sha256":"0b16743546e75e662c08b035cf36ea6356f41388f41569ee67ac08ff0dbb97d7"},"schema_version":"1.0","source":{"id":"1307.5863","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.5863","created_at":"2026-05-18T02:30:40Z"},{"alias_kind":"arxiv_version","alias_value":"1307.5863v3","created_at":"2026-05-18T02:30:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.5863","created_at":"2026-05-18T02:30:40Z"},{"alias_kind":"pith_short_12","alias_value":"3SLYWJZLXO5M","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_16","alias_value":"3SLYWJZLXO5MYKEL","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_8","alias_value":"3SLYWJZL","created_at":"2026-05-18T12:27:32Z"}],"graph_snapshots":[{"event_id":"sha256:dfe6a237d2e8c97e2db0bda286fddeeeba0dcdeeb54ece1fd9a57d834bdb7221","target":"graph","created_at":"2026-05-18T02:30:40Z","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":"Let $\\{f(t): t\\in T\\}$ be a smooth Gaussian random field over a parameter space $T$, where $T$ may be a subset of Euclidean space or, more generally, a Riemannian manifold. For any local maximum of $f(t)$ located at $t_0$ in the interior of $T$, we provide general formulae and asymptotic approximations for both the tail distribution of the height of a local maximum $\\mathbb{P}\\{f(t_0)>u | t_0 \\text{is a local maximum of} f(t) \\}$ and the overshoot distribution of a local maximum $\\mathbb{P}\\{f(t_0)>u+v | t_0 \\text{is a local maximum of} f(t) \\text{and} f(t_0)>v\\}$. Assuming further that $f$ is","authors_text":"Armin Schwartzman, Dan Cheng","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-07-22T20:03:25Z","title":"Distribution of the Height of Local Maxima of Gaussian Random Fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.5863","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:f295e9086812c09c70f7f5095bd77afaa79183ddf5c5dd93b558c244bf200533","target":"record","created_at":"2026-05-18T02:30:40Z","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":"ce0fd50ca4e4251eb7138b332cea244b60e87f0a76521a7ff989771d3d61a863","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-07-22T20:03:25Z","title_canon_sha256":"0b16743546e75e662c08b035cf36ea6356f41388f41569ee67ac08ff0dbb97d7"},"schema_version":"1.0","source":{"id":"1307.5863","kind":"arxiv","version":3}},"canonical_sha256":"dc978b272bbbbacc288bf2462044bf72999c2f1f432622c7f97888ed1308573b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dc978b272bbbbacc288bf2462044bf72999c2f1f432622c7f97888ed1308573b","first_computed_at":"2026-05-18T02:30:40.596040Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:30:40.596040Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EIu0TZL2k7k37O4rJTWnGmxtgdmdhmJ38EZjN3AtEc9KlUasRox6iOrYAGZ62xwqdKNZI7jTWYFoQBMxsaEoAg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:30:40.596449Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.5863","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f295e9086812c09c70f7f5095bd77afaa79183ddf5c5dd93b558c244bf200533","sha256:dfe6a237d2e8c97e2db0bda286fddeeeba0dcdeeb54ece1fd9a57d834bdb7221"],"state_sha256":"326cfe159999d955daabf9d65cbccd88d6d2930890a330fea7c1303de68cf463"}