{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:NTT4C55EEKLVCUW2L7XAX6XKN3","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":"b3611957b5d3647e149a7cbc98b2247a378ac588baa72c6cfa596393fc82d4f9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-09-18T17:55:01Z","title_canon_sha256":"78887367d2096b4692b56fec2c2c86510a384f4e9d8411183084c032c3733729"},"schema_version":"1.0","source":{"id":"1109.3895","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.3895","created_at":"2026-05-18T04:12:45Z"},{"alias_kind":"arxiv_version","alias_value":"1109.3895v1","created_at":"2026-05-18T04:12:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.3895","created_at":"2026-05-18T04:12:45Z"},{"alias_kind":"pith_short_12","alias_value":"NTT4C55EEKLV","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_16","alias_value":"NTT4C55EEKLVCUW2","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_8","alias_value":"NTT4C55E","created_at":"2026-05-18T12:26:37Z"}],"graph_snapshots":[{"event_id":"sha256:c8dc61f701c8d2220b19e2100f07671e0e2e30cf1fb6e230aa534c3cb65299f0","target":"graph","created_at":"2026-05-18T04:12:45Z","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 study the probability distribution of the maximum $M_S $ of a smooth stationary Gaussian field defined on a fractal subset $S$ of $\\R^n$. Our main result is the equivalent of the asymptotic behavior of the tail of the distribution $\\P(M_S>u)$ as $u\\rightarrow +\\infty.$ The basic tool is Rice formula for the moments of the number of local maxima of a random field.","authors_text":"Jean-Marc Aza\\\"is, Mario Wschebor","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-09-18T17:55:01Z","title":"The tail of the maximum of smooth Gaussian fields on fractal sets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.3895","kind":"arxiv","version":1},"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:ba1e482e6f8aca9e73b096c2a303cda791520513bcafda2f086278cb543d43eb","target":"record","created_at":"2026-05-18T04:12:45Z","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":"b3611957b5d3647e149a7cbc98b2247a378ac588baa72c6cfa596393fc82d4f9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-09-18T17:55:01Z","title_canon_sha256":"78887367d2096b4692b56fec2c2c86510a384f4e9d8411183084c032c3733729"},"schema_version":"1.0","source":{"id":"1109.3895","kind":"arxiv","version":1}},"canonical_sha256":"6ce7c177a422975152da5fee0bfaea6ee05d1966ae068b9ed07d060d167a96b2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6ce7c177a422975152da5fee0bfaea6ee05d1966ae068b9ed07d060d167a96b2","first_computed_at":"2026-05-18T04:12:45.665220Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:12:45.665220Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KAJs87y5iPdPO7fqs70cI7vRxO1AjFJcySIlEg1DXNkaxF/QMwbNu1z/NjhdYQVi3fx6eLia4BxCpju5v+QYCg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:12:45.666060Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.3895","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ba1e482e6f8aca9e73b096c2a303cda791520513bcafda2f086278cb543d43eb","sha256:c8dc61f701c8d2220b19e2100f07671e0e2e30cf1fb6e230aa534c3cb65299f0"],"state_sha256":"22a8747325e4f0fbe0461ce37819d0dc1c0452baaf8a1f5808e23a0592322e36"}