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The local correlation is assumed to satisfy\n  \\[\n  1-r(\\boldsymbol{t},\\boldsymbol{s})\\sim |t_1-s_1|^\\alpha+|t_2-s_2|^\\alpha,\n  \\qquad 0<\\alpha<\\beta .\n  \\]\n  This product form of the standa"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2605.22760","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-05-21T17:24:12Z","cross_cats_sorted":[],"title_canon_sha256":"64578002491f3c1053df49a8499fa7d5dcd0ffa8584725c6224388974e318a8d","abstract_canon_sha256":"bf6628a83ed549d3525d75d19cf4f05704a8067604104caf87c07d7bb1cc04c0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-22T02:04:53.819751Z","signature_b64":"q2sm2AykB5TWKg/1x8X2/4ePGIOqALqiXdLqiU174/mXJH+fzjCL8scL35uzN955spRvs4vvMIrETJqNRSvqAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"66106115d88e61951a1322d6e7b9dce6dca8f2627583946f533f95941ad2a272","last_reissued_at":"2026-05-22T02:04:53.819309Z","signature_status":"signed_v1","first_computed_at":"2026-05-22T02:04:53.819309Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Extremes of Gaussian fields with a product term in the variance","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Svyatoslav Novikov","submitted_at":"2026-05-21T17:24:12Z","abstract_excerpt":"We study the high excursion probability of a centered Gaussian field on a square.\n  Writing \\(\\sigma\\) and \\(r\\) for its standard deviation and correlation function,\n  we assume that \\(\\sigma\\) has a unique maximum at the corner\n  \\(\\boldsymbol{0}=(0,0)\\) and\n  \\[\n  1-\\sigma(\\boldsymbol{t}) \\sim t_1^\\beta+t_2^\\beta+t_1^a t_2^a ,\n  \\qquad \\boldsymbol{t}=(t_1,t_2)\\to\\boldsymbol{0}\n  \\]\n  in \\(\\mathbb R_+^2\\). The local correlation is assumed to satisfy\n  \\[\n  1-r(\\boldsymbol{t},\\boldsymbol{s})\\sim |t_1-s_1|^\\alpha+|t_2-s_2|^\\alpha,\n  \\qquad 0<\\alpha<\\beta .\n  \\]\n  This product form of the standa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.22760","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.22760/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2605.22760","created_at":"2026-05-22T02:04:53.819382+00:00"},{"alias_kind":"arxiv_version","alias_value":"2605.22760v1","created_at":"2026-05-22T02:04:53.819382+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.22760","created_at":"2026-05-22T02:04:53.819382+00:00"},{"alias_kind":"pith_short_12","alias_value":"MYIGCFOYRZQZ","created_at":"2026-05-22T02:04:53.819382+00:00"},{"alias_kind":"pith_short_16","alias_value":"MYIGCFOYRZQZKGQT","created_at":"2026-05-22T02:04:53.819382+00:00"},{"alias_kind":"pith_short_8","alias_value":"MYIGCFOY","created_at":"2026-05-22T02:04:53.819382+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/MYIGCFOYRZQZKGQTELLOPOO443","json":"https://pith.science/pith/MYIGCFOYRZQZKGQTELLOPOO443.json","graph_json":"https://pith.science/api/pith-number/MYIGCFOYRZQZKGQTELLOPOO443/graph.json","events_json":"https://pith.science/api/pith-number/MYIGCFOYRZQZKGQTELLOPOO443/events.json","paper":"https://pith.science/paper/MYIGCFOY"},"agent_actions":{"view_html":"https://pith.science/pith/MYIGCFOYRZQZKGQTELLOPOO443","download_json":"https://pith.science/pith/MYIGCFOYRZQZKGQTELLOPOO443.json","view_paper":"https://pith.science/paper/MYIGCFOY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2605.22760&json=true","fetch_graph":"https://pith.science/api/pith-number/MYIGCFOYRZQZKGQTELLOPOO443/graph.json","fetch_events":"https://pith.science/api/pith-number/MYIGCFOYRZQZKGQTELLOPOO443/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MYIGCFOYRZQZKGQTELLOPOO443/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MYIGCFOYRZQZKGQTELLOPOO443/action/storage_attestation","attest_author":"https://pith.science/pith/MYIGCFOYRZQZKGQTELLOPOO443/action/author_attestation","sign_citation":"https://pith.science/pith/MYIGCFOYRZQZKGQTELLOPOO443/action/citation_signature","submit_replication":"https://pith.science/pith/MYIGCFOYRZQZKGQTELLOPOO443/action/replication_record"}},"created_at":"2026-05-22T02:04:53.819382+00:00","updated_at":"2026-05-22T02:04:53.819382+00:00"}