{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:JBOM7KRGSUI35DIQZPIKMZ2S45","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":"01278e9e0e7e16eeaf810316d6b95c6e302c9271a0ca69c84f69ba48b3f51105","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-10-16T14:26:28Z","title_canon_sha256":"27996d49cc493e1339eb8428e3fc647a2d160fdb703b09c0386610f23f69144d"},"schema_version":"1.0","source":{"id":"1810.07033","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.07033","created_at":"2026-05-18T00:03:10Z"},{"alias_kind":"arxiv_version","alias_value":"1810.07033v1","created_at":"2026-05-18T00:03:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.07033","created_at":"2026-05-18T00:03:10Z"},{"alias_kind":"pith_short_12","alias_value":"JBOM7KRGSUI3","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_16","alias_value":"JBOM7KRGSUI35DIQ","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_8","alias_value":"JBOM7KRG","created_at":"2026-05-18T12:32:31Z"}],"graph_snapshots":[{"event_id":"sha256:ee76e8fd8b38da26ea24de8fcc5216cf26ed6ea6bcab0d1a8f2b1e1eff830bf3","target":"graph","created_at":"2026-05-18T00:03:10Z","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 extremes for a class of a symmetric stable random fields with long range dependence. We prove functional extremal theorems both in the space of sup measures and in the space of cadlag functions of several variables. The limits in both types of theorems are of a new kind, and only in a certain range of parameters these limits have the Fr\\'{e}chet distribution.","authors_text":"Gennady Samorodnitsky, Zaoli Chen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-10-16T14:26:28Z","title":"Extremal Value Theory for Long Range Dependent Stable Random Fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.07033","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:f7cdfd6e4cd1c7bb9f2a456e4980a5c9cdd185a68bf32c289c59f7a75f453c40","target":"record","created_at":"2026-05-18T00:03:10Z","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":"01278e9e0e7e16eeaf810316d6b95c6e302c9271a0ca69c84f69ba48b3f51105","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-10-16T14:26:28Z","title_canon_sha256":"27996d49cc493e1339eb8428e3fc647a2d160fdb703b09c0386610f23f69144d"},"schema_version":"1.0","source":{"id":"1810.07033","kind":"arxiv","version":1}},"canonical_sha256":"485ccfaa269511be8d10cbd0a66752e76bee8d5c1dcd48c613c1f7778e1e30cd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"485ccfaa269511be8d10cbd0a66752e76bee8d5c1dcd48c613c1f7778e1e30cd","first_computed_at":"2026-05-18T00:03:10.700678Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:03:10.700678Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"E73qnlxS1ZOeO8eBETsi6HbXvhGF3rOwhGAEPsSfSG5lgQCDWchNCBDORG+B2LQSIArSH98fO2gkGOq7tk0wDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:03:10.701400Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.07033","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f7cdfd6e4cd1c7bb9f2a456e4980a5c9cdd185a68bf32c289c59f7a75f453c40","sha256:ee76e8fd8b38da26ea24de8fcc5216cf26ed6ea6bcab0d1a8f2b1e1eff830bf3"],"state_sha256":"598a0b6d65864361f8add0e3325dea20744d18d287931afe9546731c544a9cb1"}