{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:GT5QYGEZR4S4MXYIDIY5D36CVV","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":"29220477afcbefe2eeda86a1c53c96d4bf1754ff8e303335f4227c46844a97cf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-06-08T04:27:59Z","title_canon_sha256":"688594e8bc1ddd7aaaa1c6c864b1f1724147f4c47835df421b96245684a943a3"},"schema_version":"1.0","source":{"id":"1806.02965","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.02965","created_at":"2026-05-17T23:52:52Z"},{"alias_kind":"arxiv_version","alias_value":"1806.02965v4","created_at":"2026-05-17T23:52:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.02965","created_at":"2026-05-17T23:52:52Z"},{"alias_kind":"pith_short_12","alias_value":"GT5QYGEZR4S4","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_16","alias_value":"GT5QYGEZR4S4MXYI","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_8","alias_value":"GT5QYGEZ","created_at":"2026-05-18T12:32:25Z"}],"graph_snapshots":[{"event_id":"sha256:48dd60e3f1c9e49c6ddacba528d4f6729e0850e69f00332d725cb2d2bc6d00ab","target":"graph","created_at":"2026-05-17T23:52:52Z","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 $\\{B_\\beta (x), x \\in \\mathbb{S}^N\\}$ be a fractional Brownian motion on the $N$-dimensional unit sphere $\\mathbb{S}^N$ with Hurst index $\\beta$. We study the excursion probability $\\mathbb{P}\\{\\sup_{x\\in T} B_\\beta(x) > u \\}$ and obtain the asymptotics as $u\\to \\infty$, where $T$ can be the entire sphere $\\mathbb{S}^N$ or a geodesic disc on $\\mathbb{S}^N$.","authors_text":"Dan Cheng, Peng Liu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-06-08T04:27:59Z","title":"Extremes of Spherical Fractional Brownian Motion"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.02965","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":"sha256:549702b069d9be470f01eade89c9cd87924e29a37da43aa188043ebcca67b55a","target":"record","created_at":"2026-05-17T23:52:52Z","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":"29220477afcbefe2eeda86a1c53c96d4bf1754ff8e303335f4227c46844a97cf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-06-08T04:27:59Z","title_canon_sha256":"688594e8bc1ddd7aaaa1c6c864b1f1724147f4c47835df421b96245684a943a3"},"schema_version":"1.0","source":{"id":"1806.02965","kind":"arxiv","version":4}},"canonical_sha256":"34fb0c18998f25c65f081a31d1efc2ad78303998f5eac55449905c7f898397b1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"34fb0c18998f25c65f081a31d1efc2ad78303998f5eac55449905c7f898397b1","first_computed_at":"2026-05-17T23:52:52.909478Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:52:52.909478Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Hccps5nFSYvx3pmnYhZslyMejzykTdPS81eeNu966elGRlt1mgejjCNfWuJdC9CVlgtAED6kseMH7gHCIn+bAQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:52:52.910204Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.02965","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:549702b069d9be470f01eade89c9cd87924e29a37da43aa188043ebcca67b55a","sha256:48dd60e3f1c9e49c6ddacba528d4f6729e0850e69f00332d725cb2d2bc6d00ab"],"state_sha256":"585a0caa2542b99fbe6cc500914acc7af42ebffb5b6aa7860b5e8abc5550f8b6"}