{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:ZN2AXU6SASDYTN3UCPUUSEOPNA","short_pith_number":"pith:ZN2AXU6S","canonical_record":{"source":{"id":"1307.1849","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-07-07T10:58:02Z","cross_cats_sorted":[],"title_canon_sha256":"02f1265f72b87307f00e009ca56a61b9761a26c5cafd51d10a2a4d3c3fc810f1","abstract_canon_sha256":"5d64dde92d1511aa853d607326100c584218ccbb6c46a807862f62fcc5b14f02"},"schema_version":"1.0"},"canonical_sha256":"cb740bd3d2048789b77413e94911cf6824360fc0a74d6e50dc08b759487f5e66","source":{"kind":"arxiv","id":"1307.1849","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.1849","created_at":"2026-05-18T02:48:24Z"},{"alias_kind":"arxiv_version","alias_value":"1307.1849v2","created_at":"2026-05-18T02:48:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.1849","created_at":"2026-05-18T02:48:24Z"},{"alias_kind":"pith_short_12","alias_value":"ZN2AXU6SASDY","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"ZN2AXU6SASDYTN3U","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"ZN2AXU6S","created_at":"2026-05-18T12:28:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:ZN2AXU6SASDYTN3UCPUUSEOPNA","target":"record","payload":{"canonical_record":{"source":{"id":"1307.1849","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-07-07T10:58:02Z","cross_cats_sorted":[],"title_canon_sha256":"02f1265f72b87307f00e009ca56a61b9761a26c5cafd51d10a2a4d3c3fc810f1","abstract_canon_sha256":"5d64dde92d1511aa853d607326100c584218ccbb6c46a807862f62fcc5b14f02"},"schema_version":"1.0"},"canonical_sha256":"cb740bd3d2048789b77413e94911cf6824360fc0a74d6e50dc08b759487f5e66","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:48:24.704798Z","signature_b64":"EDAkvUwsPUXV+d8YUCazejHc5x1wR/JEwauD/qRPqiZn4Tl3BQ7jzMEnX6a0SwsGvElO2Fdvu4K90Tt8Di80CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cb740bd3d2048789b77413e94911cf6824360fc0a74d6e50dc08b759487f5e66","last_reissued_at":"2026-05-18T02:48:24.704355Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:48:24.704355Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1307.1849","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:48:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"y+vMdD7cG88wPsNJQgl8qIG858t2DhBwhZj8COmeqq8lsVii/aLllpKnOA9Y156V82Xsl4KECKRCeMiEr2R2Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T12:38:21.957676Z"},"content_sha256":"0a23ddc444fbaaa94a5850efdaf85b90bf48a94d3beedff09e9529d1274473d1","schema_version":"1.0","event_id":"sha256:0a23ddc444fbaaa94a5850efdaf85b90bf48a94d3beedff09e9529d1274473d1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:ZN2AXU6SASDYTN3UCPUUSEOPNA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Sojourn measures of Student and Fisher-Snedecor random fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Andriy Olenko, Nikolai Leonenko","submitted_at":"2013-07-07T10:58:02Z","abstract_excerpt":"Limit theorems for the volumes of excursion sets of weakly and strongly dependent heavy-tailed random fields are proved. Some generalizations to sojourn measures above moving levels and for cross-correlated scenarios are presented. Special attention is paid to Student and Fisher-Snedecor random fields. Some simulation results are also presented."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.1849","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:48:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"c/mdhTUSbX2n9zjkcN1A8TlZ6Utg68dJpo1K298UGNfnz+TXuubEXpm+gN5zF4ohvrzpnueMBL0Y/LsMy4GeCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T12:38:21.958212Z"},"content_sha256":"a48caa3b82655c5f9a665dd9d3ad8a2951447ce0bb0e38f47657523a8992fd5c","schema_version":"1.0","event_id":"sha256:a48caa3b82655c5f9a665dd9d3ad8a2951447ce0bb0e38f47657523a8992fd5c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZN2AXU6SASDYTN3UCPUUSEOPNA/bundle.json","state_url":"https://pith.science/pith/ZN2AXU6SASDYTN3UCPUUSEOPNA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZN2AXU6SASDYTN3UCPUUSEOPNA/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-03T12:38:21Z","links":{"resolver":"https://pith.science/pith/ZN2AXU6SASDYTN3UCPUUSEOPNA","bundle":"https://pith.science/pith/ZN2AXU6SASDYTN3UCPUUSEOPNA/bundle.json","state":"https://pith.science/pith/ZN2AXU6SASDYTN3UCPUUSEOPNA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZN2AXU6SASDYTN3UCPUUSEOPNA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:ZN2AXU6SASDYTN3UCPUUSEOPNA","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":"5d64dde92d1511aa853d607326100c584218ccbb6c46a807862f62fcc5b14f02","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-07-07T10:58:02Z","title_canon_sha256":"02f1265f72b87307f00e009ca56a61b9761a26c5cafd51d10a2a4d3c3fc810f1"},"schema_version":"1.0","source":{"id":"1307.1849","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.1849","created_at":"2026-05-18T02:48:24Z"},{"alias_kind":"arxiv_version","alias_value":"1307.1849v2","created_at":"2026-05-18T02:48:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.1849","created_at":"2026-05-18T02:48:24Z"},{"alias_kind":"pith_short_12","alias_value":"ZN2AXU6SASDY","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"ZN2AXU6SASDYTN3U","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"ZN2AXU6S","created_at":"2026-05-18T12:28:09Z"}],"graph_snapshots":[{"event_id":"sha256:a48caa3b82655c5f9a665dd9d3ad8a2951447ce0bb0e38f47657523a8992fd5c","target":"graph","created_at":"2026-05-18T02:48:24Z","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":"Limit theorems for the volumes of excursion sets of weakly and strongly dependent heavy-tailed random fields are proved. Some generalizations to sojourn measures above moving levels and for cross-correlated scenarios are presented. Special attention is paid to Student and Fisher-Snedecor random fields. Some simulation results are also presented.","authors_text":"Andriy Olenko, Nikolai Leonenko","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-07-07T10:58:02Z","title":"Sojourn measures of Student and Fisher-Snedecor random fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.1849","kind":"arxiv","version":2},"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":"sha256:0a23ddc444fbaaa94a5850efdaf85b90bf48a94d3beedff09e9529d1274473d1","target":"record","created_at":"2026-05-18T02:48:24Z","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":"5d64dde92d1511aa853d607326100c584218ccbb6c46a807862f62fcc5b14f02","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-07-07T10:58:02Z","title_canon_sha256":"02f1265f72b87307f00e009ca56a61b9761a26c5cafd51d10a2a4d3c3fc810f1"},"schema_version":"1.0","source":{"id":"1307.1849","kind":"arxiv","version":2}},"canonical_sha256":"cb740bd3d2048789b77413e94911cf6824360fc0a74d6e50dc08b759487f5e66","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cb740bd3d2048789b77413e94911cf6824360fc0a74d6e50dc08b759487f5e66","first_computed_at":"2026-05-18T02:48:24.704355Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:48:24.704355Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EDAkvUwsPUXV+d8YUCazejHc5x1wR/JEwauD/qRPqiZn4Tl3BQ7jzMEnX6a0SwsGvElO2Fdvu4K90Tt8Di80CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:48:24.704798Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.1849","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0a23ddc444fbaaa94a5850efdaf85b90bf48a94d3beedff09e9529d1274473d1","sha256:a48caa3b82655c5f9a665dd9d3ad8a2951447ce0bb0e38f47657523a8992fd5c"],"state_sha256":"3d5a30f0f5fd58ae6a3bad0d2fa40d6f7cc15215225b46afdb370aa4296d1bfc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GwXD/Yt3dnhoaLY5G4UGQaRXD3OawFNl2APynGHRlc0R0/RTAipj9b3dSr9L0eNBYgHlD3SRHrd4IsILz3UXBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T12:38:21.960578Z","bundle_sha256":"b4433dc775dfe54e022a64148d58dab5efcce141abac52a8f3369929ce7330a2"}}