{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:TFOUZXLRMOMFJ6VE5EHMXRIPO5","short_pith_number":"pith:TFOUZXLR","canonical_record":{"source":{"id":"1505.03325","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-05-13T10:50:51Z","cross_cats_sorted":[],"title_canon_sha256":"eac9047b89a08770ce0af2af6d5e6dd17e278c2f84418beb75f718583c1746ba","abstract_canon_sha256":"382dec5c8d0a9f38b4bce64e0ae996a80f0a1ece012ff3ed8a9bcfd547b3ead5"},"schema_version":"1.0"},"canonical_sha256":"995d4cdd71639854faa4e90ecbc50f7755e2a644ae8cb388c322daa00c3985ea","source":{"kind":"arxiv","id":"1505.03325","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.03325","created_at":"2026-05-18T01:15:00Z"},{"alias_kind":"arxiv_version","alias_value":"1505.03325v2","created_at":"2026-05-18T01:15:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.03325","created_at":"2026-05-18T01:15:00Z"},{"alias_kind":"pith_short_12","alias_value":"TFOUZXLRMOMF","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"TFOUZXLRMOMFJ6VE","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"TFOUZXLR","created_at":"2026-05-18T12:29:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:TFOUZXLRMOMFJ6VE5EHMXRIPO5","target":"record","payload":{"canonical_record":{"source":{"id":"1505.03325","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-05-13T10:50:51Z","cross_cats_sorted":[],"title_canon_sha256":"eac9047b89a08770ce0af2af6d5e6dd17e278c2f84418beb75f718583c1746ba","abstract_canon_sha256":"382dec5c8d0a9f38b4bce64e0ae996a80f0a1ece012ff3ed8a9bcfd547b3ead5"},"schema_version":"1.0"},"canonical_sha256":"995d4cdd71639854faa4e90ecbc50f7755e2a644ae8cb388c322daa00c3985ea","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:15:00.398753Z","signature_b64":"YFrrzF2oz/kEaAJH/mUgJngIA8otfr9BCeqFM+QkycRUEc42hUsC76R7xGaue/g5XbaIQH2/tAgJ3VWwJhpfCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"995d4cdd71639854faa4e90ecbc50f7755e2a644ae8cb388c322daa00c3985ea","last_reissued_at":"2026-05-18T01:15:00.398321Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:15:00.398321Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1505.03325","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":"2026-05-18T01:15:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ND3JEMV5UVgvEoMEjY54KrOWwg68EL76rKn0ktEMLm9AlnuPmMStFVlki/4YsnQ+EgqZdscbZZYQAvERr53bDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T08:14:07.788788Z"},"content_sha256":"2294a93536971c369fb3b6109da32fc11813d6ddb84761642931de7fd01caafa","schema_version":"1.0","event_id":"sha256:2294a93536971c369fb3b6109da32fc11813d6ddb84761642931de7fd01caafa"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:TFOUZXLRMOMFJ6VE5EHMXRIPO5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Joint exceedances of random products","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Anja Jan{\\ss}en, Holger Drees","submitted_at":"2015-05-13T10:50:51Z","abstract_excerpt":"We analyze the joint extremal behavior of $n$ random products of the form $\\prod_{j=1}^m X_j^{a_{ij}}, 1 \\leq i \\leq n,$ for non-negative, independent regularly varying random variables $X_1, \\ldots, X_m$ and general coefficients $a_{ij} \\in \\mathbb{R}$. Products of this form appear for example if one observes a linear time series with gamma type innovations at $n$ points in time. We combine arguments of linear optimization and a generalized concept of regular variation on cones to show that the asymptotic behavior of joint exceedance probabilities of these products is determined by the soluti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.03325","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":"2026-05-18T01:15:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dFW1bBwyY/6MvE683cOoNRZGghO+Jysamq5WhyMhmkARy8f47fCvniOzNBrLkbuGcidRyB9AND4dwDmf22igDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T08:14:07.789146Z"},"content_sha256":"75a7155979bb3a87fbe3e63370d8e53a93836c6dd027206bb697dca13598dc1b","schema_version":"1.0","event_id":"sha256:75a7155979bb3a87fbe3e63370d8e53a93836c6dd027206bb697dca13598dc1b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TFOUZXLRMOMFJ6VE5EHMXRIPO5/bundle.json","state_url":"https://pith.science/pith/TFOUZXLRMOMFJ6VE5EHMXRIPO5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TFOUZXLRMOMFJ6VE5EHMXRIPO5/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":"2026-06-24T08:14:07Z","links":{"resolver":"https://pith.science/pith/TFOUZXLRMOMFJ6VE5EHMXRIPO5","bundle":"https://pith.science/pith/TFOUZXLRMOMFJ6VE5EHMXRIPO5/bundle.json","state":"https://pith.science/pith/TFOUZXLRMOMFJ6VE5EHMXRIPO5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TFOUZXLRMOMFJ6VE5EHMXRIPO5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:TFOUZXLRMOMFJ6VE5EHMXRIPO5","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":"382dec5c8d0a9f38b4bce64e0ae996a80f0a1ece012ff3ed8a9bcfd547b3ead5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-05-13T10:50:51Z","title_canon_sha256":"eac9047b89a08770ce0af2af6d5e6dd17e278c2f84418beb75f718583c1746ba"},"schema_version":"1.0","source":{"id":"1505.03325","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.03325","created_at":"2026-05-18T01:15:00Z"},{"alias_kind":"arxiv_version","alias_value":"1505.03325v2","created_at":"2026-05-18T01:15:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.03325","created_at":"2026-05-18T01:15:00Z"},{"alias_kind":"pith_short_12","alias_value":"TFOUZXLRMOMF","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"TFOUZXLRMOMFJ6VE","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"TFOUZXLR","created_at":"2026-05-18T12:29:42Z"}],"graph_snapshots":[{"event_id":"sha256:75a7155979bb3a87fbe3e63370d8e53a93836c6dd027206bb697dca13598dc1b","target":"graph","created_at":"2026-05-18T01:15:00Z","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 analyze the joint extremal behavior of $n$ random products of the form $\\prod_{j=1}^m X_j^{a_{ij}}, 1 \\leq i \\leq n,$ for non-negative, independent regularly varying random variables $X_1, \\ldots, X_m$ and general coefficients $a_{ij} \\in \\mathbb{R}$. Products of this form appear for example if one observes a linear time series with gamma type innovations at $n$ points in time. We combine arguments of linear optimization and a generalized concept of regular variation on cones to show that the asymptotic behavior of joint exceedance probabilities of these products is determined by the soluti","authors_text":"Anja Jan{\\ss}en, Holger Drees","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-05-13T10:50:51Z","title":"Joint exceedances of random products"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.03325","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":"sha256:2294a93536971c369fb3b6109da32fc11813d6ddb84761642931de7fd01caafa","target":"record","created_at":"2026-05-18T01:15:00Z","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":"382dec5c8d0a9f38b4bce64e0ae996a80f0a1ece012ff3ed8a9bcfd547b3ead5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-05-13T10:50:51Z","title_canon_sha256":"eac9047b89a08770ce0af2af6d5e6dd17e278c2f84418beb75f718583c1746ba"},"schema_version":"1.0","source":{"id":"1505.03325","kind":"arxiv","version":2}},"canonical_sha256":"995d4cdd71639854faa4e90ecbc50f7755e2a644ae8cb388c322daa00c3985ea","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"995d4cdd71639854faa4e90ecbc50f7755e2a644ae8cb388c322daa00c3985ea","first_computed_at":"2026-05-18T01:15:00.398321Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:15:00.398321Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YFrrzF2oz/kEaAJH/mUgJngIA8otfr9BCeqFM+QkycRUEc42hUsC76R7xGaue/g5XbaIQH2/tAgJ3VWwJhpfCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:15:00.398753Z","signed_message":"canonical_sha256_bytes"},"source_id":"1505.03325","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2294a93536971c369fb3b6109da32fc11813d6ddb84761642931de7fd01caafa","sha256:75a7155979bb3a87fbe3e63370d8e53a93836c6dd027206bb697dca13598dc1b"],"state_sha256":"3573dfea1af28fbf60502fd60227a35924d93d06fb2203919c79435318c7d1ec"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MgA18Z4tZ9qLlvQ7FyIaNH5VWz/3yacejWiDNpgkuBt+6zVSHv/ldQH9yMFlunBq0BnipGPC6PWGnkeFBkixCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T08:14:07.791105Z","bundle_sha256":"70fafc94a6caa11e13f7160527fc7a49c2bbfb0282716db921b3a1e72f57eaba"}}