{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:UK2VKXN3TZ7CQ7AJK272PGTIPH","short_pith_number":"pith:UK2VKXN3","canonical_record":{"source":{"id":"1405.2455","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-05-10T17:39:05Z","cross_cats_sorted":[],"title_canon_sha256":"f12a1f40e8cdc7bf89be12add4f1ae6882a59ce417cc7cf1df1880952434274e","abstract_canon_sha256":"43fa5214f1df0ba570355042500cb63eefe383926b1dcf46c2ec3f760c0f48b7"},"schema_version":"1.0"},"canonical_sha256":"a2b5555dbb9e7e287c0956bfa79a6879f53723121f129195ebbb235317020365","source":{"kind":"arxiv","id":"1405.2455","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.2455","created_at":"2026-05-18T02:31:35Z"},{"alias_kind":"arxiv_version","alias_value":"1405.2455v1","created_at":"2026-05-18T02:31:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.2455","created_at":"2026-05-18T02:31:35Z"},{"alias_kind":"pith_short_12","alias_value":"UK2VKXN3TZ7C","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_16","alias_value":"UK2VKXN3TZ7CQ7AJ","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_8","alias_value":"UK2VKXN3","created_at":"2026-05-18T12:28:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:UK2VKXN3TZ7CQ7AJK272PGTIPH","target":"record","payload":{"canonical_record":{"source":{"id":"1405.2455","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-05-10T17:39:05Z","cross_cats_sorted":[],"title_canon_sha256":"f12a1f40e8cdc7bf89be12add4f1ae6882a59ce417cc7cf1df1880952434274e","abstract_canon_sha256":"43fa5214f1df0ba570355042500cb63eefe383926b1dcf46c2ec3f760c0f48b7"},"schema_version":"1.0"},"canonical_sha256":"a2b5555dbb9e7e287c0956bfa79a6879f53723121f129195ebbb235317020365","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:31:35.921031Z","signature_b64":"XMsfEFrkd7NvEHGv+Zknqekuiz9yU694ydkcFCwaoJrqjEu8aOSAo9rLkeEhiSCJnjdZsXp5NQkoQPStIAQMDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a2b5555dbb9e7e287c0956bfa79a6879f53723121f129195ebbb235317020365","last_reissued_at":"2026-05-18T02:31:35.920582Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:31:35.920582Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1405.2455","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:31:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lfJOg6EWJVd3ykYq3Q6xeZrjRBRchwyr48+s5TgMFTPC3aIXtsOHSdwvcam//se7WEz+Z/CN4rf9F2QQvdQGDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T21:22:56.053786Z"},"content_sha256":"9fc5a1f9a4825408634393d59e185d528f103aab71729bd5dc8230747c7a6d04","schema_version":"1.0","event_id":"sha256:9fc5a1f9a4825408634393d59e185d528f103aab71729bd5dc8230747c7a6d04"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:UK2VKXN3TZ7CQ7AJK272PGTIPH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Tail asymptotic of Weibull-type risks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"E. Hashorva, Z. Weng","submitted_at":"2014-05-10T17:39:05Z","abstract_excerpt":"In this paper we derive the tail asymptotics of the product of two dependent Weibull-type risks, which is of interest in various statistical and applied probability problems. Our results extend some recent findings of Schlueter and Fischer (2012) and Bose et al. (2012)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.2455","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":""},"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":"2026-05-18T02:31:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vrwmvzhIiWm9pIfp96mciM8vZolt8Eh2TWLBCfb5lUMB/WbluXFy9ZFv/SqT434NbvTy+I3VLqS+0UOoNrf8CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T21:22:56.054119Z"},"content_sha256":"3670f1fec3e56077a6cdbdb32d1bda475b2a69f92873e32b9c0d5000968993fd","schema_version":"1.0","event_id":"sha256:3670f1fec3e56077a6cdbdb32d1bda475b2a69f92873e32b9c0d5000968993fd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UK2VKXN3TZ7CQ7AJK272PGTIPH/bundle.json","state_url":"https://pith.science/pith/UK2VKXN3TZ7CQ7AJK272PGTIPH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UK2VKXN3TZ7CQ7AJK272PGTIPH/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":"2026-07-01T21:22:56Z","links":{"resolver":"https://pith.science/pith/UK2VKXN3TZ7CQ7AJK272PGTIPH","bundle":"https://pith.science/pith/UK2VKXN3TZ7CQ7AJK272PGTIPH/bundle.json","state":"https://pith.science/pith/UK2VKXN3TZ7CQ7AJK272PGTIPH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UK2VKXN3TZ7CQ7AJK272PGTIPH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:UK2VKXN3TZ7CQ7AJK272PGTIPH","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":"43fa5214f1df0ba570355042500cb63eefe383926b1dcf46c2ec3f760c0f48b7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-05-10T17:39:05Z","title_canon_sha256":"f12a1f40e8cdc7bf89be12add4f1ae6882a59ce417cc7cf1df1880952434274e"},"schema_version":"1.0","source":{"id":"1405.2455","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.2455","created_at":"2026-05-18T02:31:35Z"},{"alias_kind":"arxiv_version","alias_value":"1405.2455v1","created_at":"2026-05-18T02:31:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.2455","created_at":"2026-05-18T02:31:35Z"},{"alias_kind":"pith_short_12","alias_value":"UK2VKXN3TZ7C","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_16","alias_value":"UK2VKXN3TZ7CQ7AJ","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_8","alias_value":"UK2VKXN3","created_at":"2026-05-18T12:28:52Z"}],"graph_snapshots":[{"event_id":"sha256:3670f1fec3e56077a6cdbdb32d1bda475b2a69f92873e32b9c0d5000968993fd","target":"graph","created_at":"2026-05-18T02:31:35Z","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":"In this paper we derive the tail asymptotics of the product of two dependent Weibull-type risks, which is of interest in various statistical and applied probability problems. Our results extend some recent findings of Schlueter and Fischer (2012) and Bose et al. (2012).","authors_text":"E. Hashorva, Z. Weng","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-05-10T17:39:05Z","title":"Tail asymptotic of Weibull-type risks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.2455","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":"sha256:9fc5a1f9a4825408634393d59e185d528f103aab71729bd5dc8230747c7a6d04","target":"record","created_at":"2026-05-18T02:31:35Z","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":"43fa5214f1df0ba570355042500cb63eefe383926b1dcf46c2ec3f760c0f48b7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-05-10T17:39:05Z","title_canon_sha256":"f12a1f40e8cdc7bf89be12add4f1ae6882a59ce417cc7cf1df1880952434274e"},"schema_version":"1.0","source":{"id":"1405.2455","kind":"arxiv","version":1}},"canonical_sha256":"a2b5555dbb9e7e287c0956bfa79a6879f53723121f129195ebbb235317020365","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a2b5555dbb9e7e287c0956bfa79a6879f53723121f129195ebbb235317020365","first_computed_at":"2026-05-18T02:31:35.920582Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:31:35.920582Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XMsfEFrkd7NvEHGv+Zknqekuiz9yU694ydkcFCwaoJrqjEu8aOSAo9rLkeEhiSCJnjdZsXp5NQkoQPStIAQMDg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:31:35.921031Z","signed_message":"canonical_sha256_bytes"},"source_id":"1405.2455","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9fc5a1f9a4825408634393d59e185d528f103aab71729bd5dc8230747c7a6d04","sha256:3670f1fec3e56077a6cdbdb32d1bda475b2a69f92873e32b9c0d5000968993fd"],"state_sha256":"d51330f75f9cf34fe83c061da2105a1bc8159ab2a070f9bc9b57b39da937c3e8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AZwHuihTUVyw+oklwKjQjFjlFYXA61yEgpZPVAVUUdhY6FZftYWFYQEirTMol13P8FTW6VfH2YN0JmPSypjkCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-01T21:22:56.056165Z","bundle_sha256":"8fac14671fa1bf33b384fc5c5068ae675f941f41beeeafa41b19ec9d07242f82"}}