{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:BNVNLTMX43VYJP5S77M7ZQZTVV","short_pith_number":"pith:BNVNLTMX","canonical_record":{"source":{"id":"1608.02091","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-08-06T10:25:19Z","cross_cats_sorted":[],"title_canon_sha256":"f48d25a5261f58b8253706c60a7e12e01d21c52fedaba170ab7a5ed431177ee0","abstract_canon_sha256":"8adacb392782d4f6bf415bffa5d17b2f44735de0d63d12d9d44ab3e4a31c3dd0"},"schema_version":"1.0"},"canonical_sha256":"0b6ad5cd97e6eb84bfb2ffd9fcc333ad5f1af9d72ae82eaa8926b55bc11a7d1d","source":{"kind":"arxiv","id":"1608.02091","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.02091","created_at":"2026-05-18T01:09:40Z"},{"alias_kind":"arxiv_version","alias_value":"1608.02091v1","created_at":"2026-05-18T01:09:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.02091","created_at":"2026-05-18T01:09:40Z"},{"alias_kind":"pith_short_12","alias_value":"BNVNLTMX43VY","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_16","alias_value":"BNVNLTMX43VYJP5S","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_8","alias_value":"BNVNLTMX","created_at":"2026-05-18T12:30:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:BNVNLTMX43VYJP5S77M7ZQZTVV","target":"record","payload":{"canonical_record":{"source":{"id":"1608.02091","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-08-06T10:25:19Z","cross_cats_sorted":[],"title_canon_sha256":"f48d25a5261f58b8253706c60a7e12e01d21c52fedaba170ab7a5ed431177ee0","abstract_canon_sha256":"8adacb392782d4f6bf415bffa5d17b2f44735de0d63d12d9d44ab3e4a31c3dd0"},"schema_version":"1.0"},"canonical_sha256":"0b6ad5cd97e6eb84bfb2ffd9fcc333ad5f1af9d72ae82eaa8926b55bc11a7d1d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:09:40.991560Z","signature_b64":"n3tRb+kfzyza6UmHXWVOD0MsuZ5++pJp5fJe1yDq4Xw76oLMaOqxdfoEU4PibdAsvZSLXexCmTLX4Ki91nd1BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0b6ad5cd97e6eb84bfb2ffd9fcc333ad5f1af9d72ae82eaa8926b55bc11a7d1d","last_reissued_at":"2026-05-18T01:09:40.990962Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:09:40.990962Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1608.02091","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":"2026-05-18T01:09:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UE8tP9TyjHNfW8MzP4dOTQ/DUYGBKRztDsNXqk01CbetZfxlSJWqatStmq+6ViqnUG4dnksypmYzr53RyoomBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T04:34:07.730173Z"},"content_sha256":"42135cc9fe8a4d267df2fdf608bd7127ae6add44456061cb68dc7c2a717f5107","schema_version":"1.0","event_id":"sha256:42135cc9fe8a4d267df2fdf608bd7127ae6add44456061cb68dc7c2a717f5107"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:BNVNLTMX43VYJP5S77M7ZQZTVV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Second-order asymptotics on distributions of maxima of bivariate elliptical arrays","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Xin Liao, Zhichao Weng, Zuoxiang Peng","submitted_at":"2016-08-06T10:25:19Z","abstract_excerpt":"Let $\\{ (\\xi_{ni}, \\eta_{ni}), 1\\leq i \\leq n, n\\geq 1 \\}$ be a triangular array of independent bivariate elliptical random vectors with the same distribution function as $(S_{1}, \\rho_{n}S_{1}+\\sqrt{1-\\rho_{n}^2}S_{2})$, $\\rho_{n}\\in (0,1)$, where $(S_{1},S_{2})$ is a bivariate spherical random vector. For the distribution function of radius $\\sqrt{S_{1}^2+S_{2}^2}$ belonging to the max-domain of attraction of the Weibull distribution, Hashorva (2006) derived the limiting distribution of maximum of this triangular array if convergence rate of $\\rho_{n}$ to $1$ is given. In this paper, under t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.02091","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":"2026-05-18T01:09:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ViSoTEdVyNmZQNubPsU8ns9hUleiaHqb0c/FTy9wO6lRKKqfurI3bONdWFPL407KwLIp8R974wURC3nJurt0CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T04:34:07.730826Z"},"content_sha256":"90162b30ca100f050150ec203931125ac38bdc605734d7500d5da60a4dc6104d","schema_version":"1.0","event_id":"sha256:90162b30ca100f050150ec203931125ac38bdc605734d7500d5da60a4dc6104d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BNVNLTMX43VYJP5S77M7ZQZTVV/bundle.json","state_url":"https://pith.science/pith/BNVNLTMX43VYJP5S77M7ZQZTVV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BNVNLTMX43VYJP5S77M7ZQZTVV/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":"2026-05-31T04:34:07Z","links":{"resolver":"https://pith.science/pith/BNVNLTMX43VYJP5S77M7ZQZTVV","bundle":"https://pith.science/pith/BNVNLTMX43VYJP5S77M7ZQZTVV/bundle.json","state":"https://pith.science/pith/BNVNLTMX43VYJP5S77M7ZQZTVV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BNVNLTMX43VYJP5S77M7ZQZTVV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:BNVNLTMX43VYJP5S77M7ZQZTVV","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":"8adacb392782d4f6bf415bffa5d17b2f44735de0d63d12d9d44ab3e4a31c3dd0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-08-06T10:25:19Z","title_canon_sha256":"f48d25a5261f58b8253706c60a7e12e01d21c52fedaba170ab7a5ed431177ee0"},"schema_version":"1.0","source":{"id":"1608.02091","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.02091","created_at":"2026-05-18T01:09:40Z"},{"alias_kind":"arxiv_version","alias_value":"1608.02091v1","created_at":"2026-05-18T01:09:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.02091","created_at":"2026-05-18T01:09:40Z"},{"alias_kind":"pith_short_12","alias_value":"BNVNLTMX43VY","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_16","alias_value":"BNVNLTMX43VYJP5S","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_8","alias_value":"BNVNLTMX","created_at":"2026-05-18T12:30:07Z"}],"graph_snapshots":[{"event_id":"sha256:90162b30ca100f050150ec203931125ac38bdc605734d7500d5da60a4dc6104d","target":"graph","created_at":"2026-05-18T01:09:40Z","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 $\\{ (\\xi_{ni}, \\eta_{ni}), 1\\leq i \\leq n, n\\geq 1 \\}$ be a triangular array of independent bivariate elliptical random vectors with the same distribution function as $(S_{1}, \\rho_{n}S_{1}+\\sqrt{1-\\rho_{n}^2}S_{2})$, $\\rho_{n}\\in (0,1)$, where $(S_{1},S_{2})$ is a bivariate spherical random vector. For the distribution function of radius $\\sqrt{S_{1}^2+S_{2}^2}$ belonging to the max-domain of attraction of the Weibull distribution, Hashorva (2006) derived the limiting distribution of maximum of this triangular array if convergence rate of $\\rho_{n}$ to $1$ is given. In this paper, under t","authors_text":"Xin Liao, Zhichao Weng, Zuoxiang Peng","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-08-06T10:25:19Z","title":"Second-order asymptotics on distributions of maxima of bivariate elliptical arrays"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.02091","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":"sha256:42135cc9fe8a4d267df2fdf608bd7127ae6add44456061cb68dc7c2a717f5107","target":"record","created_at":"2026-05-18T01:09:40Z","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":"8adacb392782d4f6bf415bffa5d17b2f44735de0d63d12d9d44ab3e4a31c3dd0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-08-06T10:25:19Z","title_canon_sha256":"f48d25a5261f58b8253706c60a7e12e01d21c52fedaba170ab7a5ed431177ee0"},"schema_version":"1.0","source":{"id":"1608.02091","kind":"arxiv","version":1}},"canonical_sha256":"0b6ad5cd97e6eb84bfb2ffd9fcc333ad5f1af9d72ae82eaa8926b55bc11a7d1d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0b6ad5cd97e6eb84bfb2ffd9fcc333ad5f1af9d72ae82eaa8926b55bc11a7d1d","first_computed_at":"2026-05-18T01:09:40.990962Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:09:40.990962Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"n3tRb+kfzyza6UmHXWVOD0MsuZ5++pJp5fJe1yDq4Xw76oLMaOqxdfoEU4PibdAsvZSLXexCmTLX4Ki91nd1BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:09:40.991560Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.02091","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:42135cc9fe8a4d267df2fdf608bd7127ae6add44456061cb68dc7c2a717f5107","sha256:90162b30ca100f050150ec203931125ac38bdc605734d7500d5da60a4dc6104d"],"state_sha256":"0cc3aa3b889e9241ca9fef1fd1b0e448b7960559b4b480527a3b515606c02ba0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9LzUZIysq4KZSoAGrGgucbiQjCq578IdKYSH4PkLs4JrBF3nBwgqOZOf+E/951BEf2x19RpGG9pFyCWrs8cRCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T04:34:07.734057Z","bundle_sha256":"d1677a01abb19f12fd1cbc00736b83019cc08873372a645aacd7901ac30dbb06"}}