{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2008:XDH3IVXZ4LSFR5GGFIIPFFNQUX","short_pith_number":"pith:XDH3IVXZ","canonical_record":{"source":{"id":"0810.1547","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2008-10-08T22:16:55Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"b24b1703b93a10fc036a531c2809124e2dc4ecba46cca20c314fd919a412d39e","abstract_canon_sha256":"e7e92f208347f9c9170c3731b617543880e0d813270b8729151d2987383249e8"},"schema_version":"1.0"},"canonical_sha256":"b8cfb456f9e2e458f4c62a10f295b0a5f354c170d80ccca4b43e8db140f29e28","source":{"kind":"arxiv","id":"0810.1547","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0810.1547","created_at":"2026-05-18T03:26:00Z"},{"alias_kind":"arxiv_version","alias_value":"0810.1547v1","created_at":"2026-05-18T03:26:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0810.1547","created_at":"2026-05-18T03:26:00Z"},{"alias_kind":"pith_short_12","alias_value":"XDH3IVXZ4LSF","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"XDH3IVXZ4LSFR5GG","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"XDH3IVXZ","created_at":"2026-05-18T12:25:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2008:XDH3IVXZ4LSFR5GGFIIPFFNQUX","target":"record","payload":{"canonical_record":{"source":{"id":"0810.1547","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2008-10-08T22:16:55Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"b24b1703b93a10fc036a531c2809124e2dc4ecba46cca20c314fd919a412d39e","abstract_canon_sha256":"e7e92f208347f9c9170c3731b617543880e0d813270b8729151d2987383249e8"},"schema_version":"1.0"},"canonical_sha256":"b8cfb456f9e2e458f4c62a10f295b0a5f354c170d80ccca4b43e8db140f29e28","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:26:00.021813Z","signature_b64":"6+cmLszhR2aWR1DJdRv1DTjYt1+NQgu5mhXNamwzbH8gYcWSAbEI1+4kn0sVTX05Z0bPUUKKBPCko57iVaUZBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b8cfb456f9e2e458f4c62a10f295b0a5f354c170d80ccca4b43e8db140f29e28","last_reissued_at":"2026-05-18T03:26:00.021240Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:26:00.021240Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0810.1547","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":"2026-05-18T03:26:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ws6JuQmTxzuLaOAdtHoHH+ahOqzg7GldpctKx1/olwFjVHwMTB4SQZ/4zjJRPY+H67J/wprGaDSR2bYgYFaDCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T05:13:37.706902Z"},"content_sha256":"f85990bb5d3ef065b69694a80a199b231365b215e08f5dd558e81805bf19a9a7","schema_version":"1.0","event_id":"sha256:f85990bb5d3ef065b69694a80a199b231365b215e08f5dd558e81805bf19a9a7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2008:XDH3IVXZ4LSFR5GGFIIPFFNQUX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Conditional Limit Results for Type I Polar Distributions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Enkelejd Hashorva","submitted_at":"2008-10-08T22:16:55Z","abstract_excerpt":"Let (S_1,S_2)=(R \\cos(\\Theta), R \\sin (\\Theta)) be a bivariate random vector with associated random radius R which has distribution function $F$ being further independent of the random angle \\Theta. In this paper we investigate the asymptotic behaviour of the conditional survivor probability \\Psi_{\\rho,u}(y):=\\pk{\\rho S_1+ \\sqrt{1- \\rho^2} S_2> y \\lvert S_1> u}, \\rho \\in (-1,1),\\in R when u approaches the upper endpoint of F. On the density function of \\Theta we require a certain local asymptotic behaviour at 0, whereas for F we require that it belongs to the Gumbel max-domain of attraction. T"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0810.1547","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":"2026-05-18T03:26:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kO8TCOHA/scBJHJjA+UMEp73ayYL7iXAt4Jmgsru8oLtdXC9pnahV1lAcXxTgOnrqTu6vKE5GqoGKBEF7MukDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T05:13:37.707663Z"},"content_sha256":"cb039f54fa0b6061b5a446916a583d8c517644b7e7fd3484ac8569317c2402fc","schema_version":"1.0","event_id":"sha256:cb039f54fa0b6061b5a446916a583d8c517644b7e7fd3484ac8569317c2402fc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XDH3IVXZ4LSFR5GGFIIPFFNQUX/bundle.json","state_url":"https://pith.science/pith/XDH3IVXZ4LSFR5GGFIIPFFNQUX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XDH3IVXZ4LSFR5GGFIIPFFNQUX/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":"2026-06-08T05:13:37Z","links":{"resolver":"https://pith.science/pith/XDH3IVXZ4LSFR5GGFIIPFFNQUX","bundle":"https://pith.science/pith/XDH3IVXZ4LSFR5GGFIIPFFNQUX/bundle.json","state":"https://pith.science/pith/XDH3IVXZ4LSFR5GGFIIPFFNQUX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XDH3IVXZ4LSFR5GGFIIPFFNQUX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:XDH3IVXZ4LSFR5GGFIIPFFNQUX","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":"e7e92f208347f9c9170c3731b617543880e0d813270b8729151d2987383249e8","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2008-10-08T22:16:55Z","title_canon_sha256":"b24b1703b93a10fc036a531c2809124e2dc4ecba46cca20c314fd919a412d39e"},"schema_version":"1.0","source":{"id":"0810.1547","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0810.1547","created_at":"2026-05-18T03:26:00Z"},{"alias_kind":"arxiv_version","alias_value":"0810.1547v1","created_at":"2026-05-18T03:26:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0810.1547","created_at":"2026-05-18T03:26:00Z"},{"alias_kind":"pith_short_12","alias_value":"XDH3IVXZ4LSF","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"XDH3IVXZ4LSFR5GG","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"XDH3IVXZ","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:cb039f54fa0b6061b5a446916a583d8c517644b7e7fd3484ac8569317c2402fc","target":"graph","created_at":"2026-05-18T03:26:00Z","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":"Let (S_1,S_2)=(R \\cos(\\Theta), R \\sin (\\Theta)) be a bivariate random vector with associated random radius R which has distribution function $F$ being further independent of the random angle \\Theta. In this paper we investigate the asymptotic behaviour of the conditional survivor probability \\Psi_{\\rho,u}(y):=\\pk{\\rho S_1+ \\sqrt{1- \\rho^2} S_2> y \\lvert S_1> u}, \\rho \\in (-1,1),\\in R when u approaches the upper endpoint of F. On the density function of \\Theta we require a certain local asymptotic behaviour at 0, whereas for F we require that it belongs to the Gumbel max-domain of attraction. T","authors_text":"Enkelejd Hashorva","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2008-10-08T22:16:55Z","title":"Conditional Limit Results for Type I Polar Distributions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0810.1547","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:f85990bb5d3ef065b69694a80a199b231365b215e08f5dd558e81805bf19a9a7","target":"record","created_at":"2026-05-18T03:26:00Z","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":"e7e92f208347f9c9170c3731b617543880e0d813270b8729151d2987383249e8","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2008-10-08T22:16:55Z","title_canon_sha256":"b24b1703b93a10fc036a531c2809124e2dc4ecba46cca20c314fd919a412d39e"},"schema_version":"1.0","source":{"id":"0810.1547","kind":"arxiv","version":1}},"canonical_sha256":"b8cfb456f9e2e458f4c62a10f295b0a5f354c170d80ccca4b43e8db140f29e28","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b8cfb456f9e2e458f4c62a10f295b0a5f354c170d80ccca4b43e8db140f29e28","first_computed_at":"2026-05-18T03:26:00.021240Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:26:00.021240Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6+cmLszhR2aWR1DJdRv1DTjYt1+NQgu5mhXNamwzbH8gYcWSAbEI1+4kn0sVTX05Z0bPUUKKBPCko57iVaUZBg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:26:00.021813Z","signed_message":"canonical_sha256_bytes"},"source_id":"0810.1547","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f85990bb5d3ef065b69694a80a199b231365b215e08f5dd558e81805bf19a9a7","sha256:cb039f54fa0b6061b5a446916a583d8c517644b7e7fd3484ac8569317c2402fc"],"state_sha256":"0fe9e5402510f94c5315dca86369052717ea692371991e2b50ff691be4234c91"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"V65no/f+uQRd8mBU/6xaIHB8j2MG9hKli03XrwzksxorLQoiLrYEt1Idq477xBUvfwNjcYwtacgdeNI6HDXHAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T05:13:37.712266Z","bundle_sha256":"33f80dadeb4b0272c8be9b1b412172a2770b43614c413c2f5fe32c8142a48324"}}