{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:YACFJWZG6M22YNPR7ME3KWJFZW","short_pith_number":"pith:YACFJWZG","canonical_record":{"source":{"id":"1211.1318","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-11-06T17:26:52Z","cross_cats_sorted":[],"title_canon_sha256":"602be77d90e5bf6ad23263309bbb722472381202ce65d606592849d5f3ae2504","abstract_canon_sha256":"7db755636414bf3a13e40b3f13477de0cd91f2d2dfe7701b266f77d3cbaa7175"},"schema_version":"1.0"},"canonical_sha256":"c00454db26f335ac35f1fb09b55925cd9f4a26aaed7adb9825c43a8c14d787b2","source":{"kind":"arxiv","id":"1211.1318","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.1318","created_at":"2026-05-18T02:07:32Z"},{"alias_kind":"arxiv_version","alias_value":"1211.1318v2","created_at":"2026-05-18T02:07:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.1318","created_at":"2026-05-18T02:07:32Z"},{"alias_kind":"pith_short_12","alias_value":"YACFJWZG6M22","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_16","alias_value":"YACFJWZG6M22YNPR","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_8","alias_value":"YACFJWZG","created_at":"2026-05-18T12:27:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:YACFJWZG6M22YNPR7ME3KWJFZW","target":"record","payload":{"canonical_record":{"source":{"id":"1211.1318","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-11-06T17:26:52Z","cross_cats_sorted":[],"title_canon_sha256":"602be77d90e5bf6ad23263309bbb722472381202ce65d606592849d5f3ae2504","abstract_canon_sha256":"7db755636414bf3a13e40b3f13477de0cd91f2d2dfe7701b266f77d3cbaa7175"},"schema_version":"1.0"},"canonical_sha256":"c00454db26f335ac35f1fb09b55925cd9f4a26aaed7adb9825c43a8c14d787b2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:07:32.531876Z","signature_b64":"QiUOWYdaiv9RnoW1sRvEN9+21/nbc2xVT9cVhq1wrjYhUDEnq5Q6Wt76JkRwEzN9m7TprSjeVD2ly5B4LP6RCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c00454db26f335ac35f1fb09b55925cd9f4a26aaed7adb9825c43a8c14d787b2","last_reissued_at":"2026-05-18T02:07:32.531235Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:07:32.531235Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1211.1318","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":"2026-05-18T02:07:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"U1P+d+/SoTr4tWp9Pz2Y0lNV6YJ+kO4fCpTFO67WfzP/epyk9BonaGK3d13vW8sVZbLuNfmLsALuzhP5yonADg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T03:59:31.807814Z"},"content_sha256":"ddcfd09bade64dc6454613e68864ef2d032eead83877251d72f052bb40d8ea55","schema_version":"1.0","event_id":"sha256:ddcfd09bade64dc6454613e68864ef2d032eead83877251d72f052bb40d8ea55"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:YACFJWZG6M22YNPR7ME3KWJFZW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Logarithmic asymptotics for multidimensional extremes under non-linear scalings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Kamil Marcin Kosinski, Michel Mandjes","submitted_at":"2012-11-06T17:26:52Z","abstract_excerpt":"Let $\\boldsymbol W=\\{\\boldsymbol W_n:n\\in\\mathbb N\\}$ be a sequence of random vectors in $\\mathbb R^d$, $d\\ge 1$. This paper considers the logarithmic asymptotics of the extremes of $\\boldsymbol W$, that is, for any vector $\\boldsymbol q>\\boldsymbol 0$ in $\\mathbb R^d$, we find $$\\log\\mathbb P\\left(\\exists{n\\in\\mathbb N}:\\boldsymbol W_n> u \\boldsymbol q\\right), \\quad\\text{as} u\\to\\infty.$$ We follow the approach of the restricted large deviation principle introduced in Duffy et al. \\textit{Logarithmic asymptotics for the supremum of a stochastic process} (Ann. Appl. Probab., 13:430--445, 2003)"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.1318","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":"2026-05-18T02:07:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"V+aMkp0RL68I+Bks8AaDh+e+a21buDTw7NmjEXlXXby1oggsfqz2+lm8xDQ1KPiAMa/rPgwWptzh+pdeUovrCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T03:59:31.808214Z"},"content_sha256":"b11934a574d83e78165974eebb64ac9321e6bc19c6b00036da58cf92267b7745","schema_version":"1.0","event_id":"sha256:b11934a574d83e78165974eebb64ac9321e6bc19c6b00036da58cf92267b7745"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YACFJWZG6M22YNPR7ME3KWJFZW/bundle.json","state_url":"https://pith.science/pith/YACFJWZG6M22YNPR7ME3KWJFZW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YACFJWZG6M22YNPR7ME3KWJFZW/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":"2026-06-11T03:59:31Z","links":{"resolver":"https://pith.science/pith/YACFJWZG6M22YNPR7ME3KWJFZW","bundle":"https://pith.science/pith/YACFJWZG6M22YNPR7ME3KWJFZW/bundle.json","state":"https://pith.science/pith/YACFJWZG6M22YNPR7ME3KWJFZW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YACFJWZG6M22YNPR7ME3KWJFZW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:YACFJWZG6M22YNPR7ME3KWJFZW","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":"7db755636414bf3a13e40b3f13477de0cd91f2d2dfe7701b266f77d3cbaa7175","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-11-06T17:26:52Z","title_canon_sha256":"602be77d90e5bf6ad23263309bbb722472381202ce65d606592849d5f3ae2504"},"schema_version":"1.0","source":{"id":"1211.1318","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.1318","created_at":"2026-05-18T02:07:32Z"},{"alias_kind":"arxiv_version","alias_value":"1211.1318v2","created_at":"2026-05-18T02:07:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.1318","created_at":"2026-05-18T02:07:32Z"},{"alias_kind":"pith_short_12","alias_value":"YACFJWZG6M22","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_16","alias_value":"YACFJWZG6M22YNPR","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_8","alias_value":"YACFJWZG","created_at":"2026-05-18T12:27:27Z"}],"graph_snapshots":[{"event_id":"sha256:b11934a574d83e78165974eebb64ac9321e6bc19c6b00036da58cf92267b7745","target":"graph","created_at":"2026-05-18T02:07:32Z","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 $\\boldsymbol W=\\{\\boldsymbol W_n:n\\in\\mathbb N\\}$ be a sequence of random vectors in $\\mathbb R^d$, $d\\ge 1$. This paper considers the logarithmic asymptotics of the extremes of $\\boldsymbol W$, that is, for any vector $\\boldsymbol q>\\boldsymbol 0$ in $\\mathbb R^d$, we find $$\\log\\mathbb P\\left(\\exists{n\\in\\mathbb N}:\\boldsymbol W_n> u \\boldsymbol q\\right), \\quad\\text{as} u\\to\\infty.$$ We follow the approach of the restricted large deviation principle introduced in Duffy et al. \\textit{Logarithmic asymptotics for the supremum of a stochastic process} (Ann. Appl. Probab., 13:430--445, 2003)","authors_text":"Kamil Marcin Kosinski, Michel Mandjes","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-11-06T17:26:52Z","title":"Logarithmic asymptotics for multidimensional extremes under non-linear scalings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.1318","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:ddcfd09bade64dc6454613e68864ef2d032eead83877251d72f052bb40d8ea55","target":"record","created_at":"2026-05-18T02:07:32Z","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":"7db755636414bf3a13e40b3f13477de0cd91f2d2dfe7701b266f77d3cbaa7175","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-11-06T17:26:52Z","title_canon_sha256":"602be77d90e5bf6ad23263309bbb722472381202ce65d606592849d5f3ae2504"},"schema_version":"1.0","source":{"id":"1211.1318","kind":"arxiv","version":2}},"canonical_sha256":"c00454db26f335ac35f1fb09b55925cd9f4a26aaed7adb9825c43a8c14d787b2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c00454db26f335ac35f1fb09b55925cd9f4a26aaed7adb9825c43a8c14d787b2","first_computed_at":"2026-05-18T02:07:32.531235Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:07:32.531235Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QiUOWYdaiv9RnoW1sRvEN9+21/nbc2xVT9cVhq1wrjYhUDEnq5Q6Wt76JkRwEzN9m7TprSjeVD2ly5B4LP6RCA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:07:32.531876Z","signed_message":"canonical_sha256_bytes"},"source_id":"1211.1318","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ddcfd09bade64dc6454613e68864ef2d032eead83877251d72f052bb40d8ea55","sha256:b11934a574d83e78165974eebb64ac9321e6bc19c6b00036da58cf92267b7745"],"state_sha256":"2a94bb2d8cdbc1a8b97f4294cec91b547e4c5b7c7c4a0015c3b37a280eb6a26a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"undCfQ4nY6gvcHMVh//s5waDt8y79G5DhNfEQa29oTo6elhd6r6LEyrdJXf9K6YkmCZdlhHwxKU4kHN5/k8RBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T03:59:31.810653Z","bundle_sha256":"1239fc026558aea3855e08f604bba0f306c5f0e6ce9254283c3045e90a30b17a"}}