{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:W7DNOIQ43MI3ENO2ZEGE5PZMAW","short_pith_number":"pith:W7DNOIQ4","canonical_record":{"source":{"id":"1607.04848","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2016-07-17T10:46:59Z","cross_cats_sorted":[],"title_canon_sha256":"c50846ff20f3315ec3e0f95926e207adc9e6993c4fb6974ff4cda4584ebfa8a3","abstract_canon_sha256":"7817c86ad4f21e940aec1d97bf3cd06980e38e849e5c8a7650a96f7ac267fd01"},"schema_version":"1.0"},"canonical_sha256":"b7c6d7221cdb11b235dac90c4ebf2c059272842a86119802950a7a2eb4ae5cc7","source":{"kind":"arxiv","id":"1607.04848","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.04848","created_at":"2026-05-18T01:10:56Z"},{"alias_kind":"arxiv_version","alias_value":"1607.04848v1","created_at":"2026-05-18T01:10:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.04848","created_at":"2026-05-18T01:10:56Z"},{"alias_kind":"pith_short_12","alias_value":"W7DNOIQ43MI3","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_16","alias_value":"W7DNOIQ43MI3ENO2","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_8","alias_value":"W7DNOIQ4","created_at":"2026-05-18T12:30:48Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:W7DNOIQ43MI3ENO2ZEGE5PZMAW","target":"record","payload":{"canonical_record":{"source":{"id":"1607.04848","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2016-07-17T10:46:59Z","cross_cats_sorted":[],"title_canon_sha256":"c50846ff20f3315ec3e0f95926e207adc9e6993c4fb6974ff4cda4584ebfa8a3","abstract_canon_sha256":"7817c86ad4f21e940aec1d97bf3cd06980e38e849e5c8a7650a96f7ac267fd01"},"schema_version":"1.0"},"canonical_sha256":"b7c6d7221cdb11b235dac90c4ebf2c059272842a86119802950a7a2eb4ae5cc7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:10:56.499928Z","signature_b64":"Heco1B+pWCPzcm1o/QA9MegGQbaQTWF2ya0SBuVUQvJAXJM4GAZ11vRRK3NNujECdTUW1v0P8heo0x0uFoZ6Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b7c6d7221cdb11b235dac90c4ebf2c059272842a86119802950a7a2eb4ae5cc7","last_reissued_at":"2026-05-18T01:10:56.499387Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:10:56.499387Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1607.04848","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":"2026-05-18T01:10:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VC68pySha9VYvRPk6V24uhtTUM177+afWiSp/m5yLyMEUGDF+zxSJOc7ErOYUy4zIbgrHrSc8TqWbKMkk/0gAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T11:19:32.241090Z"},"content_sha256":"94b2510e2a095df6e4a257e394c55a9839b77aef0441eda261a5ec38efb05188","schema_version":"1.0","event_id":"sha256:94b2510e2a095df6e4a257e394c55a9839b77aef0441eda261a5ec38efb05188"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:W7DNOIQ43MI3ENO2ZEGE5PZMAW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A note on the asymptotic normality of sums of extreme values","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.ME","authors_text":"Gane Samb Lo","submitted_at":"2016-07-17T10:46:59Z","abstract_excerpt":"Let $X_1$, $X_2$,... be a sequence of independent random variables with common distribution function $F$ in the domain of attraction of a Gumbel extreme value distribution and for each integer $n\\geq 1$, let $X_{1,n} \\leq ... X_{n,n}$ denote the order statistics based on the first $n$ of these random variables. Along with related results it is shown that for any sequence of positive integers $k_n \\rightarrow +\\infty$ and $k_{n}/n \\rightarrow 0$ as $n \\rightarrow 0$ the sum of the upper $k_n$ extreme values $X_{n-k_{n},n}+...+X_{n,n}$, when properly centered and normalized, converges in distrib"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.04848","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":"2026-05-18T01:10:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Rz6T9ZvVssDVod6UTRDDGUU7h5UQ1i/V3kT4M+qWp0N2R6QQmSetAL9L9c12Wmyg5gUhIp2ghjcp8jrOKTAJCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T11:19:32.241456Z"},"content_sha256":"60f03549f21054254cca88c11a5f62f82631751af3ef0f30d2733e189c98271e","schema_version":"1.0","event_id":"sha256:60f03549f21054254cca88c11a5f62f82631751af3ef0f30d2733e189c98271e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/W7DNOIQ43MI3ENO2ZEGE5PZMAW/bundle.json","state_url":"https://pith.science/pith/W7DNOIQ43MI3ENO2ZEGE5PZMAW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/W7DNOIQ43MI3ENO2ZEGE5PZMAW/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":"2026-06-25T11:19:32Z","links":{"resolver":"https://pith.science/pith/W7DNOIQ43MI3ENO2ZEGE5PZMAW","bundle":"https://pith.science/pith/W7DNOIQ43MI3ENO2ZEGE5PZMAW/bundle.json","state":"https://pith.science/pith/W7DNOIQ43MI3ENO2ZEGE5PZMAW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/W7DNOIQ43MI3ENO2ZEGE5PZMAW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:W7DNOIQ43MI3ENO2ZEGE5PZMAW","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":"7817c86ad4f21e940aec1d97bf3cd06980e38e849e5c8a7650a96f7ac267fd01","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2016-07-17T10:46:59Z","title_canon_sha256":"c50846ff20f3315ec3e0f95926e207adc9e6993c4fb6974ff4cda4584ebfa8a3"},"schema_version":"1.0","source":{"id":"1607.04848","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.04848","created_at":"2026-05-18T01:10:56Z"},{"alias_kind":"arxiv_version","alias_value":"1607.04848v1","created_at":"2026-05-18T01:10:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.04848","created_at":"2026-05-18T01:10:56Z"},{"alias_kind":"pith_short_12","alias_value":"W7DNOIQ43MI3","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_16","alias_value":"W7DNOIQ43MI3ENO2","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_8","alias_value":"W7DNOIQ4","created_at":"2026-05-18T12:30:48Z"}],"graph_snapshots":[{"event_id":"sha256:60f03549f21054254cca88c11a5f62f82631751af3ef0f30d2733e189c98271e","target":"graph","created_at":"2026-05-18T01:10:56Z","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 $X_1$, $X_2$,... be a sequence of independent random variables with common distribution function $F$ in the domain of attraction of a Gumbel extreme value distribution and for each integer $n\\geq 1$, let $X_{1,n} \\leq ... X_{n,n}$ denote the order statistics based on the first $n$ of these random variables. Along with related results it is shown that for any sequence of positive integers $k_n \\rightarrow +\\infty$ and $k_{n}/n \\rightarrow 0$ as $n \\rightarrow 0$ the sum of the upper $k_n$ extreme values $X_{n-k_{n},n}+...+X_{n,n}$, when properly centered and normalized, converges in distrib","authors_text":"Gane Samb Lo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2016-07-17T10:46:59Z","title":"A note on the asymptotic normality of sums of extreme values"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.04848","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":"sha256:94b2510e2a095df6e4a257e394c55a9839b77aef0441eda261a5ec38efb05188","target":"record","created_at":"2026-05-18T01:10:56Z","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":"7817c86ad4f21e940aec1d97bf3cd06980e38e849e5c8a7650a96f7ac267fd01","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2016-07-17T10:46:59Z","title_canon_sha256":"c50846ff20f3315ec3e0f95926e207adc9e6993c4fb6974ff4cda4584ebfa8a3"},"schema_version":"1.0","source":{"id":"1607.04848","kind":"arxiv","version":1}},"canonical_sha256":"b7c6d7221cdb11b235dac90c4ebf2c059272842a86119802950a7a2eb4ae5cc7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b7c6d7221cdb11b235dac90c4ebf2c059272842a86119802950a7a2eb4ae5cc7","first_computed_at":"2026-05-18T01:10:56.499387Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:10:56.499387Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Heco1B+pWCPzcm1o/QA9MegGQbaQTWF2ya0SBuVUQvJAXJM4GAZ11vRRK3NNujECdTUW1v0P8heo0x0uFoZ6Cw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:10:56.499928Z","signed_message":"canonical_sha256_bytes"},"source_id":"1607.04848","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:94b2510e2a095df6e4a257e394c55a9839b77aef0441eda261a5ec38efb05188","sha256:60f03549f21054254cca88c11a5f62f82631751af3ef0f30d2733e189c98271e"],"state_sha256":"ec382efbaba9227773b4a2a99501980b0198aa1df446e314608a842ba4d40084"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sYUcOCptBl4b5j9y0cvvq3laXTl1PU9W9DW2iz3Ig5U+j3BKGRdJSpmrpjlRLT+5GEoNsY2MhB9LlhFnbYtEAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T11:19:32.243429Z","bundle_sha256":"ba737783b9bee812ab087f6ec4b5ca9ef142d722a149e4bfafb161b2f1dcf06c"}}