{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:OIZWF6BDWJIBMZ2DFDDRINWDJ3","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":"dc25757a35391ce4b4d8e87a23da77fce8d4dea2f53134f66703078fba680e2e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-07-29T01:29:18Z","title_canon_sha256":"ea4735db24114314947a377ffa85ee2990e302d169cc00c99462fecafe5d5ed4"},"schema_version":"1.0","source":{"id":"1607.08674","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.08674","created_at":"2026-05-18T01:10:16Z"},{"alias_kind":"arxiv_version","alias_value":"1607.08674v1","created_at":"2026-05-18T01:10:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.08674","created_at":"2026-05-18T01:10:16Z"},{"alias_kind":"pith_short_12","alias_value":"OIZWF6BDWJIB","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_16","alias_value":"OIZWF6BDWJIBMZ2D","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_8","alias_value":"OIZWF6BD","created_at":"2026-05-18T12:30:36Z"}],"graph_snapshots":[{"event_id":"sha256:7aa50740efa083e9f9a6fcfbb3132544bb5cac6644a313970f838fd4bca43e93","target":"graph","created_at":"2026-05-18T01:10:16Z","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":"For integers $n\\geq r$, we treat the $r$th largest of a sample of size $n$ as an $\\mathbb{R}^\\infty$-valued stochastic process in $r$ which we denote $\\mathbf{M}^{(r)}$. We show that the sequence regarded in this way satisfies the Markov property. We go on to study the asymptotic behaviour of $\\mathbf{M}^{(r)}$ as $r\\to\\infty$, and, borrowing from classical extreme value theory, show that left-tail domain of attraction conditions on the underlying distribution of the sample guarantee weak limits for both the range of $\\mathbf{M}^{(r)}$ and $\\mathbf{M}^{(r)}$ itself, after norming and centering","authors_text":"Boris Buchmann, Ross Maller, Sidney Resnick","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-07-29T01:29:18Z","title":"Processes of rth Largest"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.08674","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":"sha256:5edd62fb30f20fe666075407b7b011250946660eb735145126f80fcbe564fb47","target":"record","created_at":"2026-05-18T01:10:16Z","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":"dc25757a35391ce4b4d8e87a23da77fce8d4dea2f53134f66703078fba680e2e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-07-29T01:29:18Z","title_canon_sha256":"ea4735db24114314947a377ffa85ee2990e302d169cc00c99462fecafe5d5ed4"},"schema_version":"1.0","source":{"id":"1607.08674","kind":"arxiv","version":1}},"canonical_sha256":"723362f823b25016674328c71436c34ed468280a0cb37f2fd8a66bcd4c6cc5d4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"723362f823b25016674328c71436c34ed468280a0cb37f2fd8a66bcd4c6cc5d4","first_computed_at":"2026-05-18T01:10:16.074569Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:10:16.074569Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GiLSlxPCtaUeE5NBUcI/BPcuJj8sj+OB1IyricdTJkl+lx1JkIL9Xy/6O80SQcc1FzeqIekavHZsS8MxnG/QDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:10:16.075068Z","signed_message":"canonical_sha256_bytes"},"source_id":"1607.08674","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5edd62fb30f20fe666075407b7b011250946660eb735145126f80fcbe564fb47","sha256:7aa50740efa083e9f9a6fcfbb3132544bb5cac6644a313970f838fd4bca43e93"],"state_sha256":"a8c920f30d4af6c81893dffd205c70efbabc9c11ecc7dc7bb85ba956068b0460"}