{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:W3XCXWJIAEEUWHHDVPUJZQLS4J","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":"ba3269f241b90b81880e07d9e8e7c6b8fa09c050b7ff9b5700a258876dec3402","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-09-06T15:22:35Z","title_canon_sha256":"f56d33a35cf435a0a8a0748b99e6d475aa23c44c98281cd1c4579fb65d50a31e"},"schema_version":"1.0","source":{"id":"1609.01601","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.01601","created_at":"2026-05-18T01:05:39Z"},{"alias_kind":"arxiv_version","alias_value":"1609.01601v1","created_at":"2026-05-18T01:05:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.01601","created_at":"2026-05-18T01:05:39Z"},{"alias_kind":"pith_short_12","alias_value":"W3XCXWJIAEEU","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_16","alias_value":"W3XCXWJIAEEUWHHD","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_8","alias_value":"W3XCXWJI","created_at":"2026-05-18T12:30:48Z"}],"graph_snapshots":[{"event_id":"sha256:982be9d0a3a647a59cd188ff66bfcda749c257194c74fad0a8a32289e6f43729","target":"graph","created_at":"2026-05-18T01:05:39Z","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":"We show that the maximal value in a size $n$ sample from GEM$(\\theta)$ distribution is distributed as a sum of independent geometric random variables. This implies that the maximal value grows as $\\theta\\log(n)$ as $n\\to\\infty$. For the two-parametric GEM$(\\alpha,\\theta)$ distribution we show that the maximal value grows as a random factor of $n^{\\alpha/(1-\\alpha)}$ and find the limiting distribution.","authors_text":"Jim Pitman, Yuri Yakubovich","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-09-06T15:22:35Z","title":"Successive maxima of samples from a GEM distribution"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.01601","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":"sha256:968ea927bdde39dcd62a97c07d2f7ee56c8f59e508d3cbd38608b877fbebf64a","target":"record","created_at":"2026-05-18T01:05:39Z","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":"ba3269f241b90b81880e07d9e8e7c6b8fa09c050b7ff9b5700a258876dec3402","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-09-06T15:22:35Z","title_canon_sha256":"f56d33a35cf435a0a8a0748b99e6d475aa23c44c98281cd1c4579fb65d50a31e"},"schema_version":"1.0","source":{"id":"1609.01601","kind":"arxiv","version":1}},"canonical_sha256":"b6ee2bd92801094b1ce3abe89cc172e2594399e118bf47581a67fd9aeddd6c8f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b6ee2bd92801094b1ce3abe89cc172e2594399e118bf47581a67fd9aeddd6c8f","first_computed_at":"2026-05-18T01:05:39.173449Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:05:39.173449Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Swbr4pSSVcrJ/dtiHAUkfGFTD9TZ4I3H8o2ys/BCmhkFJcWsjscQ5HBnWkivvQjH0G3Of+LPCasSGxN4JcEMCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:05:39.173936Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.01601","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:968ea927bdde39dcd62a97c07d2f7ee56c8f59e508d3cbd38608b877fbebf64a","sha256:982be9d0a3a647a59cd188ff66bfcda749c257194c74fad0a8a32289e6f43729"],"state_sha256":"f8bd5680a2436f49d9c7a7215f0549bfc5fb044a603d1c38626fbf49e36b676e"}