{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:QXZX5TGIH4MKYIEEOIHJUPHUYZ","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":"753a5b64fb96dad6c9e5c790344c94b2f7c31b13733d42a6cfa3d7b46eec85b8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-07-24T13:17:37Z","title_canon_sha256":"345c63fc6ceaddd5b17432209b2fb478ede03b22ee5479a92af49ad039959a5d"},"schema_version":"1.0","source":{"id":"1107.4754","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.4754","created_at":"2026-05-18T03:35:38Z"},{"alias_kind":"arxiv_version","alias_value":"1107.4754v2","created_at":"2026-05-18T03:35:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.4754","created_at":"2026-05-18T03:35:38Z"},{"alias_kind":"pith_short_12","alias_value":"QXZX5TGIH4MK","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"QXZX5TGIH4MKYIEE","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"QXZX5TGI","created_at":"2026-05-18T12:26:39Z"}],"graph_snapshots":[{"event_id":"sha256:3fa09e09be9fec1cc041e92fc604e8c3a342f3a099642bae56139594c9d7f5f8","target":"graph","created_at":"2026-05-18T03:35:38Z","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 a given sequence of weights (non-negative numbers), we consider partitions of the positive integer n. Each n-partition is selected uniformly at random from the set of all such partitions. Under a classical scheme of assumptions on the weight sequence, which are due to Meinardus (1954), we show that the largest part in a random weighted partition, appropriately normalized, converges weakly, as n tends to infinity, to a random variable having the extreme value (Gumbel's) distribution. This limit theorem extends some known results on particular types of integer partitions and on the Bose-Eins","authors_text":"Ljuben Mutafchiev","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-07-24T13:17:37Z","title":"The Size of the Largest Part of Random Weighted Partitions of Large Integers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.4754","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":"sha256:9c8fb3b109d451a6ca365ce179c0bb20a3d3ab8ba424c4ef97753f7213fd45e5","target":"record","created_at":"2026-05-18T03:35:38Z","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":"753a5b64fb96dad6c9e5c790344c94b2f7c31b13733d42a6cfa3d7b46eec85b8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-07-24T13:17:37Z","title_canon_sha256":"345c63fc6ceaddd5b17432209b2fb478ede03b22ee5479a92af49ad039959a5d"},"schema_version":"1.0","source":{"id":"1107.4754","kind":"arxiv","version":2}},"canonical_sha256":"85f37eccc83f18ac2084720e9a3cf4c67245b175f40c6a43d20429ea856bbb65","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"85f37eccc83f18ac2084720e9a3cf4c67245b175f40c6a43d20429ea856bbb65","first_computed_at":"2026-05-18T03:35:38.800636Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:35:38.800636Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4YCdQtTi1LK14959I59Vk9u0ZGr+BljH0d+nh6iFvuHwrco2YRMDzqoYuEXdzMcV3n0N9MlkanuNpvyqkfG2Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T03:35:38.801427Z","signed_message":"canonical_sha256_bytes"},"source_id":"1107.4754","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9c8fb3b109d451a6ca365ce179c0bb20a3d3ab8ba424c4ef97753f7213fd45e5","sha256:3fa09e09be9fec1cc041e92fc604e8c3a342f3a099642bae56139594c9d7f5f8"],"state_sha256":"dacad01d06640f6b569ba3071ec37f72e0e4e190062746c3e2ffb8b3818ad78c"}