{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:QXZX5TGIH4MKYIEEOIHJUPHUYZ","short_pith_number":"pith:QXZX5TGI","schema_version":"1.0","canonical_sha256":"85f37eccc83f18ac2084720e9a3cf4c67245b175f40c6a43d20429ea856bbb65","source":{"kind":"arxiv","id":"1107.4754","version":2},"attestation_state":"computed","paper":{"title":"The Size of the Largest Part of Random Weighted Partitions of Large Integers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Ljuben Mutafchiev","submitted_at":"2011-07-24T13:17:37Z","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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1107.4754","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-07-24T13:17:37Z","cross_cats_sorted":[],"title_canon_sha256":"345c63fc6ceaddd5b17432209b2fb478ede03b22ee5479a92af49ad039959a5d","abstract_canon_sha256":"753a5b64fb96dad6c9e5c790344c94b2f7c31b13733d42a6cfa3d7b46eec85b8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:35:38.801427Z","signature_b64":"4YCdQtTi1LK14959I59Vk9u0ZGr+BljH0d+nh6iFvuHwrco2YRMDzqoYuEXdzMcV3n0N9MlkanuNpvyqkfG2Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"85f37eccc83f18ac2084720e9a3cf4c67245b175f40c6a43d20429ea856bbb65","last_reissued_at":"2026-05-18T03:35:38.800636Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:35:38.800636Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Size of the Largest Part of Random Weighted Partitions of Large Integers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Ljuben Mutafchiev","submitted_at":"2011-07-24T13:17:37Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.4754","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1107.4754","created_at":"2026-05-18T03:35:38.800786+00:00"},{"alias_kind":"arxiv_version","alias_value":"1107.4754v2","created_at":"2026-05-18T03:35:38.800786+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.4754","created_at":"2026-05-18T03:35:38.800786+00:00"},{"alias_kind":"pith_short_12","alias_value":"QXZX5TGIH4MK","created_at":"2026-05-18T12:26:39.201973+00:00"},{"alias_kind":"pith_short_16","alias_value":"QXZX5TGIH4MKYIEE","created_at":"2026-05-18T12:26:39.201973+00:00"},{"alias_kind":"pith_short_8","alias_value":"QXZX5TGI","created_at":"2026-05-18T12:26:39.201973+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/QXZX5TGIH4MKYIEEOIHJUPHUYZ","json":"https://pith.science/pith/QXZX5TGIH4MKYIEEOIHJUPHUYZ.json","graph_json":"https://pith.science/api/pith-number/QXZX5TGIH4MKYIEEOIHJUPHUYZ/graph.json","events_json":"https://pith.science/api/pith-number/QXZX5TGIH4MKYIEEOIHJUPHUYZ/events.json","paper":"https://pith.science/paper/QXZX5TGI"},"agent_actions":{"view_html":"https://pith.science/pith/QXZX5TGIH4MKYIEEOIHJUPHUYZ","download_json":"https://pith.science/pith/QXZX5TGIH4MKYIEEOIHJUPHUYZ.json","view_paper":"https://pith.science/paper/QXZX5TGI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1107.4754&json=true","fetch_graph":"https://pith.science/api/pith-number/QXZX5TGIH4MKYIEEOIHJUPHUYZ/graph.json","fetch_events":"https://pith.science/api/pith-number/QXZX5TGIH4MKYIEEOIHJUPHUYZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QXZX5TGIH4MKYIEEOIHJUPHUYZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QXZX5TGIH4MKYIEEOIHJUPHUYZ/action/storage_attestation","attest_author":"https://pith.science/pith/QXZX5TGIH4MKYIEEOIHJUPHUYZ/action/author_attestation","sign_citation":"https://pith.science/pith/QXZX5TGIH4MKYIEEOIHJUPHUYZ/action/citation_signature","submit_replication":"https://pith.science/pith/QXZX5TGIH4MKYIEEOIHJUPHUYZ/action/replication_record"}},"created_at":"2026-05-18T03:35:38.800786+00:00","updated_at":"2026-05-18T03:35:38.800786+00:00"}