{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:J5LSJTCQN3RPBHTDXVKL4DPLGN","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":"9ef0ac9252ed078fce808e6ccc4cff921e87d737e11b62fed03613a870568078","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-02-28T07:01:09Z","title_canon_sha256":"f9943f4f115676318b8d7ac006e65f87e123a12f224b1fcb3c730fc64e8d6bf3"},"schema_version":"1.0","source":{"id":"1102.5608","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.5608","created_at":"2026-05-18T02:03:04Z"},{"alias_kind":"arxiv_version","alias_value":"1102.5608v2","created_at":"2026-05-18T02:03:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.5608","created_at":"2026-05-18T02:03:04Z"},{"alias_kind":"pith_short_12","alias_value":"J5LSJTCQN3RP","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_16","alias_value":"J5LSJTCQN3RPBHTD","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_8","alias_value":"J5LSJTCQ","created_at":"2026-05-18T12:26:32Z"}],"graph_snapshots":[{"event_id":"sha256:aa32b4ecf71b04a05ac54ab2fa04d3e2c9d4feccd80dbc2fd2e57c3eff32b8f0","target":"graph","created_at":"2026-05-18T02:03:04Z","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":"Meinardus proved a general theorem about the asymptotics of the number of weighted partitions, when the Dirichlet generating function for weights has a single pole on the positive real axis. Continuing \\cite{GSE}, we derive asymptotics for the numbers of three basic types of decomposable combinatorial structures (or, equivalently, ideal gas models in statistical mechanics) of size $n$, when their Dirichlet generating functions have multiple simple poles on the positive real axis. Examples to which our theorem applies include ones related to vector partitions and quantum field theory. Our asymp","authors_text":"Boris Granovsky, Dudley Stark","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-02-28T07:01:09Z","title":"A Meinardus theorem with multiple singularities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.5608","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":"sha256:286389da7c34d44554f83bc585e56e9dd9f5c7b3552a8134b24c443f30522843","target":"record","created_at":"2026-05-18T02:03:04Z","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":"9ef0ac9252ed078fce808e6ccc4cff921e87d737e11b62fed03613a870568078","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-02-28T07:01:09Z","title_canon_sha256":"f9943f4f115676318b8d7ac006e65f87e123a12f224b1fcb3c730fc64e8d6bf3"},"schema_version":"1.0","source":{"id":"1102.5608","kind":"arxiv","version":2}},"canonical_sha256":"4f5724cc506ee2f09e63bd54be0deb336b5dccc2dbfdb0d3e5bcf8a8a3237be6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4f5724cc506ee2f09e63bd54be0deb336b5dccc2dbfdb0d3e5bcf8a8a3237be6","first_computed_at":"2026-05-18T02:03:04.111079Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:03:04.111079Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sn4O74LqsLaN5IX706kG8lMsid92jM6/GE/oXLBBgMhBNrMZARbWCDmFMOf/oexdHJ3kibGHa+7eUsuf+eEEAw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:03:04.111818Z","signed_message":"canonical_sha256_bytes"},"source_id":"1102.5608","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:286389da7c34d44554f83bc585e56e9dd9f5c7b3552a8134b24c443f30522843","sha256:aa32b4ecf71b04a05ac54ab2fa04d3e2c9d4feccd80dbc2fd2e57c3eff32b8f0"],"state_sha256":"81a2f9da124ccdd05eb09ded1ac1401d1bc112e542b99a44de1b9ce76bad09fe"}