{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:2DFIW3WBNHEHTP4VV4WYCSDBM3","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":"76f3da4fa642b434af427e469545d41c4941db5e2a517ddd9cae1d07dbe3d9e9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-05-25T12:53:35Z","title_canon_sha256":"126a39b189c2bd7881426d9ec1cd90917fecf6aa3b0a68c8034f9815fb829b52"},"schema_version":"1.0","source":{"id":"1905.10590","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.10590","created_at":"2026-05-17T23:45:08Z"},{"alias_kind":"arxiv_version","alias_value":"1905.10590v1","created_at":"2026-05-17T23:45:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.10590","created_at":"2026-05-17T23:45:08Z"},{"alias_kind":"pith_short_12","alias_value":"2DFIW3WBNHEH","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_16","alias_value":"2DFIW3WBNHEHTP4V","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_8","alias_value":"2DFIW3WB","created_at":"2026-05-18T12:33:07Z"}],"graph_snapshots":[{"event_id":"sha256:19299378c2103b93b88bdf042ae00b7b97eb6b326ba04e2af7178ca99f890a71","target":"graph","created_at":"2026-05-17T23:45:08Z","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 use a coin flipping model for the random partition and Chebyshev's inequality to prove the lower bound $\\lim \\frac{\\log p(n)}{\\sqrt{n}} \\ge C$ for the number of partitions $p(n)$ of $n$, where $C$ is an explicit constant.","authors_text":"Mark Wildon","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-05-25T12:53:35Z","title":"A lower bound for the partition function from Chebyshev's inequality applied to a coin flipping model for the random partition"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.10590","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:ed1f725b9b4f71960cc5e1067f83e3d9e41c44760e26b9a44a944eeae0fcf3a3","target":"record","created_at":"2026-05-17T23:45:08Z","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":"76f3da4fa642b434af427e469545d41c4941db5e2a517ddd9cae1d07dbe3d9e9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-05-25T12:53:35Z","title_canon_sha256":"126a39b189c2bd7881426d9ec1cd90917fecf6aa3b0a68c8034f9815fb829b52"},"schema_version":"1.0","source":{"id":"1905.10590","kind":"arxiv","version":1}},"canonical_sha256":"d0ca8b6ec169c879bf95af2d81486166eb3acfc8de91e3ddcd324cb45bf29ab1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d0ca8b6ec169c879bf95af2d81486166eb3acfc8de91e3ddcd324cb45bf29ab1","first_computed_at":"2026-05-17T23:45:08.007078Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:45:08.007078Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bbssuO3KSjQ84Vs9d6C78rcoU52nwkUTF5QzpPZ01/BsvSZ6T2zcrQ0kF6aMaleG4tAIO7jJz4IU3bO6tZuIAw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:45:08.007665Z","signed_message":"canonical_sha256_bytes"},"source_id":"1905.10590","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ed1f725b9b4f71960cc5e1067f83e3d9e41c44760e26b9a44a944eeae0fcf3a3","sha256:19299378c2103b93b88bdf042ae00b7b97eb6b326ba04e2af7178ca99f890a71"],"state_sha256":"b7b8ab0d5142d948b4f4ab8a54b31a27a399ce659979b42e21ef9a3a846432a4"}