{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:ZIK2RJ5DXCOYNJRJGULBUCXD7Z","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":"030ce4c108974f8256083ae421f333d88e684dbe434f7c13f2513eb681570146","cross_cats_sorted":["math.AC","math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-11-17T20:11:16Z","title_canon_sha256":"c006ea4e71695af8c57dc7dac66c06c70475a07c2bb7fcd4f96ed0d77b74513c"},"schema_version":"1.0","source":{"id":"1511.05531","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.05531","created_at":"2026-05-18T00:07:22Z"},{"alias_kind":"arxiv_version","alias_value":"1511.05531v2","created_at":"2026-05-18T00:07:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.05531","created_at":"2026-05-18T00:07:22Z"},{"alias_kind":"pith_short_12","alias_value":"ZIK2RJ5DXCOY","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"ZIK2RJ5DXCOYNJRJ","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"ZIK2RJ5D","created_at":"2026-05-18T12:29:52Z"}],"graph_snapshots":[{"event_id":"sha256:75e9ed4dca2bc31eaa0b9eafbbc70eefcb6aeb7ab698c7a791a7c0d54fa67348","target":"graph","created_at":"2026-05-18T00:07:22Z","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":"The purpose of this note is to introduce a new approach to the study of one of the most basic and seemingly intractable problems in partition theory, namely the conjecture that the partition function $p(n)$ is equidistributed modulo 2.\n  Our main result will relate the densities, say $\\delta_t$, of the odd values of the $t$-multipartition functions $p_t(n)$, for several integers $t$. In particular, we will show that if $\\delta_t>0$ for some $t\\in \\{5,7,11,13,17,19,23,25\\}$, then (assuming it exists) $\\delta_1>0$; that is, $p(n)$ itself is odd with positive density. Notice that, currently, the ","authors_text":"Fabrizio Zanello, Samuel D. Judge, William J. Keith","cross_cats":["math.AC","math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-11-17T20:11:16Z","title":"On the density of the odd values of the partition function"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.05531","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":"sha256:4e9c21466ac6241ca204e30c497599a6685b7d509ef1f1b42a76da1fd11cd0b9","target":"record","created_at":"2026-05-18T00:07:22Z","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":"030ce4c108974f8256083ae421f333d88e684dbe434f7c13f2513eb681570146","cross_cats_sorted":["math.AC","math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-11-17T20:11:16Z","title_canon_sha256":"c006ea4e71695af8c57dc7dac66c06c70475a07c2bb7fcd4f96ed0d77b74513c"},"schema_version":"1.0","source":{"id":"1511.05531","kind":"arxiv","version":2}},"canonical_sha256":"ca15a8a7a3b89d86a62935161a0ae3fe433aecb183f42d5ff7cb004186df77d3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ca15a8a7a3b89d86a62935161a0ae3fe433aecb183f42d5ff7cb004186df77d3","first_computed_at":"2026-05-18T00:07:22.028153Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:07:22.028153Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LvqFR0WvFcujJLWOiqOOhohUw1Wb+mGO9W8AV4owYwUnFLScL6EeL9wQDSVwO/Y2mvWh6czWjBFWaXKq74ocBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:07:22.028847Z","signed_message":"canonical_sha256_bytes"},"source_id":"1511.05531","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4e9c21466ac6241ca204e30c497599a6685b7d509ef1f1b42a76da1fd11cd0b9","sha256:75e9ed4dca2bc31eaa0b9eafbbc70eefcb6aeb7ab698c7a791a7c0d54fa67348"],"state_sha256":"8452545a810ea9fb1ba1a030510081de4e950f4961343e0149595b43141b0548"}