{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:7OXKTEO2NHYX6IDH72H6GQXAHP","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":"6a01d9d18a9689bd789e2227dd6b7526e8e0f15fd99cb1a5b1c1931daf737a51","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-06-17T14:54:29Z","title_canon_sha256":"b3350dc4ace8a882b6c1cda008c1812fc5f244baaa3c6964dc5bf6b52e1c5e65"},"schema_version":"1.0","source":{"id":"1506.05354","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.05354","created_at":"2026-05-18T01:19:50Z"},{"alias_kind":"arxiv_version","alias_value":"1506.05354v2","created_at":"2026-05-18T01:19:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.05354","created_at":"2026-05-18T01:19:50Z"},{"alias_kind":"pith_short_12","alias_value":"7OXKTEO2NHYX","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"7OXKTEO2NHYX6IDH","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"7OXKTEO2","created_at":"2026-05-18T12:29:10Z"}],"graph_snapshots":[{"event_id":"sha256:a7177512a52b941b8bc202fbd6c64e329cbf0bb35aef91ce53298828382c1d46","target":"graph","created_at":"2026-05-18T01:19:50Z","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":"Recently the author introduced two new integer partition quadruple functions, which satisfy Ramanujan-type congruences modulo $3$, $5$, $7$, and $13$. Here we reprove the congruences modulo $3$, $5$, and $7$ by defining a rank-type statistic that gives a combinatorial refinement of the congruences.","authors_text":"Chris Jennings-Shaffer","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-06-17T14:54:29Z","title":"Ranks For Two Partition Quadruple Functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.05354","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":"sha256:4fd8371742840bded7847689b945a2bb8fd34275d0012f4d7f8195e3850847bb","target":"record","created_at":"2026-05-18T01:19:50Z","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":"6a01d9d18a9689bd789e2227dd6b7526e8e0f15fd99cb1a5b1c1931daf737a51","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-06-17T14:54:29Z","title_canon_sha256":"b3350dc4ace8a882b6c1cda008c1812fc5f244baaa3c6964dc5bf6b52e1c5e65"},"schema_version":"1.0","source":{"id":"1506.05354","kind":"arxiv","version":2}},"canonical_sha256":"fbaea991da69f17f2067fe8fe342e03bde306b28184ef8d4d7bbd2a40026e79a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fbaea991da69f17f2067fe8fe342e03bde306b28184ef8d4d7bbd2a40026e79a","first_computed_at":"2026-05-18T01:19:50.949191Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:19:50.949191Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hohS+T3cO4fncn2txh2MjcKxY7BmTz0og3Q//y4w5S4QMaCROGwOb6HVYiGla0vDF4bpw7h5xDzqMsnnE++7Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:19:50.949771Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.05354","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4fd8371742840bded7847689b945a2bb8fd34275d0012f4d7f8195e3850847bb","sha256:a7177512a52b941b8bc202fbd6c64e329cbf0bb35aef91ce53298828382c1d46"],"state_sha256":"862c82a7937bb824ca711ab3a2f8e01998c1510159b0dc69c997895192de07d6"}