{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:BV6XQUH3P3Z65EY4BQXNTIQQRJ","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":"fa6a44ad18b36d32c03a113252ed06b601c764d13236c1140176ad455218305a","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-11-22T20:13:35Z","title_canon_sha256":"5b4c1e2ec92cd77f77f413fc8ae7aa331d7a3f20edabdffed74ddd1302b6b362"},"schema_version":"1.0","source":{"id":"1911.10236","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1911.10236","created_at":"2026-07-05T08:24:51Z"},{"alias_kind":"arxiv_version","alias_value":"1911.10236v2","created_at":"2026-07-05T08:24:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1911.10236","created_at":"2026-07-05T08:24:51Z"},{"alias_kind":"pith_short_12","alias_value":"BV6XQUH3P3Z6","created_at":"2026-07-05T08:24:51Z"},{"alias_kind":"pith_short_16","alias_value":"BV6XQUH3P3Z65EY4","created_at":"2026-07-05T08:24:51Z"},{"alias_kind":"pith_short_8","alias_value":"BV6XQUH3","created_at":"2026-07-05T08:24:51Z"}],"graph_snapshots":[{"event_id":"sha256:6c017308a8acaca714b3afc426ba2dbcb96f3f0de6fb155c96ad53b95885f675","target":"graph","created_at":"2026-07-05T08:24:51Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1911.10236/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In recent work, M. Schneider and the first author studied a curious class of integer partitions called \"sequentially congruent\" partitions: the $m$th part is congruent to the $(m+1)$th part modulo $m$, with the smallest part congruent to zero modulo the number of parts. Let $p_{\\mathcal S}(n)$ be the number of sequentially congruent partitions of $n,$ and let $p_{\\square}(n)$ be the number of partitions of $n$ wherein all parts are squares. In this note we prove bijectively, for all $n\\geq 1,$ that $p_{\\mathcal S}(n) = p_{\\square}(n).$ Our proof naturally extends to show other exotic classes o","authors_text":"Ian Wagner, James A. Sellers, Robert Schneider","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-11-22T20:13:35Z","title":"Sequentially congruent partitions and partitions into squares"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1911.10236","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":"sha256:69093e248c9f24b25ebcc31b2865580876e8bc14515d40389c7681218f4da360","target":"record","created_at":"2026-07-05T08:24:51Z","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":"fa6a44ad18b36d32c03a113252ed06b601c764d13236c1140176ad455218305a","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-11-22T20:13:35Z","title_canon_sha256":"5b4c1e2ec92cd77f77f413fc8ae7aa331d7a3f20edabdffed74ddd1302b6b362"},"schema_version":"1.0","source":{"id":"1911.10236","kind":"arxiv","version":2}},"canonical_sha256":"0d7d7850fb7ef3ee931c0c2ed9a2108a7c0830f4358370772a87b4c761e06a89","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0d7d7850fb7ef3ee931c0c2ed9a2108a7c0830f4358370772a87b4c761e06a89","first_computed_at":"2026-07-05T08:24:51.770220Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:24:51.770220Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3v7lyDh2dvnALxVq6LqLYlUmz2hbmOaLz4HFr4TrKPlrQwjC+fY2Bs26oY9K0DH766AFXIp48EFePoD/l+fhBw==","signature_status":"signed_v1","signed_at":"2026-07-05T08:24:51.770632Z","signed_message":"canonical_sha256_bytes"},"source_id":"1911.10236","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:69093e248c9f24b25ebcc31b2865580876e8bc14515d40389c7681218f4da360","sha256:6c017308a8acaca714b3afc426ba2dbcb96f3f0de6fb155c96ad53b95885f675"],"state_sha256":"764e69b3d7ffa87f20c94558f18de78d80d3b5fcee0096d2706bdeccdf8e56c2"}