{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:YMXWG26Q5MDMO36Y42CCCN2OBV","short_pith_number":"pith:YMXWG26Q","schema_version":"1.0","canonical_sha256":"c32f636bd0eb06c76fd8e68421374e0d4716b16363a2238526fa2e085fbf10fb","source":{"kind":"arxiv","id":"1511.00246","version":2},"attestation_state":"computed","paper":{"title":"New congruences for 2-color partitions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.NT","authors_text":"Shane Chern","submitted_at":"2015-11-01T13:24:20Z","abstract_excerpt":"Let $p_k(n)$ denote the number of $2$-color partitions of $n$ where one of the colors appears only in parts that are multiples of $k$. We will prove a conjecture of Ahmed, Baruah, and Dastidar on congruences modulo $5$ for $p_k(n)$. Moreover, we will present some new congruences modulo $7$ for $p_4(n)$."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1511.00246","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-11-01T13:24:20Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"966e2dd869e3220b9a58feaebb5f27f5f70fa3f5a3d71623b48c7ce94c03c4cf","abstract_canon_sha256":"c8bd5e16ee78c70b21043b0ff2750af3773a4ea9aee856ecababca2050ed8d17"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:21:08.382893Z","signature_b64":"nOrmVxEUIAveH6Bhf194TsPf68CYiA9Sp8RQq40pEKY2524cl0GdCx/L9fXiRkyUY6ENjpANg96oo3AQuQV0Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c32f636bd0eb06c76fd8e68421374e0d4716b16363a2238526fa2e085fbf10fb","last_reissued_at":"2026-05-18T01:21:08.382177Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:21:08.382177Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"New congruences for 2-color partitions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.NT","authors_text":"Shane Chern","submitted_at":"2015-11-01T13:24:20Z","abstract_excerpt":"Let $p_k(n)$ denote the number of $2$-color partitions of $n$ where one of the colors appears only in parts that are multiples of $k$. We will prove a conjecture of Ahmed, Baruah, and Dastidar on congruences modulo $5$ for $p_k(n)$. Moreover, we will present some new congruences modulo $7$ for $p_4(n)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.00246","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1511.00246","created_at":"2026-05-18T01:21:08.382294+00:00"},{"alias_kind":"arxiv_version","alias_value":"1511.00246v2","created_at":"2026-05-18T01:21:08.382294+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.00246","created_at":"2026-05-18T01:21:08.382294+00:00"},{"alias_kind":"pith_short_12","alias_value":"YMXWG26Q5MDM","created_at":"2026-05-18T12:29:50.041715+00:00"},{"alias_kind":"pith_short_16","alias_value":"YMXWG26Q5MDMO36Y","created_at":"2026-05-18T12:29:50.041715+00:00"},{"alias_kind":"pith_short_8","alias_value":"YMXWG26Q","created_at":"2026-05-18T12:29:50.041715+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/YMXWG26Q5MDMO36Y42CCCN2OBV","json":"https://pith.science/pith/YMXWG26Q5MDMO36Y42CCCN2OBV.json","graph_json":"https://pith.science/api/pith-number/YMXWG26Q5MDMO36Y42CCCN2OBV/graph.json","events_json":"https://pith.science/api/pith-number/YMXWG26Q5MDMO36Y42CCCN2OBV/events.json","paper":"https://pith.science/paper/YMXWG26Q"},"agent_actions":{"view_html":"https://pith.science/pith/YMXWG26Q5MDMO36Y42CCCN2OBV","download_json":"https://pith.science/pith/YMXWG26Q5MDMO36Y42CCCN2OBV.json","view_paper":"https://pith.science/paper/YMXWG26Q","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1511.00246&json=true","fetch_graph":"https://pith.science/api/pith-number/YMXWG26Q5MDMO36Y42CCCN2OBV/graph.json","fetch_events":"https://pith.science/api/pith-number/YMXWG26Q5MDMO36Y42CCCN2OBV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YMXWG26Q5MDMO36Y42CCCN2OBV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YMXWG26Q5MDMO36Y42CCCN2OBV/action/storage_attestation","attest_author":"https://pith.science/pith/YMXWG26Q5MDMO36Y42CCCN2OBV/action/author_attestation","sign_citation":"https://pith.science/pith/YMXWG26Q5MDMO36Y42CCCN2OBV/action/citation_signature","submit_replication":"https://pith.science/pith/YMXWG26Q5MDMO36Y42CCCN2OBV/action/replication_record"}},"created_at":"2026-05-18T01:21:08.382294+00:00","updated_at":"2026-05-18T01:21:08.382294+00:00"}