{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:CC3H45BF6ZGZM5O2ZQYCWSAQ6X","short_pith_number":"pith:CC3H45BF","schema_version":"1.0","canonical_sha256":"10b67e7425f64d9675dacc302b4810f5c7dd4c4f5be7bad4e5b8fe6183ddb6f7","source":{"kind":"arxiv","id":"1510.01202","version":1},"attestation_state":"computed","paper":{"title":"l-adic properties of partition functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Alexandra Musat, Eva Belmont, Holden Lee, Sarah Trebat-Leder","submitted_at":"2015-10-05T16:08:31Z","abstract_excerpt":"Folsom, Kent, and Ono used the theory of modular forms modulo $\\ell$ to establish remarkable ``self-similarity'' properties of the partition function and give an overarching explanation of many partition congruences. We generalize their work to analyze powers $p_r$ of the partition function as well as Andrews's spt-function. By showing that certain generating functions reside in a small space made up of reductions of modular forms, we set up a general framework for congruences for $p_r$ and spt on arithmetic progressions of the form $\\ell^mn+\\delta$ modulo powers of $\\ell$. Our work gives a co"},"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":"1510.01202","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-10-05T16:08:31Z","cross_cats_sorted":[],"title_canon_sha256":"d0d67249edd06e38ea7a8252acc059dd4ebfeb83de839f8dc57dfb8e80919e6b","abstract_canon_sha256":"14e8af214d0e56e81feec8d8ed515707b5d8681f6242017895160f1597e4e6d2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:31:04.571996Z","signature_b64":"6P4e8i7R6ugSx5rNenqs9Rq++Hyy4AJ8fU5UHHwwnmjsJEh1qSlBQyF6hnw69d8u0s9ZvTipPFX0AewIHbnQBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"10b67e7425f64d9675dacc302b4810f5c7dd4c4f5be7bad4e5b8fe6183ddb6f7","last_reissued_at":"2026-05-18T01:31:04.571389Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:31:04.571389Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"l-adic properties of partition functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Alexandra Musat, Eva Belmont, Holden Lee, Sarah Trebat-Leder","submitted_at":"2015-10-05T16:08:31Z","abstract_excerpt":"Folsom, Kent, and Ono used the theory of modular forms modulo $\\ell$ to establish remarkable ``self-similarity'' properties of the partition function and give an overarching explanation of many partition congruences. We generalize their work to analyze powers $p_r$ of the partition function as well as Andrews's spt-function. By showing that certain generating functions reside in a small space made up of reductions of modular forms, we set up a general framework for congruences for $p_r$ and spt on arithmetic progressions of the form $\\ell^mn+\\delta$ modulo powers of $\\ell$. Our work gives a co"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.01202","kind":"arxiv","version":1},"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":"1510.01202","created_at":"2026-05-18T01:31:04.571465+00:00"},{"alias_kind":"arxiv_version","alias_value":"1510.01202v1","created_at":"2026-05-18T01:31:04.571465+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.01202","created_at":"2026-05-18T01:31:04.571465+00:00"},{"alias_kind":"pith_short_12","alias_value":"CC3H45BF6ZGZ","created_at":"2026-05-18T12:29:14.074870+00:00"},{"alias_kind":"pith_short_16","alias_value":"CC3H45BF6ZGZM5O2","created_at":"2026-05-18T12:29:14.074870+00:00"},{"alias_kind":"pith_short_8","alias_value":"CC3H45BF","created_at":"2026-05-18T12:29:14.074870+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/CC3H45BF6ZGZM5O2ZQYCWSAQ6X","json":"https://pith.science/pith/CC3H45BF6ZGZM5O2ZQYCWSAQ6X.json","graph_json":"https://pith.science/api/pith-number/CC3H45BF6ZGZM5O2ZQYCWSAQ6X/graph.json","events_json":"https://pith.science/api/pith-number/CC3H45BF6ZGZM5O2ZQYCWSAQ6X/events.json","paper":"https://pith.science/paper/CC3H45BF"},"agent_actions":{"view_html":"https://pith.science/pith/CC3H45BF6ZGZM5O2ZQYCWSAQ6X","download_json":"https://pith.science/pith/CC3H45BF6ZGZM5O2ZQYCWSAQ6X.json","view_paper":"https://pith.science/paper/CC3H45BF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1510.01202&json=true","fetch_graph":"https://pith.science/api/pith-number/CC3H45BF6ZGZM5O2ZQYCWSAQ6X/graph.json","fetch_events":"https://pith.science/api/pith-number/CC3H45BF6ZGZM5O2ZQYCWSAQ6X/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CC3H45BF6ZGZM5O2ZQYCWSAQ6X/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CC3H45BF6ZGZM5O2ZQYCWSAQ6X/action/storage_attestation","attest_author":"https://pith.science/pith/CC3H45BF6ZGZM5O2ZQYCWSAQ6X/action/author_attestation","sign_citation":"https://pith.science/pith/CC3H45BF6ZGZM5O2ZQYCWSAQ6X/action/citation_signature","submit_replication":"https://pith.science/pith/CC3H45BF6ZGZM5O2ZQYCWSAQ6X/action/replication_record"}},"created_at":"2026-05-18T01:31:04.571465+00:00","updated_at":"2026-05-18T01:31:04.571465+00:00"}