{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:INJ4W53NIA56WGUTJJNJ4F4Q5F","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":"87f9c5264efe20b24465c995dce70a6d9aa373c753a8337c3273cebb298f19ca","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-07-15T19:46:28Z","title_canon_sha256":"1c605f07cd3a48edd19f38a9e23a4ae245f990a8706024ff69d6f6d77405a3cc"},"schema_version":"1.0","source":{"id":"1907.06716","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.06716","created_at":"2026-05-17T23:40:29Z"},{"alias_kind":"arxiv_version","alias_value":"1907.06716v1","created_at":"2026-05-17T23:40:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.06716","created_at":"2026-05-17T23:40:29Z"},{"alias_kind":"pith_short_12","alias_value":"INJ4W53NIA56","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_16","alias_value":"INJ4W53NIA56WGUT","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_8","alias_value":"INJ4W53N","created_at":"2026-05-18T12:33:18Z"}],"graph_snapshots":[{"event_id":"sha256:13b7da73138db1b1e3abcc9bf962a3cf0d59130819f7ef9ecb7a661152cf5d54","target":"graph","created_at":"2026-05-17T23:40:29Z","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":"For rational $\\alpha$, the fractional partition functions $p_\\alpha(n)$ are given by the coefficients of the generating function $(q;q)^\\alpha_\\infty$. When $\\alpha=-1$, one obtains the usual partition function. Congruences of the form $p(\\ell n + c)\\equiv 0 \\pmod{\\ell}$ for a prime $\\ell$ and integer $c$ were studied by Ramanujan. Such congruences exist only for $\\ell\\in\\{5,7,11\\}.$ Chan and Wang [4] recently studied congruences for the fractional partition functions and gave several infinite families of congruences using identities of the Dedekind eta-function. Following their work, we use t","authors_text":"Erin Bevilacqua, Kapil Chandran, Yunseo Choi","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-07-15T19:46:28Z","title":"Ramanujan Congruences for Fractional Partition Functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.06716","kind":"arxiv","version":1},"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":"sha256:2383f4db369360c57f161da40fb259418ba0d4e8b5ef5620c71242f238803383","target":"record","created_at":"2026-05-17T23:40:29Z","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":"87f9c5264efe20b24465c995dce70a6d9aa373c753a8337c3273cebb298f19ca","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-07-15T19:46:28Z","title_canon_sha256":"1c605f07cd3a48edd19f38a9e23a4ae245f990a8706024ff69d6f6d77405a3cc"},"schema_version":"1.0","source":{"id":"1907.06716","kind":"arxiv","version":1}},"canonical_sha256":"4353cb776d403beb1a934a5a9e1790e9520b6a619f8f527bf7377132943263f8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4353cb776d403beb1a934a5a9e1790e9520b6a619f8f527bf7377132943263f8","first_computed_at":"2026-05-17T23:40:29.375721Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:40:29.375721Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3OvzJXbIbFdvxzyZ6eUThlAC7dzCcdrjjpkPL7nl2ys+jmxFJa/X6uI0BSoaN+P0qnobfqe7anwbeWh+clUaDA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:40:29.376340Z","signed_message":"canonical_sha256_bytes"},"source_id":"1907.06716","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2383f4db369360c57f161da40fb259418ba0d4e8b5ef5620c71242f238803383","sha256:13b7da73138db1b1e3abcc9bf962a3cf0d59130819f7ef9ecb7a661152cf5d54"],"state_sha256":"93b2209bf44f41cb0b3be160d390202825f5dab87713c17437d8f66335575385"}