{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:B6XRL7NVLLPMWEBXQF7L7P2UOA","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":"dab17104a2cb049fa938ed80b2518a4d7a91fedb2e9d974ff9ef64bd92233357","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-05-03T03:55:29Z","title_canon_sha256":"361cf6b8781ca6ec69b0852dfde0760df81f53ee33110691446af8b96582d40c"},"schema_version":"1.0","source":{"id":"1805.01103","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.01103","created_at":"2026-07-05T06:26:36Z"},{"alias_kind":"arxiv_version","alias_value":"1805.01103v1","created_at":"2026-07-05T06:26:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.01103","created_at":"2026-07-05T06:26:36Z"},{"alias_kind":"pith_short_12","alias_value":"B6XRL7NVLLPM","created_at":"2026-07-05T06:26:36Z"},{"alias_kind":"pith_short_16","alias_value":"B6XRL7NVLLPMWEBX","created_at":"2026-07-05T06:26:36Z"},{"alias_kind":"pith_short_8","alias_value":"B6XRL7NV","created_at":"2026-07-05T06:26:36Z"}],"graph_snapshots":[{"event_id":"sha256:5c3111a3330c305d89cd33c5611690a545b7aa488908539a9c20311f8c83c506","target":"graph","created_at":"2026-07-05T06:26:36Z","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/1805.01103/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper provides algebraic proofs for several types of congruences involving the multipartition function and self-convolutions of the divisor function. Our computations use methods of Differential Algebra in $\\mathbb{Z}/q\\mathbb{Z}$, implemented in a couple of MAPLE programs available as ancillary files on arXiv.\n  The first results of the paper are Ramanujan-type congruences of the form $p^{*k}(qn+r) \\equiv_q 0$ and $\\sigma^{*k}(qn+r) \\equiv_q 0$, where $p(n)$ and $\\sigma(n)$ are the partition and divisor functions, $q > 3$ is prime, and $^{*k}$ denotes $k^{th}$-order self-convolution. We ","authors_text":"Alexandru Pascadi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-05-03T03:55:29Z","title":"Computer-Assisted Proofs of Congruences for Multipartitions and Divisor Function Convolutions, based on Methods of Differential Algebra"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.01103","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":"sha256:8f6d14f595acad57642e677736a5275e0e29765d9eb46a939e563770c8b87ce0","target":"record","created_at":"2026-07-05T06:26:36Z","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":"dab17104a2cb049fa938ed80b2518a4d7a91fedb2e9d974ff9ef64bd92233357","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-05-03T03:55:29Z","title_canon_sha256":"361cf6b8781ca6ec69b0852dfde0760df81f53ee33110691446af8b96582d40c"},"schema_version":"1.0","source":{"id":"1805.01103","kind":"arxiv","version":1}},"canonical_sha256":"0faf15fdb55adecb1037817ebfbf547038a0aaa555de3b2a98756df6ada57dbc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0faf15fdb55adecb1037817ebfbf547038a0aaa555de3b2a98756df6ada57dbc","first_computed_at":"2026-07-05T06:26:36.505529Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:26:36.505529Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fC5Be+iRWn62EqFnQUk8Rzt78gvoE4KVlKoueQEv6dPd6oro7ax2qSAuiFg2uQPSNmozImjrZE0rxbkeBFEVDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T06:26:36.506037Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.01103","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8f6d14f595acad57642e677736a5275e0e29765d9eb46a939e563770c8b87ce0","sha256:5c3111a3330c305d89cd33c5611690a545b7aa488908539a9c20311f8c83c506"],"state_sha256":"bb1f06353d5478fdd307b46a6be98770b9e86948a6fe48476817479284824e46"}