{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:5LPGSGX2VEMQSLJJD2WMXZ3W4Y","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":"59916dc698dd1ad523f74ae7945e7492e48b630cb79e48d82b01b76cfe77bd97","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-12-09T07:42:07Z","title_canon_sha256":"ab8491b93a0729106046c2056a76395312acdda081e7aa78c6fd95dd389bf06e"},"schema_version":"1.0","source":{"id":"1212.1864","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.1864","created_at":"2026-05-18T02:53:15Z"},{"alias_kind":"arxiv_version","alias_value":"1212.1864v2","created_at":"2026-05-18T02:53:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.1864","created_at":"2026-05-18T02:53:15Z"},{"alias_kind":"pith_short_12","alias_value":"5LPGSGX2VEMQ","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"5LPGSGX2VEMQSLJJ","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"5LPGSGX2","created_at":"2026-05-18T12:26:56Z"}],"graph_snapshots":[{"event_id":"sha256:c7748fa34ca6f28b8780634313c150748a3bdc06a4add4445a707f763e7c483e","target":"graph","created_at":"2026-05-18T02:53:15Z","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":"Let $K$ be a number field. This paper considers arithmetic functions over $K$, that are, complex valued functions on the set of nonzero integral ideals in $K$. Firstly we generalize some basic results on arithmetic functions. Next we define the generalized Ramanujan sums over $K$ and show some properties.","authors_text":"Yusuke Fujisawa","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-12-09T07:42:07Z","title":"On a generalization of arithmetic functions and the Ramanujan sums"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.1864","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:b5308847267e49fcba7b677f76a13d756097586732223674f42eabf0dda1e06b","target":"record","created_at":"2026-05-18T02:53:15Z","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":"59916dc698dd1ad523f74ae7945e7492e48b630cb79e48d82b01b76cfe77bd97","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-12-09T07:42:07Z","title_canon_sha256":"ab8491b93a0729106046c2056a76395312acdda081e7aa78c6fd95dd389bf06e"},"schema_version":"1.0","source":{"id":"1212.1864","kind":"arxiv","version":2}},"canonical_sha256":"eade691afaa919092d291eaccbe776e61af09f00e57d4a578133084f32c9ecac","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eade691afaa919092d291eaccbe776e61af09f00e57d4a578133084f32c9ecac","first_computed_at":"2026-05-18T02:53:15.490210Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:53:15.490210Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"y+ovj25s4MvpbLA8y8+zi1Pa5pEIFn9zSN+ihRrRb95mExl0SuQMhm4uS3F9wVdYYZGtzx8x+Mqzob11QX5GAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:53:15.490776Z","signed_message":"canonical_sha256_bytes"},"source_id":"1212.1864","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b5308847267e49fcba7b677f76a13d756097586732223674f42eabf0dda1e06b","sha256:c7748fa34ca6f28b8780634313c150748a3bdc06a4add4445a707f763e7c483e"],"state_sha256":"2cea996873eb6d344fa3420fba777b4e446981e29fb6af2c575301bfa0b8431e"}