{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:EUPS5BG44PP24PHZ3EO5HL2YZT","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":"efbda64c0d56e52be8e6a2fbca1b9a15d8238960702cfe7b8bf24213e2b5f3b0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2015-12-03T07:30:16Z","title_canon_sha256":"17a35c110b6abc21be68cb36e2ef8320edce477e959cc807e2cbf738ac5fde6f"},"schema_version":"1.0","source":{"id":"1512.00973","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.00973","created_at":"2026-05-18T01:25:23Z"},{"alias_kind":"arxiv_version","alias_value":"1512.00973v1","created_at":"2026-05-18T01:25:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.00973","created_at":"2026-05-18T01:25:23Z"},{"alias_kind":"pith_short_12","alias_value":"EUPS5BG44PP2","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_16","alias_value":"EUPS5BG44PP24PHZ","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_8","alias_value":"EUPS5BG4","created_at":"2026-05-18T12:29:19Z"}],"graph_snapshots":[{"event_id":"sha256:04ae9bad85ca413468958bf625e4a6b56ef5013b48fe8f7a6e45f532ae07e58b","target":"graph","created_at":"2026-05-18T01:25:23Z","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 $R$ be a finite ring and let $\\Cent(R)$ denote the set of all distinct centralizers of $R$. $R$ is called an $n$-centralizer ring if $|Cent(R)| = n$. In this paper, we characterize $n$-centralizer finite rings for $n \\leq 7$.","authors_text":"Dhiren K. Basnet, Jutirekha Dutta, Rajat K. Nath","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2015-12-03T07:30:16Z","title":"A note on $n$-centralizer finite rings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.00973","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":"sha256:56eea529534a7990d1686bd74331f3c5e796b50f1cc79b10545824e3c73cd419","target":"record","created_at":"2026-05-18T01:25:23Z","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":"efbda64c0d56e52be8e6a2fbca1b9a15d8238960702cfe7b8bf24213e2b5f3b0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2015-12-03T07:30:16Z","title_canon_sha256":"17a35c110b6abc21be68cb36e2ef8320edce477e959cc807e2cbf738ac5fde6f"},"schema_version":"1.0","source":{"id":"1512.00973","kind":"arxiv","version":1}},"canonical_sha256":"251f2e84dce3dfae3cf9d91dd3af58ccd867817a4f7195e963e3aadda2eb1664","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"251f2e84dce3dfae3cf9d91dd3af58ccd867817a4f7195e963e3aadda2eb1664","first_computed_at":"2026-05-18T01:25:23.703841Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:25:23.703841Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"W3Z2NPOOAjV+5pH95dM6b4UFMTqh2by4n9jpxxSgjryQbJfIEosAPnJLEH7NVcIdoFsYQmtrXKgO+w547SfICw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:25:23.704236Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.00973","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:56eea529534a7990d1686bd74331f3c5e796b50f1cc79b10545824e3c73cd419","sha256:04ae9bad85ca413468958bf625e4a6b56ef5013b48fe8f7a6e45f532ae07e58b"],"state_sha256":"0210b057653cc660521819453a50a692a2b0014058be7a118c09227989a82eea"}