{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:XMCKTZ6LILFV7A4CHRLT3J5FGA","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":"a7d16cf8563262f1fdbc5ed2197c60f2a3d761344a5606af4c7dd4f3729ff7fc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-03-15T09:28:19Z","title_canon_sha256":"3f6b5cc8b67d47a3c8079b5269b01ddbf5dfb6d4ad1b8a06450f5f3110c95ada"},"schema_version":"1.0","source":{"id":"1703.05039","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.05039","created_at":"2026-05-18T00:48:38Z"},{"alias_kind":"arxiv_version","alias_value":"1703.05039v1","created_at":"2026-05-18T00:48:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.05039","created_at":"2026-05-18T00:48:38Z"},{"alias_kind":"pith_short_12","alias_value":"XMCKTZ6LILFV","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_16","alias_value":"XMCKTZ6LILFV7A4C","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_8","alias_value":"XMCKTZ6L","created_at":"2026-05-18T12:31:56Z"}],"graph_snapshots":[{"event_id":"sha256:f837419dc754ab4506fdaf7b09220bc22ba0a7bfe4265cdf22e4823727150690","target":"graph","created_at":"2026-05-18T00:48:38Z","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":"The non-commuting graph $\\Gamma_R$ of a finite ring $R$ with center $Z(R)$ is a simple undirected graph whose vertex set is $R \\setminus Z(R)$ and two distinct vertices $a$ and $b$ are adjacent if and only if $ab \\ne ba$. In this paper, we show that $\\Gamma_R$ is not isomorphic to certain graphs of any finite non-commutative ring $R$. Some connections between $\\Gamma_R$ and commuting probability of $R$ are also obtained. Further, it is shown that the non-commuting graphs of two $\\mathbb{Z}$-isoclinic rings are isomorphic if the centers of the rings have same order","authors_text":"D. K. Basnet, J. Dutta","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-03-15T09:28:19Z","title":"On non-commuting graph of a finite ring"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.05039","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":"sha256:32251273ff0ed3d04a749e75a7aa742c20d47323cc916cb0e11bbbdd9b663e63","target":"record","created_at":"2026-05-18T00:48:38Z","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":"a7d16cf8563262f1fdbc5ed2197c60f2a3d761344a5606af4c7dd4f3729ff7fc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-03-15T09:28:19Z","title_canon_sha256":"3f6b5cc8b67d47a3c8079b5269b01ddbf5dfb6d4ad1b8a06450f5f3110c95ada"},"schema_version":"1.0","source":{"id":"1703.05039","kind":"arxiv","version":1}},"canonical_sha256":"bb04a9e7cb42cb5f83823c573da7a5302a57338962e5811a4b083a5ccb6a4da8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bb04a9e7cb42cb5f83823c573da7a5302a57338962e5811a4b083a5ccb6a4da8","first_computed_at":"2026-05-18T00:48:38.548444Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:48:38.548444Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"F5Zy1WccdX6YvQ+68FRDeZCU7NvKRleVSYxpRBSu6hUPdCuaAb2vvbs43TygRaSWWqa9cdywEhrn0VyMdLntBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:48:38.549075Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.05039","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:32251273ff0ed3d04a749e75a7aa742c20d47323cc916cb0e11bbbdd9b663e63","sha256:f837419dc754ab4506fdaf7b09220bc22ba0a7bfe4265cdf22e4823727150690"],"state_sha256":"a870c787e99a2b1faf0998e85b191f5d526a15df9d8e4b4cdb2f54ff742f2676"}