{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:S3M7P3WPLZY7S5NUFWFR7SXEBZ","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":"a7c62f71b42dbf8cc4c1a0e2ff5601b0699b46bc8cac2ef9e1d7f7c5fe7d6896","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-05-22T11:28:38Z","title_canon_sha256":"bccfb3c3a109b9ad49a50734528e17b1ae93b859e6b46a3fbba5f9125d6d045b"},"schema_version":"1.0","source":{"id":"1705.07677","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.07677","created_at":"2026-05-18T00:44:04Z"},{"alias_kind":"arxiv_version","alias_value":"1705.07677v1","created_at":"2026-05-18T00:44:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.07677","created_at":"2026-05-18T00:44:04Z"},{"alias_kind":"pith_short_12","alias_value":"S3M7P3WPLZY7","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_16","alias_value":"S3M7P3WPLZY7S5NU","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_8","alias_value":"S3M7P3WP","created_at":"2026-05-18T12:31:43Z"}],"graph_snapshots":[{"event_id":"sha256:dae5e1d0a939121d8ea68f147295b13f5c4380924b5a400c75f4c64eba2c28c7","target":"graph","created_at":"2026-05-18T00:44:04Z","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":"In this article, the concept of nil clean graph of a ring has been generalised to weakly nil clean graph of a ring and graph theoretic properties like girth, clique number, diameter and chromatic index of the graph have been studied for a finite commutative ring.","authors_text":"Ajay Sharma, Dhiren Kumar Basnet, Jayanta Bhattacharyya","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-05-22T11:28:38Z","title":"Weakly nil clean graphs of rings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.07677","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":"sha256:507efaa842bbab59d5ab33dc8eb08586323d5a1031ffb925ddb4d5edead31aad","target":"record","created_at":"2026-05-18T00:44:04Z","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":"a7c62f71b42dbf8cc4c1a0e2ff5601b0699b46bc8cac2ef9e1d7f7c5fe7d6896","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-05-22T11:28:38Z","title_canon_sha256":"bccfb3c3a109b9ad49a50734528e17b1ae93b859e6b46a3fbba5f9125d6d045b"},"schema_version":"1.0","source":{"id":"1705.07677","kind":"arxiv","version":1}},"canonical_sha256":"96d9f7eecf5e71f975b42d8b1fcae40e6536fcf6a8451313855ca72dd7a91d3b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"96d9f7eecf5e71f975b42d8b1fcae40e6536fcf6a8451313855ca72dd7a91d3b","first_computed_at":"2026-05-18T00:44:04.887767Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:44:04.887767Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"m9vZHAL8QR0vcnv87TijNp9tdhh61ApmhB557UhhklsSWLNwwCwRXt7K2KUdzzxCH1zMEZeUBWA5u3GcMYaHAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:44:04.888291Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.07677","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:507efaa842bbab59d5ab33dc8eb08586323d5a1031ffb925ddb4d5edead31aad","sha256:dae5e1d0a939121d8ea68f147295b13f5c4380924b5a400c75f4c64eba2c28c7"],"state_sha256":"eac512fe3f25beabf9379fc933c13d95cb8d6ced8e13aee7879746744c73f2fa"}