{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:6CK5SIO2F3SRQMTVWK4UDQCTS6","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":"c53f604b0fc2dda705c8c2b47b5cef0dfc634681c99dbe90e8a9ecbcb4c42ace","cross_cats_sorted":["math.CO"],"license":"http://creativecommons.org/licenses/publicdomain/","primary_cat":"math.AC","submitted_at":"2013-05-27T18:29:12Z","title_canon_sha256":"5b1563f97c4596518a763799478a4570648de2cb8e085da43b89cfead059f939"},"schema_version":"1.0","source":{"id":"1305.6287","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.6287","created_at":"2026-05-18T03:24:51Z"},{"alias_kind":"arxiv_version","alias_value":"1305.6287v1","created_at":"2026-05-18T03:24:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.6287","created_at":"2026-05-18T03:24:51Z"},{"alias_kind":"pith_short_12","alias_value":"6CK5SIO2F3SR","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_16","alias_value":"6CK5SIO2F3SRQMTV","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_8","alias_value":"6CK5SIO2","created_at":"2026-05-18T12:27:36Z"}],"graph_snapshots":[{"event_id":"sha256:7a3047393b48ee6aee284f668e29759818b7cadaf5136c6b1516edbe60c24c81","target":"graph","created_at":"2026-05-18T03:24:51Z","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":"A graph is called weakly perfect if its vertex chromatic number equals its clique number. Let $R$ be a ring and $I(R)^*$ be the set of all left proper non-trivial ideals of $R$. The intersection graph of ideals of $R$, denoted by $G(R)$, is a graph with the vertex set $I(R)^*$ and two distinct vertices $I$ and $J$ are adjacent if and only if $I\\cap J\\neq 0$. In this paper, it is shown that $G(\\mathbb{Z}_n)$, for every positive integer $n$, is a weakly perfect graph. Also, for some values of $n$, we give an explicit formula for the vertex chromatic number of $G(\\mathbb{Z}_n)$. Furthermore, it i","authors_text":"M.J. Nikmehr, R.Nikandish","cross_cats":["math.CO"],"headline":"","license":"http://creativecommons.org/licenses/publicdomain/","primary_cat":"math.AC","submitted_at":"2013-05-27T18:29:12Z","title":"The intersection graph of ideals of $\\mathbb{Z}_n$ is\\\\ weakly perfect"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.6287","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":"sha256:12756d5c0588248bea7f2ded702e29d873fddc2d11783a3e23952bcde01fdede","target":"record","created_at":"2026-05-18T03:24:51Z","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":"c53f604b0fc2dda705c8c2b47b5cef0dfc634681c99dbe90e8a9ecbcb4c42ace","cross_cats_sorted":["math.CO"],"license":"http://creativecommons.org/licenses/publicdomain/","primary_cat":"math.AC","submitted_at":"2013-05-27T18:29:12Z","title_canon_sha256":"5b1563f97c4596518a763799478a4570648de2cb8e085da43b89cfead059f939"},"schema_version":"1.0","source":{"id":"1305.6287","kind":"arxiv","version":1}},"canonical_sha256":"f095d921da2ee5183275b2b941c05397995b7bd98df81a564324a434935f86fa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f095d921da2ee5183275b2b941c05397995b7bd98df81a564324a434935f86fa","first_computed_at":"2026-05-18T03:24:51.665941Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:24:51.665941Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nqMQ4uUT8X7S07QzTPlOfEBKlgKs6JJu92TwNslAPqFFpAoqQahYEz2B3QeMC7pGnZNcz0eE1NVax5w3NUHTBg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:24:51.666513Z","signed_message":"canonical_sha256_bytes"},"source_id":"1305.6287","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:12756d5c0588248bea7f2ded702e29d873fddc2d11783a3e23952bcde01fdede","sha256:7a3047393b48ee6aee284f668e29759818b7cadaf5136c6b1516edbe60c24c81"],"state_sha256":"55827f824327bf0a99bdd6422cb86bc5ec9bb55579e1480a429cfdce97cadd93"}