{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:T5ZCFCEFNK5BFMMVPP4UNAOLN6","short_pith_number":"pith:T5ZCFCEF","schema_version":"1.0","canonical_sha256":"9f722288856aba12b1957bf94681cb6fa53fe13831fe3e7ddf6273daa2517de1","source":{"kind":"arxiv","id":"1501.00370","version":1},"attestation_state":"computed","paper":{"title":"The coloring of the regular graph of ideals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Farzad Shaveisi","submitted_at":"2015-01-02T09:22:39Z","abstract_excerpt":"The regular graph of ideals of the commutative ring $R$, denoted by $\\Gamma_{reg}(R)$, is a graph whose vertex set is the set of all non-trivial ideals of $R$ and two distinct vertices $I$ and $J$ are adjacent if and only if either $I$ contains a $J$-regular element or $J$ contains an $I$-regular element. In this paper, it is shown that for every Artinian ring $R$, the edge chromatic number of $\\Gamma_{reg}(R)$ equals its maximum degree. Then a formula for the clique number of $\\Gamma_{reg}(R)$ is given. Also, it is proved that for every reduced ring $R$ with $n(\\geq3)$ minimal prime ideals, t"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1501.00370","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-01-02T09:22:39Z","cross_cats_sorted":[],"title_canon_sha256":"7e86d1fd79f53176bbcddbc143a18070d06bd7222ecfe950bf27fbbfb691c1f8","abstract_canon_sha256":"2df2264713030cb8a090ac3adcae28258b17ed30fa32df481a6d870813fdcd4d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:30:09.366363Z","signature_b64":"gowSq2LBAhfAZL56sGsZwXX0XvNnkRmpnlb+JyZVbDjEQZNupa57BwTuY3pHmnrS61dtqwrJQ6UctiU3aAwWAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9f722288856aba12b1957bf94681cb6fa53fe13831fe3e7ddf6273daa2517de1","last_reissued_at":"2026-05-18T02:30:09.365891Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:30:09.365891Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The coloring of the regular graph of ideals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Farzad Shaveisi","submitted_at":"2015-01-02T09:22:39Z","abstract_excerpt":"The regular graph of ideals of the commutative ring $R$, denoted by $\\Gamma_{reg}(R)$, is a graph whose vertex set is the set of all non-trivial ideals of $R$ and two distinct vertices $I$ and $J$ are adjacent if and only if either $I$ contains a $J$-regular element or $J$ contains an $I$-regular element. In this paper, it is shown that for every Artinian ring $R$, the edge chromatic number of $\\Gamma_{reg}(R)$ equals its maximum degree. Then a formula for the clique number of $\\Gamma_{reg}(R)$ is given. Also, it is proved that for every reduced ring $R$ with $n(\\geq3)$ minimal prime ideals, t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.00370","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1501.00370","created_at":"2026-05-18T02:30:09.365969+00:00"},{"alias_kind":"arxiv_version","alias_value":"1501.00370v1","created_at":"2026-05-18T02:30:09.365969+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.00370","created_at":"2026-05-18T02:30:09.365969+00:00"},{"alias_kind":"pith_short_12","alias_value":"T5ZCFCEFNK5B","created_at":"2026-05-18T12:29:42.218222+00:00"},{"alias_kind":"pith_short_16","alias_value":"T5ZCFCEFNK5BFMMV","created_at":"2026-05-18T12:29:42.218222+00:00"},{"alias_kind":"pith_short_8","alias_value":"T5ZCFCEF","created_at":"2026-05-18T12:29:42.218222+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/T5ZCFCEFNK5BFMMVPP4UNAOLN6","json":"https://pith.science/pith/T5ZCFCEFNK5BFMMVPP4UNAOLN6.json","graph_json":"https://pith.science/api/pith-number/T5ZCFCEFNK5BFMMVPP4UNAOLN6/graph.json","events_json":"https://pith.science/api/pith-number/T5ZCFCEFNK5BFMMVPP4UNAOLN6/events.json","paper":"https://pith.science/paper/T5ZCFCEF"},"agent_actions":{"view_html":"https://pith.science/pith/T5ZCFCEFNK5BFMMVPP4UNAOLN6","download_json":"https://pith.science/pith/T5ZCFCEFNK5BFMMVPP4UNAOLN6.json","view_paper":"https://pith.science/paper/T5ZCFCEF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1501.00370&json=true","fetch_graph":"https://pith.science/api/pith-number/T5ZCFCEFNK5BFMMVPP4UNAOLN6/graph.json","fetch_events":"https://pith.science/api/pith-number/T5ZCFCEFNK5BFMMVPP4UNAOLN6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/T5ZCFCEFNK5BFMMVPP4UNAOLN6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/T5ZCFCEFNK5BFMMVPP4UNAOLN6/action/storage_attestation","attest_author":"https://pith.science/pith/T5ZCFCEFNK5BFMMVPP4UNAOLN6/action/author_attestation","sign_citation":"https://pith.science/pith/T5ZCFCEFNK5BFMMVPP4UNAOLN6/action/citation_signature","submit_replication":"https://pith.science/pith/T5ZCFCEFNK5BFMMVPP4UNAOLN6/action/replication_record"}},"created_at":"2026-05-18T02:30:09.365969+00:00","updated_at":"2026-05-18T02:30:09.365969+00:00"}