{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:PB6B7TPXZHE4TRARG4VIVNC3SA","short_pith_number":"pith:PB6B7TPX","schema_version":"1.0","canonical_sha256":"787c1fcdf7c9c9c9c411372a8ab45b90122b032f78335f7175fb2387609ac0be","source":{"kind":"arxiv","id":"1604.02865","version":1},"attestation_state":"computed","paper":{"title":"Spectrum and genus of commuting graphs of some classes of finite rings","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.SP","authors_text":"Jutirekha Dutta, Rajat Kanti Nath","submitted_at":"2016-04-11T10:20:33Z","abstract_excerpt":"The commuting graph of a non-commutative ring $R$ with center $Z(R)$ is a simple undirected graph whose vertex set is $R\\setminus Z(R)$ and two vertices $x, y$ are adjacent if and only if $xy = yx$. In this paper, we compute the spectrum and genus of commuting graphs of some classes of finite rings."},"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":"1604.02865","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.SP","submitted_at":"2016-04-11T10:20:33Z","cross_cats_sorted":["math.RA"],"title_canon_sha256":"30f85ccf3facca69ef0039825914f4df3def9e31633a9d9774d5bd44ae3f73da","abstract_canon_sha256":"5a0274ebf8c2487f8ee296087fadab8d157539e6046f2826d3015d6138c13eb3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:17:21.942087Z","signature_b64":"e9RNr7x32+FE4bL6a2xOLIUKX+tXD4P6SMlBOfRyNClTn4PvLuSDN+x7ZnKdcpruN9SV4d0O8A45tMHD/NnZBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"787c1fcdf7c9c9c9c411372a8ab45b90122b032f78335f7175fb2387609ac0be","last_reissued_at":"2026-05-18T01:17:21.941542Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:17:21.941542Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Spectrum and genus of commuting graphs of some classes of finite rings","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.SP","authors_text":"Jutirekha Dutta, Rajat Kanti Nath","submitted_at":"2016-04-11T10:20:33Z","abstract_excerpt":"The commuting graph of a non-commutative ring $R$ with center $Z(R)$ is a simple undirected graph whose vertex set is $R\\setminus Z(R)$ and two vertices $x, y$ are adjacent if and only if $xy = yx$. In this paper, we compute the spectrum and genus of commuting graphs of some classes of finite rings."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.02865","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":"1604.02865","created_at":"2026-05-18T01:17:21.941618+00:00"},{"alias_kind":"arxiv_version","alias_value":"1604.02865v1","created_at":"2026-05-18T01:17:21.941618+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.02865","created_at":"2026-05-18T01:17:21.941618+00:00"},{"alias_kind":"pith_short_12","alias_value":"PB6B7TPXZHE4","created_at":"2026-05-18T12:30:39.010887+00:00"},{"alias_kind":"pith_short_16","alias_value":"PB6B7TPXZHE4TRAR","created_at":"2026-05-18T12:30:39.010887+00:00"},{"alias_kind":"pith_short_8","alias_value":"PB6B7TPX","created_at":"2026-05-18T12:30:39.010887+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/PB6B7TPXZHE4TRARG4VIVNC3SA","json":"https://pith.science/pith/PB6B7TPXZHE4TRARG4VIVNC3SA.json","graph_json":"https://pith.science/api/pith-number/PB6B7TPXZHE4TRARG4VIVNC3SA/graph.json","events_json":"https://pith.science/api/pith-number/PB6B7TPXZHE4TRARG4VIVNC3SA/events.json","paper":"https://pith.science/paper/PB6B7TPX"},"agent_actions":{"view_html":"https://pith.science/pith/PB6B7TPXZHE4TRARG4VIVNC3SA","download_json":"https://pith.science/pith/PB6B7TPXZHE4TRARG4VIVNC3SA.json","view_paper":"https://pith.science/paper/PB6B7TPX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1604.02865&json=true","fetch_graph":"https://pith.science/api/pith-number/PB6B7TPXZHE4TRARG4VIVNC3SA/graph.json","fetch_events":"https://pith.science/api/pith-number/PB6B7TPXZHE4TRARG4VIVNC3SA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PB6B7TPXZHE4TRARG4VIVNC3SA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PB6B7TPXZHE4TRARG4VIVNC3SA/action/storage_attestation","attest_author":"https://pith.science/pith/PB6B7TPXZHE4TRARG4VIVNC3SA/action/author_attestation","sign_citation":"https://pith.science/pith/PB6B7TPXZHE4TRARG4VIVNC3SA/action/citation_signature","submit_replication":"https://pith.science/pith/PB6B7TPXZHE4TRARG4VIVNC3SA/action/replication_record"}},"created_at":"2026-05-18T01:17:21.941618+00:00","updated_at":"2026-05-18T01:17:21.941618+00:00"}