{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:UCKCRH5GTKQTHAD4T46N74JRVR","short_pith_number":"pith:UCKCRH5G","schema_version":"1.0","canonical_sha256":"a094289fa69aa133807c9f3cdff131ac52aaa2a523e90924a398dc56fff47fa8","source":{"kind":"arxiv","id":"1501.01030","version":3},"attestation_state":"computed","paper":{"title":"A note on commuting graphs of matrix rings over fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"C. Miguel","submitted_at":"2015-01-05T22:46:50Z","abstract_excerpt":"We will give a short proof of the fact that if the algebraic closure of a field $\\mathbb F$ is a finite extension, then for $n\\geq 3$ the commuting graph $\\Gamma(M_n(\\mathbb F))$ is connected and its diameter is four."},"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":"1501.01030","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2015-01-05T22:46:50Z","cross_cats_sorted":[],"title_canon_sha256":"8946f3f8772344eb295eecebdaefff80ce061a8c421330908067f33a018c2237","abstract_canon_sha256":"6d7a81502a355d4d768cdaf214962fc0ef5a3c36da26f225ee41f6c8f7ddded1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:25:55.620807Z","signature_b64":"V02s343rHN1RL0hVQAuo6X2qVaP1vRsIbobtpANBfhTyoss5x/OImbkKK1ZueJSTzwxsIvox6GKSCmC62io0AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a094289fa69aa133807c9f3cdff131ac52aaa2a523e90924a398dc56fff47fa8","last_reissued_at":"2026-05-18T02:25:55.620434Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:25:55.620434Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A note on commuting graphs of matrix rings over fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"C. Miguel","submitted_at":"2015-01-05T22:46:50Z","abstract_excerpt":"We will give a short proof of the fact that if the algebraic closure of a field $\\mathbb F$ is a finite extension, then for $n\\geq 3$ the commuting graph $\\Gamma(M_n(\\mathbb F))$ is connected and its diameter is four."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.01030","kind":"arxiv","version":3},"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":"1501.01030","created_at":"2026-05-18T02:25:55.620490+00:00"},{"alias_kind":"arxiv_version","alias_value":"1501.01030v3","created_at":"2026-05-18T02:25:55.620490+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.01030","created_at":"2026-05-18T02:25:55.620490+00:00"},{"alias_kind":"pith_short_12","alias_value":"UCKCRH5GTKQT","created_at":"2026-05-18T12:29:44.643036+00:00"},{"alias_kind":"pith_short_16","alias_value":"UCKCRH5GTKQTHAD4","created_at":"2026-05-18T12:29:44.643036+00:00"},{"alias_kind":"pith_short_8","alias_value":"UCKCRH5G","created_at":"2026-05-18T12:29:44.643036+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/UCKCRH5GTKQTHAD4T46N74JRVR","json":"https://pith.science/pith/UCKCRH5GTKQTHAD4T46N74JRVR.json","graph_json":"https://pith.science/api/pith-number/UCKCRH5GTKQTHAD4T46N74JRVR/graph.json","events_json":"https://pith.science/api/pith-number/UCKCRH5GTKQTHAD4T46N74JRVR/events.json","paper":"https://pith.science/paper/UCKCRH5G"},"agent_actions":{"view_html":"https://pith.science/pith/UCKCRH5GTKQTHAD4T46N74JRVR","download_json":"https://pith.science/pith/UCKCRH5GTKQTHAD4T46N74JRVR.json","view_paper":"https://pith.science/paper/UCKCRH5G","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1501.01030&json=true","fetch_graph":"https://pith.science/api/pith-number/UCKCRH5GTKQTHAD4T46N74JRVR/graph.json","fetch_events":"https://pith.science/api/pith-number/UCKCRH5GTKQTHAD4T46N74JRVR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UCKCRH5GTKQTHAD4T46N74JRVR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UCKCRH5GTKQTHAD4T46N74JRVR/action/storage_attestation","attest_author":"https://pith.science/pith/UCKCRH5GTKQTHAD4T46N74JRVR/action/author_attestation","sign_citation":"https://pith.science/pith/UCKCRH5GTKQTHAD4T46N74JRVR/action/citation_signature","submit_replication":"https://pith.science/pith/UCKCRH5GTKQTHAD4T46N74JRVR/action/replication_record"}},"created_at":"2026-05-18T02:25:55.620490+00:00","updated_at":"2026-05-18T02:25:55.620490+00:00"}