{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:JHTVCK4UUDL5MZKVQ6MM3MCMF7","short_pith_number":"pith:JHTVCK4U","schema_version":"1.0","canonical_sha256":"49e7512b94a0d7d665558798cdb04c2fd0faf491511f85f6be186d2cbb6c6c68","source":{"kind":"arxiv","id":"1702.02298","version":1},"attestation_state":"computed","paper":{"title":"Formal triangular matrix ring with nil clean index $4$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Dhiren Kumar Basnet, Jayanta Bhattacharyya","submitted_at":"2017-02-08T06:17:50Z","abstract_excerpt":"For an element $a \\in R$, let $\\eta(a)=\\{e\\in R\\mid e^2=e\\mbox{ and }a-e\\in \\mbox{nil}(R)\\}$. The nil clean index of $R$, denoted by NinA$(R)$, is defined as Nin$(R)=\\sup \\{\\mid \\eta(a)\\mid: a\\in R\\}$. In this article we have characterized formal triangular matrix ring $\\begin{pmatrix}A & M0 & B\\end{pmatrix}$ with nil clean index $4$."},"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":"1702.02298","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-02-08T06:17:50Z","cross_cats_sorted":[],"title_canon_sha256":"6c9bd93bedacddf3b33d16b3deca5928bbbb9ea28b165afbca3e21d7935e7a77","abstract_canon_sha256":"84b1647400f2a7dd012eb52bb66263cc135bcd3d04205e26335a2ad0504c3a78"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:51:06.283273Z","signature_b64":"E+EwTsBsWa++VaRqZ3Kx79O2r/mfw2JsvSCkDBL9GCmfgBc+gwwnq0Pxm5wrgZ+9Lf3haIwEbXbVnoqzJE4xCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"49e7512b94a0d7d665558798cdb04c2fd0faf491511f85f6be186d2cbb6c6c68","last_reissued_at":"2026-05-18T00:51:06.282810Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:51:06.282810Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Formal triangular matrix ring with nil clean index $4$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Dhiren Kumar Basnet, Jayanta Bhattacharyya","submitted_at":"2017-02-08T06:17:50Z","abstract_excerpt":"For an element $a \\in R$, let $\\eta(a)=\\{e\\in R\\mid e^2=e\\mbox{ and }a-e\\in \\mbox{nil}(R)\\}$. The nil clean index of $R$, denoted by NinA$(R)$, is defined as Nin$(R)=\\sup \\{\\mid \\eta(a)\\mid: a\\in R\\}$. In this article we have characterized formal triangular matrix ring $\\begin{pmatrix}A & M0 & B\\end{pmatrix}$ with nil clean index $4$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.02298","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":"1702.02298","created_at":"2026-05-18T00:51:06.282870+00:00"},{"alias_kind":"arxiv_version","alias_value":"1702.02298v1","created_at":"2026-05-18T00:51:06.282870+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.02298","created_at":"2026-05-18T00:51:06.282870+00:00"},{"alias_kind":"pith_short_12","alias_value":"JHTVCK4UUDL5","created_at":"2026-05-18T12:31:24.725408+00:00"},{"alias_kind":"pith_short_16","alias_value":"JHTVCK4UUDL5MZKV","created_at":"2026-05-18T12:31:24.725408+00:00"},{"alias_kind":"pith_short_8","alias_value":"JHTVCK4U","created_at":"2026-05-18T12:31:24.725408+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/JHTVCK4UUDL5MZKVQ6MM3MCMF7","json":"https://pith.science/pith/JHTVCK4UUDL5MZKVQ6MM3MCMF7.json","graph_json":"https://pith.science/api/pith-number/JHTVCK4UUDL5MZKVQ6MM3MCMF7/graph.json","events_json":"https://pith.science/api/pith-number/JHTVCK4UUDL5MZKVQ6MM3MCMF7/events.json","paper":"https://pith.science/paper/JHTVCK4U"},"agent_actions":{"view_html":"https://pith.science/pith/JHTVCK4UUDL5MZKVQ6MM3MCMF7","download_json":"https://pith.science/pith/JHTVCK4UUDL5MZKVQ6MM3MCMF7.json","view_paper":"https://pith.science/paper/JHTVCK4U","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1702.02298&json=true","fetch_graph":"https://pith.science/api/pith-number/JHTVCK4UUDL5MZKVQ6MM3MCMF7/graph.json","fetch_events":"https://pith.science/api/pith-number/JHTVCK4UUDL5MZKVQ6MM3MCMF7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JHTVCK4UUDL5MZKVQ6MM3MCMF7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JHTVCK4UUDL5MZKVQ6MM3MCMF7/action/storage_attestation","attest_author":"https://pith.science/pith/JHTVCK4UUDL5MZKVQ6MM3MCMF7/action/author_attestation","sign_citation":"https://pith.science/pith/JHTVCK4UUDL5MZKVQ6MM3MCMF7/action/citation_signature","submit_replication":"https://pith.science/pith/JHTVCK4UUDL5MZKVQ6MM3MCMF7/action/replication_record"}},"created_at":"2026-05-18T00:51:06.282870+00:00","updated_at":"2026-05-18T00:51:06.282870+00:00"}