{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:BWSC5UP5DX2EV4IMKAGTUGEPZK","short_pith_number":"pith:BWSC5UP5","canonical_record":{"source":{"id":"1709.02065","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-09-07T04:19:55Z","cross_cats_sorted":[],"title_canon_sha256":"996527a3b6125c1701ac5f163209e616a7a585f7c07c2e90f9b6fafcce69c015","abstract_canon_sha256":"0ee71df1cfe212e5c29dd12ab907184e147a3835f289f37485eaef3562c120f7"},"schema_version":"1.0"},"canonical_sha256":"0da42ed1fd1df44af10c500d3a188fcaab017b4d2d0f61982da16a6e74770cec","source":{"kind":"arxiv","id":"1709.02065","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.02065","created_at":"2026-05-18T00:35:50Z"},{"alias_kind":"arxiv_version","alias_value":"1709.02065v1","created_at":"2026-05-18T00:35:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.02065","created_at":"2026-05-18T00:35:50Z"},{"alias_kind":"pith_short_12","alias_value":"BWSC5UP5DX2E","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_16","alias_value":"BWSC5UP5DX2EV4IM","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_8","alias_value":"BWSC5UP5","created_at":"2026-05-18T12:31:08Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:BWSC5UP5DX2EV4IMKAGTUGEPZK","target":"record","payload":{"canonical_record":{"source":{"id":"1709.02065","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-09-07T04:19:55Z","cross_cats_sorted":[],"title_canon_sha256":"996527a3b6125c1701ac5f163209e616a7a585f7c07c2e90f9b6fafcce69c015","abstract_canon_sha256":"0ee71df1cfe212e5c29dd12ab907184e147a3835f289f37485eaef3562c120f7"},"schema_version":"1.0"},"canonical_sha256":"0da42ed1fd1df44af10c500d3a188fcaab017b4d2d0f61982da16a6e74770cec","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:35:50.349911Z","signature_b64":"R6ivI53uRCz5Ji66YhBRkfHxJ5+sfDZzqAhsXMpMYyCrBKU6s5QhJ0gW0tjLFGxQuUo1/KZCpbcvb+b2W88lBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0da42ed1fd1df44af10c500d3a188fcaab017b4d2d0f61982da16a6e74770cec","last_reissued_at":"2026-05-18T00:35:50.349287Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:35:50.349287Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1709.02065","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:35:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8Y1Sa1DEhgmBTsveD9aPAKmN87ztQaEdvsQ8wRONdELQzV7PwUSGl7uboVBjKRS8KWZ2DcIrShJ9ySSU4BDRCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T18:08:58.934135Z"},"content_sha256":"c23866e27dec9bd6c6af32e3eb51fd9489bb93dedeb21d8421de78885fa1485e","schema_version":"1.0","event_id":"sha256:c23866e27dec9bd6c6af32e3eb51fd9489bb93dedeb21d8421de78885fa1485e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:BWSC5UP5DX2EV4IMKAGTUGEPZK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Nil Clean Ideal","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Ajay Sharma, Dhiren Kumar Basnet","submitted_at":"2017-09-07T04:19:55Z","abstract_excerpt":"Motivated by the concept of clean ideals, we introduce the notion of nil clean ideals of a ring. We define an ideal $I$ of a ring $R$ to be nil clean ideal if every element of $I$ can be written as a sum of an idempotent and a nilpotent element of $R$. In this article we discuss various properties of nil clean ideals."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.02065","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:35:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vc4jux/9r033ZYfGmu+yqWkDBXE5NAna+2qpXl89P9TNOTy+sAUn5PoITsm50D+yvl8pwgFQGPijb0dcDgsnDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T18:08:58.934885Z"},"content_sha256":"de7f3d9ccfdf245931fb19c7e144fd4da0452e2b204395f3d8084d6e02318acc","schema_version":"1.0","event_id":"sha256:de7f3d9ccfdf245931fb19c7e144fd4da0452e2b204395f3d8084d6e02318acc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BWSC5UP5DX2EV4IMKAGTUGEPZK/bundle.json","state_url":"https://pith.science/pith/BWSC5UP5DX2EV4IMKAGTUGEPZK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BWSC5UP5DX2EV4IMKAGTUGEPZK/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-09T18:08:58Z","links":{"resolver":"https://pith.science/pith/BWSC5UP5DX2EV4IMKAGTUGEPZK","bundle":"https://pith.science/pith/BWSC5UP5DX2EV4IMKAGTUGEPZK/bundle.json","state":"https://pith.science/pith/BWSC5UP5DX2EV4IMKAGTUGEPZK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BWSC5UP5DX2EV4IMKAGTUGEPZK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:BWSC5UP5DX2EV4IMKAGTUGEPZK","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":"0ee71df1cfe212e5c29dd12ab907184e147a3835f289f37485eaef3562c120f7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-09-07T04:19:55Z","title_canon_sha256":"996527a3b6125c1701ac5f163209e616a7a585f7c07c2e90f9b6fafcce69c015"},"schema_version":"1.0","source":{"id":"1709.02065","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.02065","created_at":"2026-05-18T00:35:50Z"},{"alias_kind":"arxiv_version","alias_value":"1709.02065v1","created_at":"2026-05-18T00:35:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.02065","created_at":"2026-05-18T00:35:50Z"},{"alias_kind":"pith_short_12","alias_value":"BWSC5UP5DX2E","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_16","alias_value":"BWSC5UP5DX2EV4IM","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_8","alias_value":"BWSC5UP5","created_at":"2026-05-18T12:31:08Z"}],"graph_snapshots":[{"event_id":"sha256:de7f3d9ccfdf245931fb19c7e144fd4da0452e2b204395f3d8084d6e02318acc","target":"graph","created_at":"2026-05-18T00:35:50Z","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":"Motivated by the concept of clean ideals, we introduce the notion of nil clean ideals of a ring. We define an ideal $I$ of a ring $R$ to be nil clean ideal if every element of $I$ can be written as a sum of an idempotent and a nilpotent element of $R$. In this article we discuss various properties of nil clean ideals.","authors_text":"Ajay Sharma, Dhiren Kumar Basnet","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-09-07T04:19:55Z","title":"Nil Clean Ideal"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.02065","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:c23866e27dec9bd6c6af32e3eb51fd9489bb93dedeb21d8421de78885fa1485e","target":"record","created_at":"2026-05-18T00:35:50Z","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":"0ee71df1cfe212e5c29dd12ab907184e147a3835f289f37485eaef3562c120f7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-09-07T04:19:55Z","title_canon_sha256":"996527a3b6125c1701ac5f163209e616a7a585f7c07c2e90f9b6fafcce69c015"},"schema_version":"1.0","source":{"id":"1709.02065","kind":"arxiv","version":1}},"canonical_sha256":"0da42ed1fd1df44af10c500d3a188fcaab017b4d2d0f61982da16a6e74770cec","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0da42ed1fd1df44af10c500d3a188fcaab017b4d2d0f61982da16a6e74770cec","first_computed_at":"2026-05-18T00:35:50.349287Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:35:50.349287Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"R6ivI53uRCz5Ji66YhBRkfHxJ5+sfDZzqAhsXMpMYyCrBKU6s5QhJ0gW0tjLFGxQuUo1/KZCpbcvb+b2W88lBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:35:50.349911Z","signed_message":"canonical_sha256_bytes"},"source_id":"1709.02065","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c23866e27dec9bd6c6af32e3eb51fd9489bb93dedeb21d8421de78885fa1485e","sha256:de7f3d9ccfdf245931fb19c7e144fd4da0452e2b204395f3d8084d6e02318acc"],"state_sha256":"49ed44c7dd4541e0e433d3ee18b7819da78449b577a3524d69d9a13f2aa344ed"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LuKL2YTtoDHhjKDFh3uhDx8nqk1UEEjPKjGBUfVE1g9cDw3Aq2zA2F5J9rIICG3Ub8r01kmCyLoWyD/9ZJjRAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T18:08:58.938889Z","bundle_sha256":"06064889899940fa8433f7f38fba0791de2b9c1174b9dab68a1b8a8694577442"}}