{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:5TXBFVGXCYAOT4BOFEE2Q33OXT","short_pith_number":"pith:5TXBFVGX","canonical_record":{"source":{"id":"1810.01282","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2018-10-01T05:45:12Z","cross_cats_sorted":[],"title_canon_sha256":"874603511288840cd26cbcc8de80e1d887c6af1521776f2d457b8fd1dabf35a1","abstract_canon_sha256":"4af92b0fd577627e3b90c1014e365b8c25ab3189592dc4086ef7f90bef33c193"},"schema_version":"1.0"},"canonical_sha256":"ecee12d4d71600e9f02e2909a86f6ebccdba7f64fe221bdbdcf40c70235e32a6","source":{"kind":"arxiv","id":"1810.01282","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.01282","created_at":"2026-05-18T00:04:18Z"},{"alias_kind":"arxiv_version","alias_value":"1810.01282v1","created_at":"2026-05-18T00:04:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.01282","created_at":"2026-05-18T00:04:18Z"},{"alias_kind":"pith_short_12","alias_value":"5TXBFVGXCYAO","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_16","alias_value":"5TXBFVGXCYAOT4BO","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_8","alias_value":"5TXBFVGX","created_at":"2026-05-18T12:32:08Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:5TXBFVGXCYAOT4BOFEE2Q33OXT","target":"record","payload":{"canonical_record":{"source":{"id":"1810.01282","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2018-10-01T05:45:12Z","cross_cats_sorted":[],"title_canon_sha256":"874603511288840cd26cbcc8de80e1d887c6af1521776f2d457b8fd1dabf35a1","abstract_canon_sha256":"4af92b0fd577627e3b90c1014e365b8c25ab3189592dc4086ef7f90bef33c193"},"schema_version":"1.0"},"canonical_sha256":"ecee12d4d71600e9f02e2909a86f6ebccdba7f64fe221bdbdcf40c70235e32a6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:04:18.350567Z","signature_b64":"4PwEgEE5FVftF5SY2o1TgX34m5fqVxDIoHj8RLK5jreyNBp8busc0LLuOihjKNwc1lVAFlXiG1mjtx/5e/gcAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ecee12d4d71600e9f02e2909a86f6ebccdba7f64fe221bdbdcf40c70235e32a6","last_reissued_at":"2026-05-18T00:04:18.349746Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:04:18.349746Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1810.01282","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":"2026-05-18T00:04:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"re1VlIF8u0hE9ba0c1AB0vzkUO3OZXWiwoA92B9zP8ovgO8D074paxVJrx1H/Lae3UlxBegnArUuu5A2pIvwCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T21:15:34.850092Z"},"content_sha256":"f99b20abbfe25152ef1e728e7046a4f48f0cdd48e440de75f9e869e9c361f340","schema_version":"1.0","event_id":"sha256:f99b20abbfe25152ef1e728e7046a4f48f0cdd48e440de75f9e869e9c361f340"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:5TXBFVGXCYAOT4BOFEE2Q33OXT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Weak 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":"2018-10-01T05:45:12Z","abstract_excerpt":"As a generalization of nil clean ideal, we define weak nil clean ideal of a ring. An ideal $I$ of a ring $R$ is weak nil clean ideal if for any $x\\in I$, either $x=e+n$ or $x=-e+n$, where $n$ is a nilpotent element and $e$ is an idempotent element of $R$. Some interesting properties of weak nil clean ideal and its relation with weak nil clean ring have been discussed."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.01282","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":"2026-05-18T00:04:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"K9SYaXNfd7AjH03q/BRh5iO6w41HSY5hfktHdzJGDp2O3GiNQSu06i7kJm0vwIYAS4nRAcRlU0wQDUVmK3eDBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T21:15:34.850800Z"},"content_sha256":"0763f4e97d3f0134c2443ee23361130b1e1d4618b9a49978a89880057e6c5fd3","schema_version":"1.0","event_id":"sha256:0763f4e97d3f0134c2443ee23361130b1e1d4618b9a49978a89880057e6c5fd3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5TXBFVGXCYAOT4BOFEE2Q33OXT/bundle.json","state_url":"https://pith.science/pith/5TXBFVGXCYAOT4BOFEE2Q33OXT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5TXBFVGXCYAOT4BOFEE2Q33OXT/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":"2026-06-09T21:15:34Z","links":{"resolver":"https://pith.science/pith/5TXBFVGXCYAOT4BOFEE2Q33OXT","bundle":"https://pith.science/pith/5TXBFVGXCYAOT4BOFEE2Q33OXT/bundle.json","state":"https://pith.science/pith/5TXBFVGXCYAOT4BOFEE2Q33OXT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5TXBFVGXCYAOT4BOFEE2Q33OXT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:5TXBFVGXCYAOT4BOFEE2Q33OXT","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":"4af92b0fd577627e3b90c1014e365b8c25ab3189592dc4086ef7f90bef33c193","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2018-10-01T05:45:12Z","title_canon_sha256":"874603511288840cd26cbcc8de80e1d887c6af1521776f2d457b8fd1dabf35a1"},"schema_version":"1.0","source":{"id":"1810.01282","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.01282","created_at":"2026-05-18T00:04:18Z"},{"alias_kind":"arxiv_version","alias_value":"1810.01282v1","created_at":"2026-05-18T00:04:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.01282","created_at":"2026-05-18T00:04:18Z"},{"alias_kind":"pith_short_12","alias_value":"5TXBFVGXCYAO","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_16","alias_value":"5TXBFVGXCYAOT4BO","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_8","alias_value":"5TXBFVGX","created_at":"2026-05-18T12:32:08Z"}],"graph_snapshots":[{"event_id":"sha256:0763f4e97d3f0134c2443ee23361130b1e1d4618b9a49978a89880057e6c5fd3","target":"graph","created_at":"2026-05-18T00:04:18Z","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":"As a generalization of nil clean ideal, we define weak nil clean ideal of a ring. An ideal $I$ of a ring $R$ is weak nil clean ideal if for any $x\\in I$, either $x=e+n$ or $x=-e+n$, where $n$ is a nilpotent element and $e$ is an idempotent element of $R$. Some interesting properties of weak nil clean ideal and its relation with weak nil clean ring have been discussed.","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":"2018-10-01T05:45:12Z","title":"Weak Nil Clean Ideal"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.01282","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:f99b20abbfe25152ef1e728e7046a4f48f0cdd48e440de75f9e869e9c361f340","target":"record","created_at":"2026-05-18T00:04:18Z","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":"4af92b0fd577627e3b90c1014e365b8c25ab3189592dc4086ef7f90bef33c193","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2018-10-01T05:45:12Z","title_canon_sha256":"874603511288840cd26cbcc8de80e1d887c6af1521776f2d457b8fd1dabf35a1"},"schema_version":"1.0","source":{"id":"1810.01282","kind":"arxiv","version":1}},"canonical_sha256":"ecee12d4d71600e9f02e2909a86f6ebccdba7f64fe221bdbdcf40c70235e32a6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ecee12d4d71600e9f02e2909a86f6ebccdba7f64fe221bdbdcf40c70235e32a6","first_computed_at":"2026-05-18T00:04:18.349746Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:04:18.349746Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4PwEgEE5FVftF5SY2o1TgX34m5fqVxDIoHj8RLK5jreyNBp8busc0LLuOihjKNwc1lVAFlXiG1mjtx/5e/gcAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:04:18.350567Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.01282","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f99b20abbfe25152ef1e728e7046a4f48f0cdd48e440de75f9e869e9c361f340","sha256:0763f4e97d3f0134c2443ee23361130b1e1d4618b9a49978a89880057e6c5fd3"],"state_sha256":"640d7eac6bcb6832ffb199e77b00e01b4efc5ce999cf2627763fa755a09f2837"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GaOY9VedUNKAkzOSQmQH64PTvANBfd6/3roWPNzbPNwcPZpai1UJxZoP9AoDH23dXcDKT+Od5lnWn06xr6zEBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T21:15:34.854756Z","bundle_sha256":"23c7d0d69b306ba0b250921452cdd2e7d010300eb291c15a15637222a222fb5f"}}