{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:OZNABWJKBEEPACX5KJE3NPHI6R","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":"9e92604276f4414f3a78d9b75a6f398d636bba7216849c1f498c7d2ec9031c5a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-07-25T02:02:58Z","title_canon_sha256":"7ae7f17a38081721de2ff0e2c221138d12e926d6010f25a236eebcbcf76cb1e5"},"schema_version":"1.0","source":{"id":"1307.6623","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.6623","created_at":"2026-05-18T03:17:35Z"},{"alias_kind":"arxiv_version","alias_value":"1307.6623v1","created_at":"2026-05-18T03:17:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.6623","created_at":"2026-05-18T03:17:35Z"},{"alias_kind":"pith_short_12","alias_value":"OZNABWJKBEEP","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"OZNABWJKBEEPACX5","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"OZNABWJK","created_at":"2026-05-18T12:27:54Z"}],"graph_snapshots":[{"event_id":"sha256:d69491ba188b1038e44d5b0558c33c60c685f128337a6c4ec2f97d0db1842ca6","target":"graph","created_at":"2026-05-18T03:17:35Z","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":"We present some formulae for the Drazin inverse of difference and product of idempotents in a ring. A number of results of bounded linear operators in Banach spaces are extended to the ring case.","authors_text":"Huihui Zhu, Jianlong Chen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-07-25T02:02:58Z","title":"Representations of the Drazin inverse involving idempotents in a ring"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.6623","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":"sha256:8572f6c14770e783d805035c228446eba2612173a8704d518b53caffdb4eb43e","target":"record","created_at":"2026-05-18T03:17:35Z","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":"9e92604276f4414f3a78d9b75a6f398d636bba7216849c1f498c7d2ec9031c5a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-07-25T02:02:58Z","title_canon_sha256":"7ae7f17a38081721de2ff0e2c221138d12e926d6010f25a236eebcbcf76cb1e5"},"schema_version":"1.0","source":{"id":"1307.6623","kind":"arxiv","version":1}},"canonical_sha256":"765a00d92a0908f00afd5249b6bce8f444b640e103597b46f10375bc48bd1f29","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"765a00d92a0908f00afd5249b6bce8f444b640e103597b46f10375bc48bd1f29","first_computed_at":"2026-05-18T03:17:35.776344Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:17:35.776344Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UDKPvQmLHVxgS991P/LmFCrk+zlZAc0CW389EhlCfIzw9aMLH2QXMZBj31Qg19pzZwuQQ5tHC2lOtZ/nhuPUBg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:17:35.776851Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.6623","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8572f6c14770e783d805035c228446eba2612173a8704d518b53caffdb4eb43e","sha256:d69491ba188b1038e44d5b0558c33c60c685f128337a6c4ec2f97d0db1842ca6"],"state_sha256":"2bdf6f91be0699c7e0a8afa955606df5560642ab2ef280c069917b2dfb4f26ad"}