{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:XR5FPPEPOXU4YHUIQKW6SLKSRI","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":"d2f6d235a5907da1126a7fa877c3b527b3fb40313b18ec867eb3955e937c1549","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2014-11-08T01:27:48Z","title_canon_sha256":"1359f71261c644205d518ff9b8b974e2e546a52de9cdec98d3f7c1c5f1e35bd3"},"schema_version":"1.0","source":{"id":"1411.2067","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.2067","created_at":"2026-05-18T02:38:19Z"},{"alias_kind":"arxiv_version","alias_value":"1411.2067v1","created_at":"2026-05-18T02:38:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.2067","created_at":"2026-05-18T02:38:19Z"},{"alias_kind":"pith_short_12","alias_value":"XR5FPPEPOXU4","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_16","alias_value":"XR5FPPEPOXU4YHUI","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_8","alias_value":"XR5FPPEP","created_at":"2026-05-18T12:28:57Z"}],"graph_snapshots":[{"event_id":"sha256:08d1ffdcfe4b5e65670c2c082b3bb5291700a1d7d32723ffebdc98c751317479","target":"graph","created_at":"2026-05-18T02:38:19Z","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":"In this paper we give expressions for the generalized Drazin inverse of a (2,2,0) operator matrix and a $2\\times2$ operator matrix under certain circumstances, which generalizes and unifies several results in the literature.","authors_text":"Daochang Zhang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2014-11-08T01:27:48Z","title":"Representations for generalized Drazin inverse of operator matrices over a Banach space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.2067","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":"sha256:414d551429c23e5e31e9bb87ff8f59092a2651c60139e105de468781f18c17e6","target":"record","created_at":"2026-05-18T02:38:19Z","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":"d2f6d235a5907da1126a7fa877c3b527b3fb40313b18ec867eb3955e937c1549","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2014-11-08T01:27:48Z","title_canon_sha256":"1359f71261c644205d518ff9b8b974e2e546a52de9cdec98d3f7c1c5f1e35bd3"},"schema_version":"1.0","source":{"id":"1411.2067","kind":"arxiv","version":1}},"canonical_sha256":"bc7a57bc8f75e9cc1e8882ade92d528a21b2c3f983698298e4b14836389dfbbb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bc7a57bc8f75e9cc1e8882ade92d528a21b2c3f983698298e4b14836389dfbbb","first_computed_at":"2026-05-18T02:38:19.557515Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:38:19.557515Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VirSG2rb+Pixb2twvnKDhvFjuslGZV/C+3hvkf7xRTP+uQPZ4QHJ1iSjuGvtXE9I+v/DmqRPHQGVhUfr4W7+DA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:38:19.557983Z","signed_message":"canonical_sha256_bytes"},"source_id":"1411.2067","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:414d551429c23e5e31e9bb87ff8f59092a2651c60139e105de468781f18c17e6","sha256:08d1ffdcfe4b5e65670c2c082b3bb5291700a1d7d32723ffebdc98c751317479"],"state_sha256":"4ff9f433e87df8b0f5fa5ce223a97a37667f31d08c34242f4790ccc67cd5eae3"}