{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:YFF73YUIE3QSMW2NQRTIPWJLGT","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":"48573c6aa54c173edb749eafd496afff598e41cc7622e59eb56222a00ed5930f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-04-17T15:01:15Z","title_canon_sha256":"44f96b9bc8b7d8569d3f69ca44302c61f4a9b732903975153cb4bcf313c3c980"},"schema_version":"1.0","source":{"id":"1504.04527","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.04527","created_at":"2026-05-18T02:18:32Z"},{"alias_kind":"arxiv_version","alias_value":"1504.04527v1","created_at":"2026-05-18T02:18:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.04527","created_at":"2026-05-18T02:18:32Z"},{"alias_kind":"pith_short_12","alias_value":"YFF73YUIE3QS","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_16","alias_value":"YFF73YUIE3QSMW2N","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_8","alias_value":"YFF73YUI","created_at":"2026-05-18T12:29:50Z"}],"graph_snapshots":[{"event_id":"sha256:c9ececce02a6dc3bb652886542cceaad28e7f2a281207d2f7da93d0779a7b835","target":"graph","created_at":"2026-05-18T02:18:32Z","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 short note, we prove some basic results on pseudo Schur complement and the pseudo principal pivot transform of a block matrix. Pseudo Schur complement and pseudo principal pivot ransform are extensions of the Schur complement and the principal pivot transform, respectively, where the usual inverse is replaced by the Moore-Penrose inverse. The objective is to record these results for use in future.","authors_text":"Kavita Bisht, K.C. Sivakumar","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-04-17T15:01:15Z","title":"Pseudo Schur Complements, Pseudo Principal Pivot Transforms and Their Inheritance Properties"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.04527","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:daf4cac8975a8e322844bd4828c73631ceb55e17238e5f3a9318c5a8983ef97e","target":"record","created_at":"2026-05-18T02:18:32Z","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":"48573c6aa54c173edb749eafd496afff598e41cc7622e59eb56222a00ed5930f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-04-17T15:01:15Z","title_canon_sha256":"44f96b9bc8b7d8569d3f69ca44302c61f4a9b732903975153cb4bcf313c3c980"},"schema_version":"1.0","source":{"id":"1504.04527","kind":"arxiv","version":1}},"canonical_sha256":"c14bfde28826e1265b4d846687d92b34dbf76dac34b6ec2f7c6d7b0242a8b45c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c14bfde28826e1265b4d846687d92b34dbf76dac34b6ec2f7c6d7b0242a8b45c","first_computed_at":"2026-05-18T02:18:32.180880Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:18:32.180880Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"T4seyw6uyr2WzN7/nxwfTT4xPqb9RA0cQIXLiUlG7YRUMW45eHEue33I4lEdxifWNlJSORK8+1bv/vLPnzerBA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:18:32.181903Z","signed_message":"canonical_sha256_bytes"},"source_id":"1504.04527","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:daf4cac8975a8e322844bd4828c73631ceb55e17238e5f3a9318c5a8983ef97e","sha256:c9ececce02a6dc3bb652886542cceaad28e7f2a281207d2f7da93d0779a7b835"],"state_sha256":"5dfc6134be9adc53f82c6ead8716779b4b466e44bd2e12b529bc29833168a1c7"}