{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:YFF73YUIE3QSMW2NQRTIPWJLGT","short_pith_number":"pith:YFF73YUI","canonical_record":{"source":{"id":"1504.04527","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-04-17T15:01:15Z","cross_cats_sorted":[],"title_canon_sha256":"44f96b9bc8b7d8569d3f69ca44302c61f4a9b732903975153cb4bcf313c3c980","abstract_canon_sha256":"48573c6aa54c173edb749eafd496afff598e41cc7622e59eb56222a00ed5930f"},"schema_version":"1.0"},"canonical_sha256":"c14bfde28826e1265b4d846687d92b34dbf76dac34b6ec2f7c6d7b0242a8b45c","source":{"kind":"arxiv","id":"1504.04527","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:YFF73YUIE3QSMW2NQRTIPWJLGT","target":"record","payload":{"canonical_record":{"source":{"id":"1504.04527","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-04-17T15:01:15Z","cross_cats_sorted":[],"title_canon_sha256":"44f96b9bc8b7d8569d3f69ca44302c61f4a9b732903975153cb4bcf313c3c980","abstract_canon_sha256":"48573c6aa54c173edb749eafd496afff598e41cc7622e59eb56222a00ed5930f"},"schema_version":"1.0"},"canonical_sha256":"c14bfde28826e1265b4d846687d92b34dbf76dac34b6ec2f7c6d7b0242a8b45c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:18:32.181903Z","signature_b64":"T4seyw6uyr2WzN7/nxwfTT4xPqb9RA0cQIXLiUlG7YRUMW45eHEue33I4lEdxifWNlJSORK8+1bv/vLPnzerBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c14bfde28826e1265b4d846687d92b34dbf76dac34b6ec2f7c6d7b0242a8b45c","last_reissued_at":"2026-05-18T02:18:32.180880Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:18:32.180880Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1504.04527","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":"2026-05-18T02:18:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"i9SlQ9ckE6DP57R6yInkKRMtzfOi0Y5vSDMYMepyQSGcir45Hpox4SIerFK+cwsnXwGtOJCOKTstMx/jHZqaBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T06:33:31.641085Z"},"content_sha256":"daf4cac8975a8e322844bd4828c73631ceb55e17238e5f3a9318c5a8983ef97e","schema_version":"1.0","event_id":"sha256:daf4cac8975a8e322844bd4828c73631ceb55e17238e5f3a9318c5a8983ef97e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:YFF73YUIE3QSMW2NQRTIPWJLGT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Pseudo Schur Complements, Pseudo Principal Pivot Transforms and Their Inheritance Properties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Kavita Bisht, K.C. Sivakumar","submitted_at":"2015-04-17T15:01:15Z","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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.04527","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":"2026-05-18T02:18:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OvqiFoRlKz//t/wrPAgg63GVagehFLjy0M/02GHOFYRxlCCG0e/xtAt/m9tW2uaKA5ThDpteuoz4PGLkLD8DBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T06:33:31.641443Z"},"content_sha256":"c9ececce02a6dc3bb652886542cceaad28e7f2a281207d2f7da93d0779a7b835","schema_version":"1.0","event_id":"sha256:c9ececce02a6dc3bb652886542cceaad28e7f2a281207d2f7da93d0779a7b835"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YFF73YUIE3QSMW2NQRTIPWJLGT/bundle.json","state_url":"https://pith.science/pith/YFF73YUIE3QSMW2NQRTIPWJLGT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YFF73YUIE3QSMW2NQRTIPWJLGT/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":"2026-06-03T06:33:31Z","links":{"resolver":"https://pith.science/pith/YFF73YUIE3QSMW2NQRTIPWJLGT","bundle":"https://pith.science/pith/YFF73YUIE3QSMW2NQRTIPWJLGT/bundle.json","state":"https://pith.science/pith/YFF73YUIE3QSMW2NQRTIPWJLGT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YFF73YUIE3QSMW2NQRTIPWJLGT/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"N5lz+gX23Oyiz+LkiIhUvL4R+Zs4jJdg/DSboBMV8KCLZfCAqE8DuyH9+8yaDUrK95h4Bt2gAqDhaXY8u3F1AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T06:33:31.643572Z","bundle_sha256":"e0a7964a1ad16a5763e45953d9518bdc715df766f7651608c8998b6fec0d2170"}}