{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:GSHFDX6UULAOZRNDUXHIXQE5TL","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":"4f3fa546c228e4b28e356a51600b4b2418c777d94f90dcdbcf50aab69e892f1c","cross_cats_sorted":["math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-02-02T16:09:44Z","title_canon_sha256":"ef546255edd8fe7e325b21045134ae15edd396b914810d331ec230d865618de4"},"schema_version":"1.0","source":{"id":"1202.0473","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.0473","created_at":"2026-05-18T04:03:18Z"},{"alias_kind":"arxiv_version","alias_value":"1202.0473v1","created_at":"2026-05-18T04:03:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.0473","created_at":"2026-05-18T04:03:18Z"},{"alias_kind":"pith_short_12","alias_value":"GSHFDX6UULAO","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_16","alias_value":"GSHFDX6UULAOZRND","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_8","alias_value":"GSHFDX6U","created_at":"2026-05-18T12:27:06Z"}],"graph_snapshots":[{"event_id":"sha256:517d17e44db57a652de94fab6572a22134b731d2f3ff91194b370e56059ce0df","target":"graph","created_at":"2026-05-18T04:03:18Z","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":"This short note, in part of expository nature, points out several new or recent consequences of a quite nice decomposition for positive semi-definite matrices.","authors_text":"Eun-Young Lee, Jean-Christophe Bourin, Minghua Lin","cross_cats":["math.OA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-02-02T16:09:44Z","title":"On a decomposition lemma for positive semi-definite block-matrices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.0473","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":"sha256:0f6a7b99b35500fe1a58a27430b7304ba1bfac5b042152d98fc3460fbe265b9f","target":"record","created_at":"2026-05-18T04:03:18Z","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":"4f3fa546c228e4b28e356a51600b4b2418c777d94f90dcdbcf50aab69e892f1c","cross_cats_sorted":["math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-02-02T16:09:44Z","title_canon_sha256":"ef546255edd8fe7e325b21045134ae15edd396b914810d331ec230d865618de4"},"schema_version":"1.0","source":{"id":"1202.0473","kind":"arxiv","version":1}},"canonical_sha256":"348e51dfd4a2c0ecc5a3a5ce8bc09d9ae5d11d0cf2ec54f3795a60c02c704c8b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"348e51dfd4a2c0ecc5a3a5ce8bc09d9ae5d11d0cf2ec54f3795a60c02c704c8b","first_computed_at":"2026-05-18T04:03:18.122793Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:03:18.122793Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NTn4pzYqEPKMk5WcxatrEP37kqLmPaJ0MDUay+V01EquGgFLAI5Up+W7mSAyvTfE+8QMDX4ftS2uBwDyMgZOBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:03:18.123249Z","signed_message":"canonical_sha256_bytes"},"source_id":"1202.0473","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0f6a7b99b35500fe1a58a27430b7304ba1bfac5b042152d98fc3460fbe265b9f","sha256:517d17e44db57a652de94fab6572a22134b731d2f3ff91194b370e56059ce0df"],"state_sha256":"f81deb712333ebd3113e209d745115fa18f30d87deffacfec962c26c0e6d915b"}