{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:QPUQEW44CIJU7X57L6LQJ5BXG5","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":"f88f42a1a64f9207525f9c49668be49d66862cc6e9798b1e0cd76ceb0ac4c830","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-03-24T22:51:28Z","title_canon_sha256":"263b3dd5540b238e3875dd468a9234e4ab3b08cf6ec2ce8bb4773bfb3b5a5a08"},"schema_version":"1.0","source":{"id":"1503.07226","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.07226","created_at":"2026-05-18T02:20:28Z"},{"alias_kind":"arxiv_version","alias_value":"1503.07226v1","created_at":"2026-05-18T02:20:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.07226","created_at":"2026-05-18T02:20:28Z"},{"alias_kind":"pith_short_12","alias_value":"QPUQEW44CIJU","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_16","alias_value":"QPUQEW44CIJU7X57","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_8","alias_value":"QPUQEW44","created_at":"2026-05-18T12:29:37Z"}],"graph_snapshots":[{"event_id":"sha256:09d758583963e848a919f49533406e7f171445b91bf66d676c3082c43fa0c886","target":"graph","created_at":"2026-05-18T02:20:28Z","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 prove a conjecture about the minimal nonnegative solutions of algebraic Riccati equations associated with reducible singular M-matrices. The result enhances our understanding of the behaviour of doubling algorithms for finding the minimal nonnegative solutions.","authors_text":"Chun-Hua Guo, Di Lu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-03-24T22:51:28Z","title":"A note on algebraic Riccati equations associated with reducible singular M-matrices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.07226","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:c12040b57ad9c32c32adfb6d2beee47222803ce4e23c33a7c2e239a657c89040","target":"record","created_at":"2026-05-18T02:20:28Z","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":"f88f42a1a64f9207525f9c49668be49d66862cc6e9798b1e0cd76ceb0ac4c830","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-03-24T22:51:28Z","title_canon_sha256":"263b3dd5540b238e3875dd468a9234e4ab3b08cf6ec2ce8bb4773bfb3b5a5a08"},"schema_version":"1.0","source":{"id":"1503.07226","kind":"arxiv","version":1}},"canonical_sha256":"83e9025b9c12134fdfbf5f9704f437375a0eeea4248ddd7b6fd56e3d02832cf3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"83e9025b9c12134fdfbf5f9704f437375a0eeea4248ddd7b6fd56e3d02832cf3","first_computed_at":"2026-05-18T02:20:28.021470Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:20:28.021470Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"317Y7b1hmpeqQQy1caLun/Po9PH1gwjaw1SL5ybH6pyl7FjmVK/RvBrrQDKnBN6ubGJrg9piY6zHKdLRXBmBCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:20:28.021971Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.07226","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c12040b57ad9c32c32adfb6d2beee47222803ce4e23c33a7c2e239a657c89040","sha256:09d758583963e848a919f49533406e7f171445b91bf66d676c3082c43fa0c886"],"state_sha256":"53f89fb01da4c23fbb0574ce8be119a8a308a311a54b1e2920fbb16d4d5c449b"}