{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:EJJTHGCGQX5YC6IMK5IMPDRKBC","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":"eea28432ff8652b41de5e0e2c96587c24375f349d3cb3e72343e2532bb3dcfb2","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-06-28T05:34:02Z","title_canon_sha256":"50e9e235d75add028b78d92d4cf8a4b91a6b77afa83185a9d0a6c02b7c98e849"},"schema_version":"1.0","source":{"id":"1406.7357","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.7357","created_at":"2026-05-18T02:20:12Z"},{"alias_kind":"arxiv_version","alias_value":"1406.7357v1","created_at":"2026-05-18T02:20:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.7357","created_at":"2026-05-18T02:20:12Z"},{"alias_kind":"pith_short_12","alias_value":"EJJTHGCGQX5Y","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_16","alias_value":"EJJTHGCGQX5YC6IM","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_8","alias_value":"EJJTHGCG","created_at":"2026-05-18T12:28:25Z"}],"graph_snapshots":[{"event_id":"sha256:5fad8004d5f7f3ed97ac86f216d3f17ec6e4d65d60e2153e3c5397f8905ba520","target":"graph","created_at":"2026-05-18T02:20:12Z","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 consider the system of linear equations $Ax=b$, where $A\\in \\Bbb{R}^{n \\times n}$ is a crisp H-matrix and $b$ is a fuzzy $n$-vector. We then investigate the existence and uniqueness of a fuzzy solution to this system. The results can also be used for the class of M-matrices and strictly diagonally dominant matrices. Finally, some numerical examples are given to illustrate the presented theoretical results.","authors_text":"Davod Khojasteh Salkuyeh","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-06-28T05:34:02Z","title":"On the solution of a class of fuzzy system of linear equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.7357","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":"sha256:59387abd057e8bac0f434fc7a4559064c3786087aa06dd5f380c666adcc6c2c6","target":"record","created_at":"2026-05-18T02:20:12Z","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":"eea28432ff8652b41de5e0e2c96587c24375f349d3cb3e72343e2532bb3dcfb2","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-06-28T05:34:02Z","title_canon_sha256":"50e9e235d75add028b78d92d4cf8a4b91a6b77afa83185a9d0a6c02b7c98e849"},"schema_version":"1.0","source":{"id":"1406.7357","kind":"arxiv","version":1}},"canonical_sha256":"225333984685fb81790c5750c78e2a08a4a2d59bfd5b5019acf2d3061e591b75","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"225333984685fb81790c5750c78e2a08a4a2d59bfd5b5019acf2d3061e591b75","first_computed_at":"2026-05-18T02:20:12.567890Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:20:12.567890Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"H3kiCUMQlnsL8Kgb/Txxi85VkWX8+P4fn9gw9PSYu2BxDPFnxkN5+zQ6eCamNh3laKyGTIz5wzDqG6JnfO7JAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:20:12.568309Z","signed_message":"canonical_sha256_bytes"},"source_id":"1406.7357","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:59387abd057e8bac0f434fc7a4559064c3786087aa06dd5f380c666adcc6c2c6","sha256:5fad8004d5f7f3ed97ac86f216d3f17ec6e4d65d60e2153e3c5397f8905ba520"],"state_sha256":"e018eb2421080d00cee0e586599ec40111cf773b4a5d8d03d328dcb88b80b6f6"}