{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:NRB6FDK2SXWWRU5JH5UTXV5S4L","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":"3810adceeb1d55163f9a62239f824b44e9095810b04eacdf475d7848d29d8499","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2011-05-16T17:29:43Z","title_canon_sha256":"8206127b6bf8e21e140f86734f9a9214af38d1a9505d57782f5dc91c64d05bf3"},"schema_version":"1.0","source":{"id":"1105.3157","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.3157","created_at":"2026-05-18T02:55:18Z"},{"alias_kind":"arxiv_version","alias_value":"1105.3157v1","created_at":"2026-05-18T02:55:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.3157","created_at":"2026-05-18T02:55:18Z"},{"alias_kind":"pith_short_12","alias_value":"NRB6FDK2SXWW","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_16","alias_value":"NRB6FDK2SXWWRU5J","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_8","alias_value":"NRB6FDK2","created_at":"2026-05-18T12:26:37Z"}],"graph_snapshots":[{"event_id":"sha256:4cf698d974f3cfe56a87ab160476ba02976c909015204fbb106b856ce14a5523","target":"graph","created_at":"2026-05-18T02:55:18Z","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":"New types of systems of fuzzy relation inequalities and equations, called weakly linear, have been recently introduced in [J. Ignjatovi\\'c, M. \\'Ciri\\'c, S. Bogdanovi\\'c, On the greatest solutions to weakly linear systems of fuzzy relation inequalities and equations, Fuzzy Sets and Systems 161 (2010) 3081--3113.]. The mentioned paper dealt with homogeneous weakly linear systems, composed of fuzzy relations on a single set, and a method for computing their greatest solutions has been provided. This method is based on the computing of the greatest post-fixed point, contained in a given fuzzy rel","authors_text":"Ivana Jan\\v{c}i\\'c, Jelena Ignjatovi\\'c, Miroslav \\'Ciri\\'c, Nada Damljanovi\\'c","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2011-05-16T17:29:43Z","title":"Weakly linear systems of fuzzy relation inequalities: The heterogeneous case"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.3157","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":"sha256:4ddbe9aaf2a556585faf74b36323ca588b41790fbd544d13a72562e74cce6006","target":"record","created_at":"2026-05-18T02:55:18Z","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":"3810adceeb1d55163f9a62239f824b44e9095810b04eacdf475d7848d29d8499","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2011-05-16T17:29:43Z","title_canon_sha256":"8206127b6bf8e21e140f86734f9a9214af38d1a9505d57782f5dc91c64d05bf3"},"schema_version":"1.0","source":{"id":"1105.3157","kind":"arxiv","version":1}},"canonical_sha256":"6c43e28d5a95ed68d3a93f693bd7b2e2dddd04751b5bfb965c8ae833aeb518da","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6c43e28d5a95ed68d3a93f693bd7b2e2dddd04751b5bfb965c8ae833aeb518da","first_computed_at":"2026-05-18T02:55:18.848609Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:55:18.848609Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/KA6/mM8cBXK5K06L+WrI3ekC9TYZSY+krKbc2+GzqiwRuuSaRmG45MVRe05CUunhSYVwJmIitYff6EtPf6+DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:55:18.849018Z","signed_message":"canonical_sha256_bytes"},"source_id":"1105.3157","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4ddbe9aaf2a556585faf74b36323ca588b41790fbd544d13a72562e74cce6006","sha256:4cf698d974f3cfe56a87ab160476ba02976c909015204fbb106b856ce14a5523"],"state_sha256":"abd4c0bd09abf6549a3ec0fc97f7846cc31abe462c737e92c8b1575afc3fbd74"}