{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:YRUHX7KSTNDW43JNM4OWWB3X7B","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":"a0399ee5ac925681462ab14bc9467e46f6871c71ff7a2e78110099dfc26e994d","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2014-04-21T12:58:38Z","title_canon_sha256":"3d4d00c3d6e55be404444c83ddcb6ce43645e9bc3378a0dabf434540d27f0689"},"schema_version":"1.0","source":{"id":"1404.5184","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.5184","created_at":"2026-05-18T02:17:33Z"},{"alias_kind":"arxiv_version","alias_value":"1404.5184v3","created_at":"2026-05-18T02:17:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.5184","created_at":"2026-05-18T02:17:33Z"},{"alias_kind":"pith_short_12","alias_value":"YRUHX7KSTNDW","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_16","alias_value":"YRUHX7KSTNDW43JN","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_8","alias_value":"YRUHX7KS","created_at":"2026-05-18T12:28:57Z"}],"graph_snapshots":[{"event_id":"sha256:812d60730f4c86461d8997a0644c76df3c39a651e2d2b45a4b10d9289baa97b1","target":"graph","created_at":"2026-05-18T02:17:33Z","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 tolerances induced by irredundant coverings. Each tolerance $R$ on $U$ determines a quasiorder $\\lesssim_R$ by setting $x \\lesssim_R y$ if and only if $R(x) \\subseteq R(y)$. We prove that for a tolerance $R$ induced by a covering $\\mathcal{H}$ of $U$, the covering $\\mathcal{H}$ is irredundant if and only if the quasiordered set $(U, \\lesssim_R)$ is bounded by minimal elements and the tolerance $R$ coincides with the product ${\\gtrsim_R} \\circ {\\lesssim_R}$. We also show that in such a case $\\mathcal{H} = \\{ {\\uparrow}m \\mid \\text{$m$ is minimal in $(U,\\lesssim_R)$} \\","authors_text":"Jouni J\\\"arvinen, S\\'andor Radeleczki","cross_cats":["cs.DM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2014-04-21T12:58:38Z","title":"Tolerances induced by irredundant coverings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.5184","kind":"arxiv","version":3},"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":"sha256:994a0efe6068deca10bba7b20e0401eefba7fe1d58a5f03d98c83461aa4ed83d","target":"record","created_at":"2026-05-18T02:17:33Z","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":"a0399ee5ac925681462ab14bc9467e46f6871c71ff7a2e78110099dfc26e994d","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2014-04-21T12:58:38Z","title_canon_sha256":"3d4d00c3d6e55be404444c83ddcb6ce43645e9bc3378a0dabf434540d27f0689"},"schema_version":"1.0","source":{"id":"1404.5184","kind":"arxiv","version":3}},"canonical_sha256":"c4687bfd529b476e6d2d671d6b0777f85a3496378700c695172626e3f9494697","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c4687bfd529b476e6d2d671d6b0777f85a3496378700c695172626e3f9494697","first_computed_at":"2026-05-18T02:17:33.846598Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:17:33.846598Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"M78XahrbniStLfAd+CwCQ1MVtFAshKswsvLxWInXQcHPPf4+PAcxbB5qrd5SAv+2m59wHC2geHT2djE+KI5jDw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:17:33.847325Z","signed_message":"canonical_sha256_bytes"},"source_id":"1404.5184","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:994a0efe6068deca10bba7b20e0401eefba7fe1d58a5f03d98c83461aa4ed83d","sha256:812d60730f4c86461d8997a0644c76df3c39a651e2d2b45a4b10d9289baa97b1"],"state_sha256":"0c652493e5ce944157e6d4684f4fdd1316417afdf70a9d1d0e35ec903a7e2b9b"}