{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:YRUHX7KSTNDW43JNM4OWWB3X7B","short_pith_number":"pith:YRUHX7KS","schema_version":"1.0","canonical_sha256":"c4687bfd529b476e6d2d671d6b0777f85a3496378700c695172626e3f9494697","source":{"kind":"arxiv","id":"1404.5184","version":3},"attestation_state":"computed","paper":{"title":"Tolerances induced by irredundant coverings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.RA","authors_text":"Jouni J\\\"arvinen, S\\'andor Radeleczki","submitted_at":"2014-04-21T12:58:38Z","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 $(U,\\lesssim_R)$} \\"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1404.5184","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2014-04-21T12:58:38Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"3d4d00c3d6e55be404444c83ddcb6ce43645e9bc3378a0dabf434540d27f0689","abstract_canon_sha256":"a0399ee5ac925681462ab14bc9467e46f6871c71ff7a2e78110099dfc26e994d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:17:33.847325Z","signature_b64":"M78XahrbniStLfAd+CwCQ1MVtFAshKswsvLxWInXQcHPPf4+PAcxbB5qrd5SAv+2m59wHC2geHT2djE+KI5jDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c4687bfd529b476e6d2d671d6b0777f85a3496378700c695172626e3f9494697","last_reissued_at":"2026-05-18T02:17:33.846598Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:17:33.846598Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Tolerances induced by irredundant coverings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.RA","authors_text":"Jouni J\\\"arvinen, S\\'andor Radeleczki","submitted_at":"2014-04-21T12:58:38Z","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 $(U,\\lesssim_R)$} \\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.5184","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1404.5184","created_at":"2026-05-18T02:17:33.846720+00:00"},{"alias_kind":"arxiv_version","alias_value":"1404.5184v3","created_at":"2026-05-18T02:17:33.846720+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.5184","created_at":"2026-05-18T02:17:33.846720+00:00"},{"alias_kind":"pith_short_12","alias_value":"YRUHX7KSTNDW","created_at":"2026-05-18T12:28:57.508820+00:00"},{"alias_kind":"pith_short_16","alias_value":"YRUHX7KSTNDW43JN","created_at":"2026-05-18T12:28:57.508820+00:00"},{"alias_kind":"pith_short_8","alias_value":"YRUHX7KS","created_at":"2026-05-18T12:28:57.508820+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/YRUHX7KSTNDW43JNM4OWWB3X7B","json":"https://pith.science/pith/YRUHX7KSTNDW43JNM4OWWB3X7B.json","graph_json":"https://pith.science/api/pith-number/YRUHX7KSTNDW43JNM4OWWB3X7B/graph.json","events_json":"https://pith.science/api/pith-number/YRUHX7KSTNDW43JNM4OWWB3X7B/events.json","paper":"https://pith.science/paper/YRUHX7KS"},"agent_actions":{"view_html":"https://pith.science/pith/YRUHX7KSTNDW43JNM4OWWB3X7B","download_json":"https://pith.science/pith/YRUHX7KSTNDW43JNM4OWWB3X7B.json","view_paper":"https://pith.science/paper/YRUHX7KS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1404.5184&json=true","fetch_graph":"https://pith.science/api/pith-number/YRUHX7KSTNDW43JNM4OWWB3X7B/graph.json","fetch_events":"https://pith.science/api/pith-number/YRUHX7KSTNDW43JNM4OWWB3X7B/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YRUHX7KSTNDW43JNM4OWWB3X7B/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YRUHX7KSTNDW43JNM4OWWB3X7B/action/storage_attestation","attest_author":"https://pith.science/pith/YRUHX7KSTNDW43JNM4OWWB3X7B/action/author_attestation","sign_citation":"https://pith.science/pith/YRUHX7KSTNDW43JNM4OWWB3X7B/action/citation_signature","submit_replication":"https://pith.science/pith/YRUHX7KSTNDW43JNM4OWWB3X7B/action/replication_record"}},"created_at":"2026-05-18T02:17:33.846720+00:00","updated_at":"2026-05-18T02:17:33.846720+00:00"}