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(Of course, in this definition we could replace \"open\" with \"closed\".)\n  In this paper we prove the following two results:\n  (1) Every Lindel\\\"of-generated regular space $X$ satisfying $|X|=\\Delta(X)={\\omega}_1$ is ${\\omega}_1$-resolvable.\n  (2) Any (countable extent)-generated regular space $X$ satisfying $\\Delta(X)>{\\omega}$ is ${\\omega}$-resolvable.\n  These are significa"},"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":"1804.03019","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2018-04-09T14:24:38Z","cross_cats_sorted":[],"title_canon_sha256":"9b23259c045bdea033e708c5e2019c946df73a7060eb7463e558a8f606f6cfac","abstract_canon_sha256":"02972b3e4e3adf8cc77cc9cae275e1f9d6d3a4d01491f22b8bee782c3a550864"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:18:57.648117Z","signature_b64":"ADEJoOw8MavLVHZQTGZr2oYJ5FqdYClRk2MVLy0ucbxSDPSNG/c6hE0fKRA0+22WurVFCcY0Xk3BHlCRcSClAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4889e18adb4b2fe1319f4675eed61dfc0c0489319ab404e3792195791900e20a","last_reissued_at":"2026-05-18T00:18:57.647552Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:18:57.647552Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the resolvability of Lindel\\\"of-generated and (countable extent)-generated spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Istv\\'an Juh\\'asz, Lajos Soukup, Zolt\\'an Szentmikl\\'ossy","submitted_at":"2018-04-09T14:24:38Z","abstract_excerpt":"Given a topological property $P$, we say that the space $X$ is $P$-generated if for any subset $A\\subset X$ that is not open in $X$ there is a subspace $Y \\subset X$ with property $P$ such that $A\\cap Y$ is not open in $Y$. (Of course, in this definition we could replace \"open\" with \"closed\".)\n  In this paper we prove the following two results:\n  (1) Every Lindel\\\"of-generated regular space $X$ satisfying $|X|=\\Delta(X)={\\omega}_1$ is ${\\omega}_1$-resolvable.\n  (2) Any (countable extent)-generated regular space $X$ satisfying $\\Delta(X)>{\\omega}$ is ${\\omega}$-resolvable.\n  These are significa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.03019","kind":"arxiv","version":1},"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":"1804.03019","created_at":"2026-05-18T00:18:57.647652+00:00"},{"alias_kind":"arxiv_version","alias_value":"1804.03019v1","created_at":"2026-05-18T00:18:57.647652+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.03019","created_at":"2026-05-18T00:18:57.647652+00:00"},{"alias_kind":"pith_short_12","alias_value":"JCE6DCW3JMX6","created_at":"2026-05-18T12:32:31.084164+00:00"},{"alias_kind":"pith_short_16","alias_value":"JCE6DCW3JMX6CMM7","created_at":"2026-05-18T12:32:31.084164+00:00"},{"alias_kind":"pith_short_8","alias_value":"JCE6DCW3","created_at":"2026-05-18T12:32:31.084164+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/JCE6DCW3JMX6CMM7IZ265VQ57Q","json":"https://pith.science/pith/JCE6DCW3JMX6CMM7IZ265VQ57Q.json","graph_json":"https://pith.science/api/pith-number/JCE6DCW3JMX6CMM7IZ265VQ57Q/graph.json","events_json":"https://pith.science/api/pith-number/JCE6DCW3JMX6CMM7IZ265VQ57Q/events.json","paper":"https://pith.science/paper/JCE6DCW3"},"agent_actions":{"view_html":"https://pith.science/pith/JCE6DCW3JMX6CMM7IZ265VQ57Q","download_json":"https://pith.science/pith/JCE6DCW3JMX6CMM7IZ265VQ57Q.json","view_paper":"https://pith.science/paper/JCE6DCW3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1804.03019&json=true","fetch_graph":"https://pith.science/api/pith-number/JCE6DCW3JMX6CMM7IZ265VQ57Q/graph.json","fetch_events":"https://pith.science/api/pith-number/JCE6DCW3JMX6CMM7IZ265VQ57Q/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JCE6DCW3JMX6CMM7IZ265VQ57Q/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JCE6DCW3JMX6CMM7IZ265VQ57Q/action/storage_attestation","attest_author":"https://pith.science/pith/JCE6DCW3JMX6CMM7IZ265VQ57Q/action/author_attestation","sign_citation":"https://pith.science/pith/JCE6DCW3JMX6CMM7IZ265VQ57Q/action/citation_signature","submit_replication":"https://pith.science/pith/JCE6DCW3JMX6CMM7IZ265VQ57Q/action/replication_record"}},"created_at":"2026-05-18T00:18:57.647652+00:00","updated_at":"2026-05-18T00:18:57.647652+00:00"}