{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:NAHHQG2GOTHSI56IS2PKFYH2JI","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":"f46997fe76fab861c0d2aef31e9adabc5bf80e16a37d3e3bbf15409ad8312023","cross_cats_sorted":["math.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2015-09-04T11:57:23Z","title_canon_sha256":"9efb0a9aaf0a98383aaed472807366d1aba31668908e9d8c54e6e172d35a0684"},"schema_version":"1.0","source":{"id":"1509.01420","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.01420","created_at":"2026-05-18T01:33:57Z"},{"alias_kind":"arxiv_version","alias_value":"1509.01420v1","created_at":"2026-05-18T01:33:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.01420","created_at":"2026-05-18T01:33:57Z"},{"alias_kind":"pith_short_12","alias_value":"NAHHQG2GOTHS","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"NAHHQG2GOTHSI56I","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"NAHHQG2G","created_at":"2026-05-18T12:29:32Z"}],"graph_snapshots":[{"event_id":"sha256:530f3d27caf1deb9dc299b30e8bb8ce6999e355f620e08abc74620a792e3b91b","target":"graph","created_at":"2026-05-18T01:33:57Z","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":"All spaces are assumed to be infinite Hausdorff spaces. We call a space \"anti-Urysohn\" $($AU in short$)$ iff any two non-emty regular closed sets in it intersect. We prove that\n  $\\bullet$ for every infinite cardinal ${\\kappa}$ there is a space of size ${\\kappa}$ in which fewer than $cf({\\kappa})$ many non-empty regular closed sets always intersect;\n  $\\bullet$ there is a locally countable AU space of size $\\kappa$ iff $\\omega \\le \\kappa \\le 2^{\\mathfrak c}$.\n  A space with at least two non-isolated points is called \"strongly anti-Urysohn\" $($SAU in short$)$ iff any two infinite closed sets in","authors_text":"Istv\\'an Juh\\'asz, Lajos Soukup, Zolt\\'an Szentmikl\\'ossy","cross_cats":["math.LO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2015-09-04T11:57:23Z","title":"Anti-Urysohn spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.01420","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:c513938ecc2b812b8e2a14fba34498c5135d4434af7df0d1f7c09bb5bac823e3","target":"record","created_at":"2026-05-18T01:33:57Z","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":"f46997fe76fab861c0d2aef31e9adabc5bf80e16a37d3e3bbf15409ad8312023","cross_cats_sorted":["math.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2015-09-04T11:57:23Z","title_canon_sha256":"9efb0a9aaf0a98383aaed472807366d1aba31668908e9d8c54e6e172d35a0684"},"schema_version":"1.0","source":{"id":"1509.01420","kind":"arxiv","version":1}},"canonical_sha256":"680e781b4674cf2477c8969ea2e0fa4a1f607b149ccaca28e115894900168753","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"680e781b4674cf2477c8969ea2e0fa4a1f607b149ccaca28e115894900168753","first_computed_at":"2026-05-18T01:33:57.711734Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:33:57.711734Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ocvSwNUl9mZujOk3KS5x5VtgTy68HaIyT7mwrw4CxzDE1SM8hlA0uwaLEY3XTPYRSxlGYcA7FDyrZJuYgMStBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:33:57.712091Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.01420","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c513938ecc2b812b8e2a14fba34498c5135d4434af7df0d1f7c09bb5bac823e3","sha256:530f3d27caf1deb9dc299b30e8bb8ce6999e355f620e08abc74620a792e3b91b"],"state_sha256":"6e113cb0d217dd939af774f05f04841c5692fc78e6251edff50bb1b5e9903e0b"}