{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:X5X5TBDVNXGKSWCKHQ774U7Y6M","short_pith_number":"pith:X5X5TBDV","schema_version":"1.0","canonical_sha256":"bf6fd984756dcca9584a3c3ffe53f8f3280c3572fe4ebde7d318bd5b40ffdb89","source":{"kind":"arxiv","id":"1307.1989","version":1},"attestation_state":"computed","paper":{"title":"Strong colorings yield kappa-bounded spaces with discretely untouchable points","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Istvan Juhasz, Saharon Shelah","submitted_at":"2013-07-08T09:10:09Z","abstract_excerpt":"It is well-known that every non-isolated point in a compact Hausdorff space is the accumulation point of a discrete subset. Answering a question raised by Z. Szentmiklossy and the first author, we show that this statement fails for countably compact regular spaces, and even for omega-bounded regular spaces. In fact, there are kappa-bounded counterexamples for every infinite cardinal kappa. The proof makes essential use of the so-called 'strong colorings' that were invented by the second author."},"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":"1307.1989","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2013-07-08T09:10:09Z","cross_cats_sorted":[],"title_canon_sha256":"95678542cee37bca51e20c9993aa2de7c123b23e5f04de11812b8e3144d119be","abstract_canon_sha256":"7ad482156013cd7feed7fb74c31f107bd5826aa260a4dba21b42c80ee33d7822"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:19:02.860068Z","signature_b64":"F9zGl1f7PKLWRGnAXz/PeUuOtLRuHodpMhdJS0uv//T8AO+0bkRQFYaEW6C3p15Clu6xZkhEY+Cx58ZKmRSGDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bf6fd984756dcca9584a3c3ffe53f8f3280c3572fe4ebde7d318bd5b40ffdb89","last_reissued_at":"2026-05-18T03:19:02.859550Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:19:02.859550Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Strong colorings yield kappa-bounded spaces with discretely untouchable points","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Istvan Juhasz, Saharon Shelah","submitted_at":"2013-07-08T09:10:09Z","abstract_excerpt":"It is well-known that every non-isolated point in a compact Hausdorff space is the accumulation point of a discrete subset. Answering a question raised by Z. Szentmiklossy and the first author, we show that this statement fails for countably compact regular spaces, and even for omega-bounded regular spaces. In fact, there are kappa-bounded counterexamples for every infinite cardinal kappa. The proof makes essential use of the so-called 'strong colorings' that were invented by the second author."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.1989","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":"1307.1989","created_at":"2026-05-18T03:19:02.859633+00:00"},{"alias_kind":"arxiv_version","alias_value":"1307.1989v1","created_at":"2026-05-18T03:19:02.859633+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.1989","created_at":"2026-05-18T03:19:02.859633+00:00"},{"alias_kind":"pith_short_12","alias_value":"X5X5TBDVNXGK","created_at":"2026-05-18T12:28:06.772260+00:00"},{"alias_kind":"pith_short_16","alias_value":"X5X5TBDVNXGKSWCK","created_at":"2026-05-18T12:28:06.772260+00:00"},{"alias_kind":"pith_short_8","alias_value":"X5X5TBDV","created_at":"2026-05-18T12:28:06.772260+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/X5X5TBDVNXGKSWCKHQ774U7Y6M","json":"https://pith.science/pith/X5X5TBDVNXGKSWCKHQ774U7Y6M.json","graph_json":"https://pith.science/api/pith-number/X5X5TBDVNXGKSWCKHQ774U7Y6M/graph.json","events_json":"https://pith.science/api/pith-number/X5X5TBDVNXGKSWCKHQ774U7Y6M/events.json","paper":"https://pith.science/paper/X5X5TBDV"},"agent_actions":{"view_html":"https://pith.science/pith/X5X5TBDVNXGKSWCKHQ774U7Y6M","download_json":"https://pith.science/pith/X5X5TBDVNXGKSWCKHQ774U7Y6M.json","view_paper":"https://pith.science/paper/X5X5TBDV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1307.1989&json=true","fetch_graph":"https://pith.science/api/pith-number/X5X5TBDVNXGKSWCKHQ774U7Y6M/graph.json","fetch_events":"https://pith.science/api/pith-number/X5X5TBDVNXGKSWCKHQ774U7Y6M/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/X5X5TBDVNXGKSWCKHQ774U7Y6M/action/timestamp_anchor","attest_storage":"https://pith.science/pith/X5X5TBDVNXGKSWCKHQ774U7Y6M/action/storage_attestation","attest_author":"https://pith.science/pith/X5X5TBDVNXGKSWCKHQ774U7Y6M/action/author_attestation","sign_citation":"https://pith.science/pith/X5X5TBDVNXGKSWCKHQ774U7Y6M/action/citation_signature","submit_replication":"https://pith.science/pith/X5X5TBDVNXGKSWCKHQ774U7Y6M/action/replication_record"}},"created_at":"2026-05-18T03:19:02.859633+00:00","updated_at":"2026-05-18T03:19:02.859633+00:00"}