{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:D76PTA3BIPFTGWMBTSK5A7MMRC","short_pith_number":"pith:D76PTA3B","schema_version":"1.0","canonical_sha256":"1ffcf9836143cb3359819c95d07d8c888709092d95b0629f620cc0fb2e22d476","source":{"kind":"arxiv","id":"1109.1736","version":1},"attestation_state":"computed","paper":{"title":"Elementary chains and compact spaces with a small diagonal","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.LO"],"primary_cat":"math.GN","authors_text":"Alan Dow, Klaas Pieter Hart","submitted_at":"2011-09-08T15:00:34Z","abstract_excerpt":"It is a well known open problem if, in ZFC, each compact space with a small diagonal is metrizable. We explore properties of compact spaces with a small diagonal using elementary chains of submodels. We prove that ccc subspaces of such spaces have countable \\pi-weight. We generalize a result of Gruenhage about spaces which are metrizably fibered. Finally we discover that if there is a Luzin set of reals, then every compact space with a small diagonal will have many points of countable character."},"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":"1109.1736","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2011-09-08T15:00:34Z","cross_cats_sorted":["math.LO"],"title_canon_sha256":"be2a0344a363cc0da212f994a9216d18e8aae62b2b3eaa9a4f671a0d310c8ded","abstract_canon_sha256":"6f456d95d069f35dc7f989efee9d509578422064c9b513f6f7ae74aa36ef187a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:50:22.054425Z","signature_b64":"OJsjg/PVzEONW9GE1X91X1KqZlMUqMhNf/94E5cGi7JBAmtP2l1uOCQltq2AqrYnq1DTI2SlXd61mVpQ/XSIBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1ffcf9836143cb3359819c95d07d8c888709092d95b0629f620cc0fb2e22d476","last_reissued_at":"2026-05-18T03:50:22.053444Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:50:22.053444Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Elementary chains and compact spaces with a small diagonal","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.LO"],"primary_cat":"math.GN","authors_text":"Alan Dow, Klaas Pieter Hart","submitted_at":"2011-09-08T15:00:34Z","abstract_excerpt":"It is a well known open problem if, in ZFC, each compact space with a small diagonal is metrizable. We explore properties of compact spaces with a small diagonal using elementary chains of submodels. We prove that ccc subspaces of such spaces have countable \\pi-weight. We generalize a result of Gruenhage about spaces which are metrizably fibered. Finally we discover that if there is a Luzin set of reals, then every compact space with a small diagonal will have many points of countable character."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.1736","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":"1109.1736","created_at":"2026-05-18T03:50:22.053590+00:00"},{"alias_kind":"arxiv_version","alias_value":"1109.1736v1","created_at":"2026-05-18T03:50:22.053590+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.1736","created_at":"2026-05-18T03:50:22.053590+00:00"},{"alias_kind":"pith_short_12","alias_value":"D76PTA3BIPFT","created_at":"2026-05-18T12:26:26.731475+00:00"},{"alias_kind":"pith_short_16","alias_value":"D76PTA3BIPFTGWMB","created_at":"2026-05-18T12:26:26.731475+00:00"},{"alias_kind":"pith_short_8","alias_value":"D76PTA3B","created_at":"2026-05-18T12:26:26.731475+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/D76PTA3BIPFTGWMBTSK5A7MMRC","json":"https://pith.science/pith/D76PTA3BIPFTGWMBTSK5A7MMRC.json","graph_json":"https://pith.science/api/pith-number/D76PTA3BIPFTGWMBTSK5A7MMRC/graph.json","events_json":"https://pith.science/api/pith-number/D76PTA3BIPFTGWMBTSK5A7MMRC/events.json","paper":"https://pith.science/paper/D76PTA3B"},"agent_actions":{"view_html":"https://pith.science/pith/D76PTA3BIPFTGWMBTSK5A7MMRC","download_json":"https://pith.science/pith/D76PTA3BIPFTGWMBTSK5A7MMRC.json","view_paper":"https://pith.science/paper/D76PTA3B","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1109.1736&json=true","fetch_graph":"https://pith.science/api/pith-number/D76PTA3BIPFTGWMBTSK5A7MMRC/graph.json","fetch_events":"https://pith.science/api/pith-number/D76PTA3BIPFTGWMBTSK5A7MMRC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/D76PTA3BIPFTGWMBTSK5A7MMRC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/D76PTA3BIPFTGWMBTSK5A7MMRC/action/storage_attestation","attest_author":"https://pith.science/pith/D76PTA3BIPFTGWMBTSK5A7MMRC/action/author_attestation","sign_citation":"https://pith.science/pith/D76PTA3BIPFTGWMBTSK5A7MMRC/action/citation_signature","submit_replication":"https://pith.science/pith/D76PTA3BIPFTGWMBTSK5A7MMRC/action/replication_record"}},"created_at":"2026-05-18T03:50:22.053590+00:00","updated_at":"2026-05-18T03:50:22.053590+00:00"}