{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:D76PTA3BIPFTGWMBTSK5A7MMRC","short_pith_number":"pith:D76PTA3B","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"},"canonical_sha256":"1ffcf9836143cb3359819c95d07d8c888709092d95b0629f620cc0fb2e22d476","source":{"kind":"arxiv","id":"1109.1736","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.1736","created_at":"2026-05-18T03:50:22Z"},{"alias_kind":"arxiv_version","alias_value":"1109.1736v1","created_at":"2026-05-18T03:50:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.1736","created_at":"2026-05-18T03:50:22Z"},{"alias_kind":"pith_short_12","alias_value":"D76PTA3BIPFT","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"D76PTA3BIPFTGWMB","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"D76PTA3B","created_at":"2026-05-18T12:26:26Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:D76PTA3BIPFTGWMBTSK5A7MMRC","target":"record","payload":{"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"},"canonical_sha256":"1ffcf9836143cb3359819c95d07d8c888709092d95b0629f620cc0fb2e22d476","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"},"source_kind":"arxiv","source_id":"1109.1736","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:50:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KirXIaIuLCC4TpZi9hB5FElcGMK+4HHAD9cUPN4kc09fTTN0LlJTwQPybiLRBxAyN7T2KylUlUJE42/I/1HYBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T09:56:38.100284Z"},"content_sha256":"366239279b156f0b748cdc91cb297d0e5d3cf994a3dea1afa8f3a3e033d03206","schema_version":"1.0","event_id":"sha256:366239279b156f0b748cdc91cb297d0e5d3cf994a3dea1afa8f3a3e033d03206"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:D76PTA3BIPFTGWMBTSK5A7MMRC","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:50:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"svY5KjFz+DObVXGC4SOghLePsUDW+YZMP5JMo/wkEexfUXrR7XVkualaZytwgQNn9Y1hpigEAskmcaoHau/FBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T09:56:38.100866Z"},"content_sha256":"e567e4891e6b1841bac064c794062fde76858832604941bba88184a888eafd96","schema_version":"1.0","event_id":"sha256:e567e4891e6b1841bac064c794062fde76858832604941bba88184a888eafd96"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/D76PTA3BIPFTGWMBTSK5A7MMRC/bundle.json","state_url":"https://pith.science/pith/D76PTA3BIPFTGWMBTSK5A7MMRC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/D76PTA3BIPFTGWMBTSK5A7MMRC/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-31T09:56:38Z","links":{"resolver":"https://pith.science/pith/D76PTA3BIPFTGWMBTSK5A7MMRC","bundle":"https://pith.science/pith/D76PTA3BIPFTGWMBTSK5A7MMRC/bundle.json","state":"https://pith.science/pith/D76PTA3BIPFTGWMBTSK5A7MMRC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/D76PTA3BIPFTGWMBTSK5A7MMRC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:D76PTA3BIPFTGWMBTSK5A7MMRC","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":"6f456d95d069f35dc7f989efee9d509578422064c9b513f6f7ae74aa36ef187a","cross_cats_sorted":["math.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2011-09-08T15:00:34Z","title_canon_sha256":"be2a0344a363cc0da212f994a9216d18e8aae62b2b3eaa9a4f671a0d310c8ded"},"schema_version":"1.0","source":{"id":"1109.1736","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.1736","created_at":"2026-05-18T03:50:22Z"},{"alias_kind":"arxiv_version","alias_value":"1109.1736v1","created_at":"2026-05-18T03:50:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.1736","created_at":"2026-05-18T03:50:22Z"},{"alias_kind":"pith_short_12","alias_value":"D76PTA3BIPFT","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"D76PTA3BIPFTGWMB","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"D76PTA3B","created_at":"2026-05-18T12:26:26Z"}],"graph_snapshots":[{"event_id":"sha256:e567e4891e6b1841bac064c794062fde76858832604941bba88184a888eafd96","target":"graph","created_at":"2026-05-18T03:50:22Z","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":"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.","authors_text":"Alan Dow, Klaas Pieter Hart","cross_cats":["math.LO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2011-09-08T15:00:34Z","title":"Elementary chains and compact spaces with a small diagonal"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.1736","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":"sha256:366239279b156f0b748cdc91cb297d0e5d3cf994a3dea1afa8f3a3e033d03206","target":"record","created_at":"2026-05-18T03:50:22Z","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":"6f456d95d069f35dc7f989efee9d509578422064c9b513f6f7ae74aa36ef187a","cross_cats_sorted":["math.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2011-09-08T15:00:34Z","title_canon_sha256":"be2a0344a363cc0da212f994a9216d18e8aae62b2b3eaa9a4f671a0d310c8ded"},"schema_version":"1.0","source":{"id":"1109.1736","kind":"arxiv","version":1}},"canonical_sha256":"1ffcf9836143cb3359819c95d07d8c888709092d95b0629f620cc0fb2e22d476","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1ffcf9836143cb3359819c95d07d8c888709092d95b0629f620cc0fb2e22d476","first_computed_at":"2026-05-18T03:50:22.053444Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:50:22.053444Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OJsjg/PVzEONW9GE1X91X1KqZlMUqMhNf/94E5cGi7JBAmtP2l1uOCQltq2AqrYnq1DTI2SlXd61mVpQ/XSIBA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:50:22.054425Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.1736","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:366239279b156f0b748cdc91cb297d0e5d3cf994a3dea1afa8f3a3e033d03206","sha256:e567e4891e6b1841bac064c794062fde76858832604941bba88184a888eafd96"],"state_sha256":"d426511b2ac03243b7ac5998f2cb35db09e43f36b4640bd4d487451fc8f64e31"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1xHdu5E47yKTx1AfhfbNLmIy6+yGT9kVEu5qqqEO2sHKy+uOErQhrkfQoEE5HNCTIIN9y1h5h4rGcgHlq2WICw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T09:56:38.104528Z","bundle_sha256":"62114472af75c74594713d1bf9e950a35a73eb00e3391362b170126811c1b1d1"}}