{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:HKZ7UUP2BDCEGF5MMCSMWLSRNT","short_pith_number":"pith:HKZ7UUP2","canonical_record":{"source":{"id":"1108.1445","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2011-08-06T03:52:15Z","cross_cats_sorted":["cs.LO"],"title_canon_sha256":"5e20b41317db1cad30ecf27ca2b4361af59acb2d464f86d2bbd7fec0b9a3f28e","abstract_canon_sha256":"9dcdae5f34745d1408d189c428cff70a4b393170da6e498db49fedd058776231"},"schema_version":"1.0"},"canonical_sha256":"3ab3fa51fa08c44317ac60a4cb2e516cd81178ad1aff27c32bef7792e5dab08d","source":{"kind":"arxiv","id":"1108.1445","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.1445","created_at":"2026-05-18T03:41:29Z"},{"alias_kind":"arxiv_version","alias_value":"1108.1445v2","created_at":"2026-05-18T03:41:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.1445","created_at":"2026-05-18T03:41:29Z"},{"alias_kind":"pith_short_12","alias_value":"HKZ7UUP2BDCE","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"HKZ7UUP2BDCEGF5M","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"HKZ7UUP2","created_at":"2026-05-18T12:26:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:HKZ7UUP2BDCEGF5MMCSMWLSRNT","target":"record","payload":{"canonical_record":{"source":{"id":"1108.1445","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2011-08-06T03:52:15Z","cross_cats_sorted":["cs.LO"],"title_canon_sha256":"5e20b41317db1cad30ecf27ca2b4361af59acb2d464f86d2bbd7fec0b9a3f28e","abstract_canon_sha256":"9dcdae5f34745d1408d189c428cff70a4b393170da6e498db49fedd058776231"},"schema_version":"1.0"},"canonical_sha256":"3ab3fa51fa08c44317ac60a4cb2e516cd81178ad1aff27c32bef7792e5dab08d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:41:29.626098Z","signature_b64":"HTpQOa9YAo8bBObvQCt9zjM+Jo/ljzSkFLFI1SK892MlX2eQODUojqeyb+FV1W/li4dMxerTXemiy/0sW5VvBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3ab3fa51fa08c44317ac60a4cb2e516cd81178ad1aff27c32bef7792e5dab08d","last_reissued_at":"2026-05-18T03:41:29.625391Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:41:29.625391Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1108.1445","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:41:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TRbRkEWJSk905Z6dzsXt89uelb9C9HZoU/+1IY6ScFcKg5sELeH+XAtwcpsMyEeGXCaMXbcz8m02JN5WKPWgBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T09:37:34.305102Z"},"content_sha256":"340a1dbd8a597b433c9c74413d3b67cf2361d2e655e81b70747d7dfa4fd01132","schema_version":"1.0","event_id":"sha256:340a1dbd8a597b433c9c74413d3b67cf2361d2e655e81b70747d7dfa4fd01132"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:HKZ7UUP2BDCEGF5MMCSMWLSRNT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quasi-Polish Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LO"],"primary_cat":"math.LO","authors_text":"Matthew de Brecht","submitted_at":"2011-08-06T03:52:15Z","abstract_excerpt":"We investigate some basic descriptive set theory for countably based completely quasi-metrizable topological spaces, which we refer to as quasi-Polish spaces. These spaces naturally generalize much of the classical descriptive set theory of Polish spaces to the non-Hausdorff setting. We show that a subspace of a quasi-Polish space is quasi-Polish if and only if it is level \\Pi_2 in the Borel hierarchy. Quasi-Polish spaces can be characterized within the framework of Type-2 Theory of Effectivity as precisely the countably based spaces that have an admissible representation with a Polish domain."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.1445","kind":"arxiv","version":2},"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":"2026-05-18T03:41:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"A7keckaT0RIyBNW5/+wAQ7c2FKFI6n7hHNcqNfB+Blx5FL8iy8g5t6d/09qgC7Ab3qNGIHkBwlGcap2I7s/FBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T09:37:34.305464Z"},"content_sha256":"b0e809a1811a056d74290b70fe33c59a80d8a07ff630b56adeef27c3f13b9faf","schema_version":"1.0","event_id":"sha256:b0e809a1811a056d74290b70fe33c59a80d8a07ff630b56adeef27c3f13b9faf"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HKZ7UUP2BDCEGF5MMCSMWLSRNT/bundle.json","state_url":"https://pith.science/pith/HKZ7UUP2BDCEGF5MMCSMWLSRNT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HKZ7UUP2BDCEGF5MMCSMWLSRNT/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":"2026-06-09T09:37:34Z","links":{"resolver":"https://pith.science/pith/HKZ7UUP2BDCEGF5MMCSMWLSRNT","bundle":"https://pith.science/pith/HKZ7UUP2BDCEGF5MMCSMWLSRNT/bundle.json","state":"https://pith.science/pith/HKZ7UUP2BDCEGF5MMCSMWLSRNT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HKZ7UUP2BDCEGF5MMCSMWLSRNT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:HKZ7UUP2BDCEGF5MMCSMWLSRNT","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":"9dcdae5f34745d1408d189c428cff70a4b393170da6e498db49fedd058776231","cross_cats_sorted":["cs.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2011-08-06T03:52:15Z","title_canon_sha256":"5e20b41317db1cad30ecf27ca2b4361af59acb2d464f86d2bbd7fec0b9a3f28e"},"schema_version":"1.0","source":{"id":"1108.1445","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.1445","created_at":"2026-05-18T03:41:29Z"},{"alias_kind":"arxiv_version","alias_value":"1108.1445v2","created_at":"2026-05-18T03:41:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.1445","created_at":"2026-05-18T03:41:29Z"},{"alias_kind":"pith_short_12","alias_value":"HKZ7UUP2BDCE","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"HKZ7UUP2BDCEGF5M","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"HKZ7UUP2","created_at":"2026-05-18T12:26:30Z"}],"graph_snapshots":[{"event_id":"sha256:b0e809a1811a056d74290b70fe33c59a80d8a07ff630b56adeef27c3f13b9faf","target":"graph","created_at":"2026-05-18T03:41:29Z","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":"We investigate some basic descriptive set theory for countably based completely quasi-metrizable topological spaces, which we refer to as quasi-Polish spaces. These spaces naturally generalize much of the classical descriptive set theory of Polish spaces to the non-Hausdorff setting. We show that a subspace of a quasi-Polish space is quasi-Polish if and only if it is level \\Pi_2 in the Borel hierarchy. Quasi-Polish spaces can be characterized within the framework of Type-2 Theory of Effectivity as precisely the countably based spaces that have an admissible representation with a Polish domain.","authors_text":"Matthew de Brecht","cross_cats":["cs.LO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2011-08-06T03:52:15Z","title":"Quasi-Polish Spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.1445","kind":"arxiv","version":2},"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":"sha256:340a1dbd8a597b433c9c74413d3b67cf2361d2e655e81b70747d7dfa4fd01132","target":"record","created_at":"2026-05-18T03:41:29Z","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":"9dcdae5f34745d1408d189c428cff70a4b393170da6e498db49fedd058776231","cross_cats_sorted":["cs.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2011-08-06T03:52:15Z","title_canon_sha256":"5e20b41317db1cad30ecf27ca2b4361af59acb2d464f86d2bbd7fec0b9a3f28e"},"schema_version":"1.0","source":{"id":"1108.1445","kind":"arxiv","version":2}},"canonical_sha256":"3ab3fa51fa08c44317ac60a4cb2e516cd81178ad1aff27c32bef7792e5dab08d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3ab3fa51fa08c44317ac60a4cb2e516cd81178ad1aff27c32bef7792e5dab08d","first_computed_at":"2026-05-18T03:41:29.625391Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:41:29.625391Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HTpQOa9YAo8bBObvQCt9zjM+Jo/ljzSkFLFI1SK892MlX2eQODUojqeyb+FV1W/li4dMxerTXemiy/0sW5VvBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:41:29.626098Z","signed_message":"canonical_sha256_bytes"},"source_id":"1108.1445","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:340a1dbd8a597b433c9c74413d3b67cf2361d2e655e81b70747d7dfa4fd01132","sha256:b0e809a1811a056d74290b70fe33c59a80d8a07ff630b56adeef27c3f13b9faf"],"state_sha256":"809821cfc2ac8860457a1ad22ef93a71592a09ce8e49df4ca4db1fca9c5951cc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bk9ZNZFoBDcLQwXh2qsEKzUZiCEHYvf5+G5Yg6K+t34l24Y8MIPZZfpS6JOJP1bktgKOu8H/6xTg2lViPt7ODQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T09:37:34.307494Z","bundle_sha256":"aa995292b477d6af3e0ffabcd332fb166469ade08f5f59c82729f1142be5d6f6"}}