{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:4KJOQTW6Z25NFHYHDSRQR44VBL","short_pith_number":"pith:4KJOQTW6","canonical_record":{"source":{"id":"1607.07291","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2016-07-25T14:28:18Z","cross_cats_sorted":["cs.LO"],"title_canon_sha256":"5453969c837348cfca626b1562c5f094ec0e5f73e7f4774076133a9ff17f9150","abstract_canon_sha256":"75f4df7dc7c5c66342d04bc816e097fbdce415e33fb5ca7fdea8b09f70f1f418"},"schema_version":"1.0"},"canonical_sha256":"e292e84edecebad29f071ca308f3950af50e03f45523c949e3443ce0c98c41dc","source":{"kind":"arxiv","id":"1607.07291","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.07291","created_at":"2026-05-18T00:52:34Z"},{"alias_kind":"arxiv_version","alias_value":"1607.07291v2","created_at":"2026-05-18T00:52:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.07291","created_at":"2026-05-18T00:52:34Z"},{"alias_kind":"pith_short_12","alias_value":"4KJOQTW6Z25N","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_16","alias_value":"4KJOQTW6Z25NFHYH","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_8","alias_value":"4KJOQTW6","created_at":"2026-05-18T12:29:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:4KJOQTW6Z25NFHYHDSRQR44VBL","target":"record","payload":{"canonical_record":{"source":{"id":"1607.07291","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2016-07-25T14:28:18Z","cross_cats_sorted":["cs.LO"],"title_canon_sha256":"5453969c837348cfca626b1562c5f094ec0e5f73e7f4774076133a9ff17f9150","abstract_canon_sha256":"75f4df7dc7c5c66342d04bc816e097fbdce415e33fb5ca7fdea8b09f70f1f418"},"schema_version":"1.0"},"canonical_sha256":"e292e84edecebad29f071ca308f3950af50e03f45523c949e3443ce0c98c41dc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:52:34.182585Z","signature_b64":"HRV+Zw4+JlGOkl3BLMNT6BQb+Cy6SO1OSK4n5AanKfjjipZkk5NRVL/FyQ0oQj/VH0QMU++OFiHKykYeSpznAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e292e84edecebad29f071ca308f3950af50e03f45523c949e3443ce0c98c41dc","last_reissued_at":"2026-05-18T00:52:34.182170Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:52:34.182170Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1607.07291","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":"2026-05-18T00:52:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"M64+pXnlIomtRHKtFvK40laLbJ8JhB+Hf3BP+rcXAqKXmw6Wpht+M+cm9R8EUCG3ez/SyFwQ0Ctl/G2EbLHhAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T13:59:40.591124Z"},"content_sha256":"1e05a033c5eede92e0ff29ae08f65a421409ea91abc7f62ddebcc01766bda973","schema_version":"1.0","event_id":"sha256:1e05a033c5eede92e0ff29ae08f65a421409ea91abc7f62ddebcc01766bda973"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:4KJOQTW6Z25NFHYHDSRQR44VBL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Noetherian Quasi-Polish Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LO"],"primary_cat":"math.GN","authors_text":"Arno Pauly, Matthew de Brecht","submitted_at":"2016-07-25T14:28:18Z","abstract_excerpt":"In the presence of suitable power spaces, compactness of $\\mathbf{X}$ can be characterized as the singleton $\\{X\\}$ being open in the space $\\mathcal{O}(\\mathbf{X})$ of open subsets of $\\mathbf{X}$. Equivalently, this means that universal quantification over a compact space preserves open predicates.\n  Using the language of represented spaces, one can make sense of notions such as a $\\Sigma^0_2$-subset of the space of $\\Sigma^0_2$-subsets of a given space. This suggests higher-order analogues to compactness: We can, e.g.~, investigate the spaces $\\mathbf{X}$ where $\\{X\\}$ is a $\\Delta^0_2$-sub"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.07291","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":"2026-05-18T00:52:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"paUsKPXgWegFUEqiye/PX+II1Ye4pfkKMJMkFSyb/TWjge5QCMewjQExw6bga1GXmjeKWLgFwtFf6lfObdF/Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T13:59:40.591513Z"},"content_sha256":"2d1214b1355f4ef96343279b51aed1decc9dccd6fe7dc7078412273bdeb7f86d","schema_version":"1.0","event_id":"sha256:2d1214b1355f4ef96343279b51aed1decc9dccd6fe7dc7078412273bdeb7f86d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4KJOQTW6Z25NFHYHDSRQR44VBL/bundle.json","state_url":"https://pith.science/pith/4KJOQTW6Z25NFHYHDSRQR44VBL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4KJOQTW6Z25NFHYHDSRQR44VBL/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":"2026-06-09T13:59:40Z","links":{"resolver":"https://pith.science/pith/4KJOQTW6Z25NFHYHDSRQR44VBL","bundle":"https://pith.science/pith/4KJOQTW6Z25NFHYHDSRQR44VBL/bundle.json","state":"https://pith.science/pith/4KJOQTW6Z25NFHYHDSRQR44VBL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4KJOQTW6Z25NFHYHDSRQR44VBL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:4KJOQTW6Z25NFHYHDSRQR44VBL","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":"75f4df7dc7c5c66342d04bc816e097fbdce415e33fb5ca7fdea8b09f70f1f418","cross_cats_sorted":["cs.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2016-07-25T14:28:18Z","title_canon_sha256":"5453969c837348cfca626b1562c5f094ec0e5f73e7f4774076133a9ff17f9150"},"schema_version":"1.0","source":{"id":"1607.07291","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.07291","created_at":"2026-05-18T00:52:34Z"},{"alias_kind":"arxiv_version","alias_value":"1607.07291v2","created_at":"2026-05-18T00:52:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.07291","created_at":"2026-05-18T00:52:34Z"},{"alias_kind":"pith_short_12","alias_value":"4KJOQTW6Z25N","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_16","alias_value":"4KJOQTW6Z25NFHYH","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_8","alias_value":"4KJOQTW6","created_at":"2026-05-18T12:29:58Z"}],"graph_snapshots":[{"event_id":"sha256:2d1214b1355f4ef96343279b51aed1decc9dccd6fe7dc7078412273bdeb7f86d","target":"graph","created_at":"2026-05-18T00:52:34Z","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":"In the presence of suitable power spaces, compactness of $\\mathbf{X}$ can be characterized as the singleton $\\{X\\}$ being open in the space $\\mathcal{O}(\\mathbf{X})$ of open subsets of $\\mathbf{X}$. Equivalently, this means that universal quantification over a compact space preserves open predicates.\n  Using the language of represented spaces, one can make sense of notions such as a $\\Sigma^0_2$-subset of the space of $\\Sigma^0_2$-subsets of a given space. This suggests higher-order analogues to compactness: We can, e.g.~, investigate the spaces $\\mathbf{X}$ where $\\{X\\}$ is a $\\Delta^0_2$-sub","authors_text":"Arno Pauly, Matthew de Brecht","cross_cats":["cs.LO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2016-07-25T14:28:18Z","title":"Noetherian Quasi-Polish Spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.07291","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":"sha256:1e05a033c5eede92e0ff29ae08f65a421409ea91abc7f62ddebcc01766bda973","target":"record","created_at":"2026-05-18T00:52:34Z","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":"75f4df7dc7c5c66342d04bc816e097fbdce415e33fb5ca7fdea8b09f70f1f418","cross_cats_sorted":["cs.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2016-07-25T14:28:18Z","title_canon_sha256":"5453969c837348cfca626b1562c5f094ec0e5f73e7f4774076133a9ff17f9150"},"schema_version":"1.0","source":{"id":"1607.07291","kind":"arxiv","version":2}},"canonical_sha256":"e292e84edecebad29f071ca308f3950af50e03f45523c949e3443ce0c98c41dc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e292e84edecebad29f071ca308f3950af50e03f45523c949e3443ce0c98c41dc","first_computed_at":"2026-05-18T00:52:34.182170Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:52:34.182170Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HRV+Zw4+JlGOkl3BLMNT6BQb+Cy6SO1OSK4n5AanKfjjipZkk5NRVL/FyQ0oQj/VH0QMU++OFiHKykYeSpznAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:52:34.182585Z","signed_message":"canonical_sha256_bytes"},"source_id":"1607.07291","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1e05a033c5eede92e0ff29ae08f65a421409ea91abc7f62ddebcc01766bda973","sha256:2d1214b1355f4ef96343279b51aed1decc9dccd6fe7dc7078412273bdeb7f86d"],"state_sha256":"7a6e70f8c6d3780607022659aa673565a3accf16ca6a15d383ba155961b326e4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mT4RvaOM/60omd4/SfPZx3S7MRY+9iKnlTIX4gkjrFmHHp54jK+JL0+515xiTpWGbci4tFmiPCjAtr4D+HPfDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T13:59:40.594044Z","bundle_sha256":"a7fdcc6b7e86f151d54a11cb3e137813d36da3680cc57e46389f2a137244b2b2"}}