{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:MBXOZ74KNAYX3SCGVIFCI3Z65R","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":"45261e687dffe2f814f7ddaa2a593b820bc80431333620c66ac6adf4463b5310","cross_cats_sorted":["math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2019-08-28T00:52:21Z","title_canon_sha256":"1b70675d33e390f9cbf39a7c753a5ce83ce237a76fdc703c01df7c74435733d3"},"schema_version":"1.0","source":{"id":"1908.10510","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.10510","created_at":"2026-07-05T07:56:39Z"},{"alias_kind":"arxiv_version","alias_value":"1908.10510v2","created_at":"2026-07-05T07:56:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.10510","created_at":"2026-07-05T07:56:39Z"},{"alias_kind":"pith_short_12","alias_value":"MBXOZ74KNAYX","created_at":"2026-07-05T07:56:39Z"},{"alias_kind":"pith_short_16","alias_value":"MBXOZ74KNAYX3SCG","created_at":"2026-07-05T07:56:39Z"},{"alias_kind":"pith_short_8","alias_value":"MBXOZ74K","created_at":"2026-07-05T07:56:39Z"}],"graph_snapshots":[{"event_id":"sha256:6a1f754bc929523abedc1aed9b46a547672612a0ee50c6cced9936e6c6b77bdc","target":"graph","created_at":"2026-07-05T07:56:39Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1908.10510/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove that the category $\\mathsf{SBor}$ of standard Borel spaces is the (bi-)initial object in the 2-category of countably complete Boolean (countably) extensive categories. This means that $\\mathsf{SBor}$ is the universal category admitting some familiar algebraic operations of countable arity (e.g., countable products, unions) obeying some simple compatibility conditions (e.g., products distribute over disjoint unions). More generally, for any infinite regular cardinal $\\kappa$, the dual of the category $\\kappa\\mathsf{Bool}_\\kappa$ of $\\kappa$-presented $\\kappa$-complete Boolean algebras ","authors_text":"Ruiyuan Chen","cross_cats":["math.CT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2019-08-28T00:52:21Z","title":"A universal characterization of standard Borel spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.10510","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":"sha256:59ac70e26ba145b8847db2156a226bad146b09badd89288235423f5a7e9c6ad4","target":"record","created_at":"2026-07-05T07:56:39Z","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":"45261e687dffe2f814f7ddaa2a593b820bc80431333620c66ac6adf4463b5310","cross_cats_sorted":["math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2019-08-28T00:52:21Z","title_canon_sha256":"1b70675d33e390f9cbf39a7c753a5ce83ce237a76fdc703c01df7c74435733d3"},"schema_version":"1.0","source":{"id":"1908.10510","kind":"arxiv","version":2}},"canonical_sha256":"606eecff8a68317dc846aa0a246f3eec781af6074d16a168eacab20919494b17","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"606eecff8a68317dc846aa0a246f3eec781af6074d16a168eacab20919494b17","first_computed_at":"2026-07-05T07:56:39.810567Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:56:39.810567Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CZUS06AyxiozE4M6ERXzmfz8Hklec4apB0lK9fHpH0upYvMIHv/sxoKZ1iiXlJaFmzcTqAQGwMcwXyw2h8q9DA==","signature_status":"signed_v1","signed_at":"2026-07-05T07:56:39.810991Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.10510","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:59ac70e26ba145b8847db2156a226bad146b09badd89288235423f5a7e9c6ad4","sha256:6a1f754bc929523abedc1aed9b46a547672612a0ee50c6cced9936e6c6b77bdc"],"state_sha256":"cdedcd19a73a857bb0ecd2135d1352d5a13e1e9b755a75591cee93361ef92202"}