{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:LA3XWI3H4LN2JM4YXVMGYPKTQD","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":"c62a56f653fdbd8a7169d473a14f4062f19ebba9c176537ba9b5109921d25619","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2011-04-17T20:03:49Z","title_canon_sha256":"5cb4dd35cdd74211234573aff2c9770e14d7d113fd6c5b86ed5378e9e7640eb1"},"schema_version":"1.0","source":{"id":"1104.3343","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.3343","created_at":"2026-05-18T04:24:05Z"},{"alias_kind":"arxiv_version","alias_value":"1104.3343v1","created_at":"2026-05-18T04:24:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.3343","created_at":"2026-05-18T04:24:05Z"},{"alias_kind":"pith_short_12","alias_value":"LA3XWI3H4LN2","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_16","alias_value":"LA3XWI3H4LN2JM4Y","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_8","alias_value":"LA3XWI3H","created_at":"2026-05-18T12:26:34Z"}],"graph_snapshots":[{"event_id":"sha256:509805826eadfd0a9c5de30a5831a62593e51fa52a9a2d8e3594b026bc1d9f03","target":"graph","created_at":"2026-05-18T04:24:05Z","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 proved that any countable index, universally measurable subgroup of a Polish group is open. By consequence, any universally measurable homomorphism from a Polish group into the infinite symmetric group $S_\\infty$ is continuous. It is also shown that a universally measurable homomorphism from a Polish group into a second countable, locally compact group is necessarily continuous.","authors_text":"Christian Rosendal","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2011-04-17T20:03:49Z","title":"Universally measurable subgroups of countable index"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.3343","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:ef399a24edd5f17cc56a30dd7768828e4ee6739c45412f1beb7a9768a984fa31","target":"record","created_at":"2026-05-18T04:24:05Z","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":"c62a56f653fdbd8a7169d473a14f4062f19ebba9c176537ba9b5109921d25619","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2011-04-17T20:03:49Z","title_canon_sha256":"5cb4dd35cdd74211234573aff2c9770e14d7d113fd6c5b86ed5378e9e7640eb1"},"schema_version":"1.0","source":{"id":"1104.3343","kind":"arxiv","version":1}},"canonical_sha256":"58377b2367e2dba4b398bd586c3d5380d142ec6f8ee2ab411e0ffa3097daf7f2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"58377b2367e2dba4b398bd586c3d5380d142ec6f8ee2ab411e0ffa3097daf7f2","first_computed_at":"2026-05-18T04:24:05.273072Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:24:05.273072Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OejGpPhH+PRot/hPWrbxkQT40uwlWjDLJVkNxEWeTrdUGlMFbw7rrnKCH/RbiF9lBlv8YRgWUEOHvxNbWWBhAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:24:05.273623Z","signed_message":"canonical_sha256_bytes"},"source_id":"1104.3343","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ef399a24edd5f17cc56a30dd7768828e4ee6739c45412f1beb7a9768a984fa31","sha256:509805826eadfd0a9c5de30a5831a62593e51fa52a9a2d8e3594b026bc1d9f03"],"state_sha256":"b02facbcbcb4585234cec92b94e09d49647c09b0b531b44018ab80f39ab83384"}