{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2006:KIESX6VQIPGTNGOR57UXBJAEQB","short_pith_number":"pith:KIESX6VQ","canonical_record":{"source":{"id":"math/0601087","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"math.LO","submitted_at":"2006-01-05T05:12:29Z","cross_cats_sorted":[],"title_canon_sha256":"ed43c22e375898fee5f17ef8689c2bbcbb3d71a62025cbaf37edb4e5630e6fdd","abstract_canon_sha256":"5bd08a70c2c0d727cc261bcde534efbd803539992f13efa6e65da343b9ea42ea"},"schema_version":"1.0"},"canonical_sha256":"52092bfab043cd3699d1efe970a404805cf6f75078e298e6ca9e1dfe83e4275e","source":{"kind":"arxiv","id":"math/0601087","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0601087","created_at":"2026-05-18T01:08:50Z"},{"alias_kind":"arxiv_version","alias_value":"math/0601087v3","created_at":"2026-05-18T01:08:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0601087","created_at":"2026-05-18T01:08:50Z"},{"alias_kind":"pith_short_12","alias_value":"KIESX6VQIPGT","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_16","alias_value":"KIESX6VQIPGTNGOR","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_8","alias_value":"KIESX6VQ","created_at":"2026-05-18T12:25:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2006:KIESX6VQIPGTNGOR57UXBJAEQB","target":"record","payload":{"canonical_record":{"source":{"id":"math/0601087","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"math.LO","submitted_at":"2006-01-05T05:12:29Z","cross_cats_sorted":[],"title_canon_sha256":"ed43c22e375898fee5f17ef8689c2bbcbb3d71a62025cbaf37edb4e5630e6fdd","abstract_canon_sha256":"5bd08a70c2c0d727cc261bcde534efbd803539992f13efa6e65da343b9ea42ea"},"schema_version":"1.0"},"canonical_sha256":"52092bfab043cd3699d1efe970a404805cf6f75078e298e6ca9e1dfe83e4275e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:08:50.684459Z","signature_b64":"n7R4C/BfIxXxZOFf1GNawo3TP4+0dPm2bnyrakqA3BB10SWx08ywpeG7kEO8+2AxLdFqUSq0uGkBWhdXk4vtBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"52092bfab043cd3699d1efe970a404805cf6f75078e298e6ca9e1dfe83e4275e","last_reissued_at":"2026-05-18T01:08:50.683659Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:08:50.683659Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0601087","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:08:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/NqItORtnnr91zyIc4YLyoDWJGaFafyB8SdZ4dUTpD/IxZ8FaAWjSsL6M3jsR+WZxHTn43HdTNuXR9Wya7CVBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T02:50:52.175467Z"},"content_sha256":"e483bbaea793e732e5e974a2f548dc58f16be350f279596860f5409d0eeaab05","schema_version":"1.0","event_id":"sha256:e483bbaea793e732e5e974a2f548dc58f16be350f279596860f5409d0eeaab05"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2006:KIESX6VQIPGTNGOR57UXBJAEQB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Models of real-valued measurability","license":"","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Noam Greenberg, Saharon Shelah, Saka\\'e Fuchino","submitted_at":"2006-01-05T05:12:29Z","abstract_excerpt":"Solovay's random-real forcing (1971) is the standard way of producing real-valued measurable cardinals. Following questions of Fremlin, by giving a new construction, we show that there are combinatorial, measure-theoretic properties of Solovay's model that do not follow from the existence of real-valued measurability."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0601087","kind":"arxiv","version":3},"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":"2026-05-18T01:08:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eqLxZSrr+gg96u14IFRRWLgrhbU4RF1yZta3/iGDtwjoyoUK/7X8+vlQgjrlGjdf9Z7YJo8ou37HncwPU6vsAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T02:50:52.176064Z"},"content_sha256":"3e63197b8c1a7f9b80f7ff299f59819629f2d5757436c4a99d60bfd956707aef","schema_version":"1.0","event_id":"sha256:3e63197b8c1a7f9b80f7ff299f59819629f2d5757436c4a99d60bfd956707aef"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KIESX6VQIPGTNGOR57UXBJAEQB/bundle.json","state_url":"https://pith.science/pith/KIESX6VQIPGTNGOR57UXBJAEQB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KIESX6VQIPGTNGOR57UXBJAEQB/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":"2026-05-31T02:50:52Z","links":{"resolver":"https://pith.science/pith/KIESX6VQIPGTNGOR57UXBJAEQB","bundle":"https://pith.science/pith/KIESX6VQIPGTNGOR57UXBJAEQB/bundle.json","state":"https://pith.science/pith/KIESX6VQIPGTNGOR57UXBJAEQB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KIESX6VQIPGTNGOR57UXBJAEQB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:KIESX6VQIPGTNGOR57UXBJAEQB","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":"5bd08a70c2c0d727cc261bcde534efbd803539992f13efa6e65da343b9ea42ea","cross_cats_sorted":[],"license":"","primary_cat":"math.LO","submitted_at":"2006-01-05T05:12:29Z","title_canon_sha256":"ed43c22e375898fee5f17ef8689c2bbcbb3d71a62025cbaf37edb4e5630e6fdd"},"schema_version":"1.0","source":{"id":"math/0601087","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0601087","created_at":"2026-05-18T01:08:50Z"},{"alias_kind":"arxiv_version","alias_value":"math/0601087v3","created_at":"2026-05-18T01:08:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0601087","created_at":"2026-05-18T01:08:50Z"},{"alias_kind":"pith_short_12","alias_value":"KIESX6VQIPGT","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_16","alias_value":"KIESX6VQIPGTNGOR","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_8","alias_value":"KIESX6VQ","created_at":"2026-05-18T12:25:54Z"}],"graph_snapshots":[{"event_id":"sha256:3e63197b8c1a7f9b80f7ff299f59819629f2d5757436c4a99d60bfd956707aef","target":"graph","created_at":"2026-05-18T01:08:50Z","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":"Solovay's random-real forcing (1971) is the standard way of producing real-valued measurable cardinals. Following questions of Fremlin, by giving a new construction, we show that there are combinatorial, measure-theoretic properties of Solovay's model that do not follow from the existence of real-valued measurability.","authors_text":"Noam Greenberg, Saharon Shelah, Saka\\'e Fuchino","cross_cats":[],"headline":"","license":"","primary_cat":"math.LO","submitted_at":"2006-01-05T05:12:29Z","title":"Models of real-valued measurability"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0601087","kind":"arxiv","version":3},"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:e483bbaea793e732e5e974a2f548dc58f16be350f279596860f5409d0eeaab05","target":"record","created_at":"2026-05-18T01:08:50Z","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":"5bd08a70c2c0d727cc261bcde534efbd803539992f13efa6e65da343b9ea42ea","cross_cats_sorted":[],"license":"","primary_cat":"math.LO","submitted_at":"2006-01-05T05:12:29Z","title_canon_sha256":"ed43c22e375898fee5f17ef8689c2bbcbb3d71a62025cbaf37edb4e5630e6fdd"},"schema_version":"1.0","source":{"id":"math/0601087","kind":"arxiv","version":3}},"canonical_sha256":"52092bfab043cd3699d1efe970a404805cf6f75078e298e6ca9e1dfe83e4275e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"52092bfab043cd3699d1efe970a404805cf6f75078e298e6ca9e1dfe83e4275e","first_computed_at":"2026-05-18T01:08:50.683659Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:08:50.683659Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"n7R4C/BfIxXxZOFf1GNawo3TP4+0dPm2bnyrakqA3BB10SWx08ywpeG7kEO8+2AxLdFqUSq0uGkBWhdXk4vtBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:08:50.684459Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0601087","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e483bbaea793e732e5e974a2f548dc58f16be350f279596860f5409d0eeaab05","sha256:3e63197b8c1a7f9b80f7ff299f59819629f2d5757436c4a99d60bfd956707aef"],"state_sha256":"3d3866344d220ae44ad01a245533fa7f87fa0df4e215b61bde982d5575fa1502"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1Z6pazp5O+lI8bEtEGFOLgfCbAFhgHMdmoXP6SYJWAkkkuX+PcGHYJg742dpA5gPYE1OuwC++e2suMJ28HZ3Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T02:50:52.179367Z","bundle_sha256":"1e1cd3f5bd40ead4087bbda52321d72ecbda39b31426ba68b132e4a4784a34aa"}}