{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:ZKU6HTWTQQ5HV6W4SRFAA2VU5B","short_pith_number":"pith:ZKU6HTWT","canonical_record":{"source":{"id":"1611.08152","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2016-11-24T11:34:09Z","cross_cats_sorted":[],"title_canon_sha256":"8e35c2cd3bf6641bdb0e2050b76932cbb2e6034a0ddacc1d9bea82a6ba57f7cf","abstract_canon_sha256":"694f61e2a13f81c351b75389cc183b425f9cd6aaab754ea4a1a4962cce548047"},"schema_version":"1.0"},"canonical_sha256":"caa9e3ced3843a7afadc944a006ab4e84336718c3b633481a22ab082ab69a1fc","source":{"kind":"arxiv","id":"1611.08152","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.08152","created_at":"2026-05-18T00:56:44Z"},{"alias_kind":"arxiv_version","alias_value":"1611.08152v1","created_at":"2026-05-18T00:56:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.08152","created_at":"2026-05-18T00:56:44Z"},{"alias_kind":"pith_short_12","alias_value":"ZKU6HTWTQQ5H","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_16","alias_value":"ZKU6HTWTQQ5HV6W4","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_8","alias_value":"ZKU6HTWT","created_at":"2026-05-18T12:30:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:ZKU6HTWTQQ5HV6W4SRFAA2VU5B","target":"record","payload":{"canonical_record":{"source":{"id":"1611.08152","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2016-11-24T11:34:09Z","cross_cats_sorted":[],"title_canon_sha256":"8e35c2cd3bf6641bdb0e2050b76932cbb2e6034a0ddacc1d9bea82a6ba57f7cf","abstract_canon_sha256":"694f61e2a13f81c351b75389cc183b425f9cd6aaab754ea4a1a4962cce548047"},"schema_version":"1.0"},"canonical_sha256":"caa9e3ced3843a7afadc944a006ab4e84336718c3b633481a22ab082ab69a1fc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:56:44.206035Z","signature_b64":"v5qHE3tv4BLgTahR7zYAZqUgZtbeAcoWmFYvXRRizVs0XZ96/7pAlgc1vCotUy1PKEVKkE4tS1dxofNQphhvDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"caa9e3ced3843a7afadc944a006ab4e84336718c3b633481a22ab082ab69a1fc","last_reissued_at":"2026-05-18T00:56:44.205292Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:56:44.205292Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1611.08152","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:56:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VoUg5eoHlPwytzRAfPB0C26de9LOrkAyHpm8mQXOtoE2KXwFYPVHuX9UfpRz7o3QKehZ4wqWk0PGq0IbtUlCBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T17:23:52.621215Z"},"content_sha256":"2c70e3c1a0373e784c974b575ef5dacf61e6ec030ca7783a7563e040fae2695a","schema_version":"1.0","event_id":"sha256:2c70e3c1a0373e784c974b575ef5dacf61e6ec030ca7783a7563e040fae2695a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:ZKU6HTWTQQ5HV6W4SRFAA2VU5B","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Q","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Joerg Brendle","submitted_at":"2016-11-24T11:34:09Z","abstract_excerpt":"A Q-set is an uncountable set of reals all of whose subsets are relative $G_\\delta$ sets. We prove that, for an arbitrary uncountable cardinal kappa, there is consistently a Q-set of size $\\kappa$ whose square is not Q. This answers a question of A. Miller."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.08152","kind":"arxiv","version":1},"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":"2026-05-18T00:56:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Mti+2GCBPtN17m26Sz9GJPgmeG3VEJ5xtrKfKwdQVo5msTYlZH9Yxg4q6uPnmhvubQng6gwGdnmiFSPkCqdOAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T17:23:52.621864Z"},"content_sha256":"d64988504231281e3644bf38251f4146286f388058301b3c60cde55ccaf2f889","schema_version":"1.0","event_id":"sha256:d64988504231281e3644bf38251f4146286f388058301b3c60cde55ccaf2f889"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZKU6HTWTQQ5HV6W4SRFAA2VU5B/bundle.json","state_url":"https://pith.science/pith/ZKU6HTWTQQ5HV6W4SRFAA2VU5B/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZKU6HTWTQQ5HV6W4SRFAA2VU5B/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":"2026-05-28T17:23:52Z","links":{"resolver":"https://pith.science/pith/ZKU6HTWTQQ5HV6W4SRFAA2VU5B","bundle":"https://pith.science/pith/ZKU6HTWTQQ5HV6W4SRFAA2VU5B/bundle.json","state":"https://pith.science/pith/ZKU6HTWTQQ5HV6W4SRFAA2VU5B/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZKU6HTWTQQ5HV6W4SRFAA2VU5B/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:ZKU6HTWTQQ5HV6W4SRFAA2VU5B","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":"694f61e2a13f81c351b75389cc183b425f9cd6aaab754ea4a1a4962cce548047","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2016-11-24T11:34:09Z","title_canon_sha256":"8e35c2cd3bf6641bdb0e2050b76932cbb2e6034a0ddacc1d9bea82a6ba57f7cf"},"schema_version":"1.0","source":{"id":"1611.08152","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.08152","created_at":"2026-05-18T00:56:44Z"},{"alias_kind":"arxiv_version","alias_value":"1611.08152v1","created_at":"2026-05-18T00:56:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.08152","created_at":"2026-05-18T00:56:44Z"},{"alias_kind":"pith_short_12","alias_value":"ZKU6HTWTQQ5H","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_16","alias_value":"ZKU6HTWTQQ5HV6W4","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_8","alias_value":"ZKU6HTWT","created_at":"2026-05-18T12:30:53Z"}],"graph_snapshots":[{"event_id":"sha256:d64988504231281e3644bf38251f4146286f388058301b3c60cde55ccaf2f889","target":"graph","created_at":"2026-05-18T00:56:44Z","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":"A Q-set is an uncountable set of reals all of whose subsets are relative $G_\\delta$ sets. We prove that, for an arbitrary uncountable cardinal kappa, there is consistently a Q-set of size $\\kappa$ whose square is not Q. This answers a question of A. Miller.","authors_text":"Joerg Brendle","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2016-11-24T11:34:09Z","title":"Q"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.08152","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":"sha256:2c70e3c1a0373e784c974b575ef5dacf61e6ec030ca7783a7563e040fae2695a","target":"record","created_at":"2026-05-18T00:56:44Z","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":"694f61e2a13f81c351b75389cc183b425f9cd6aaab754ea4a1a4962cce548047","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2016-11-24T11:34:09Z","title_canon_sha256":"8e35c2cd3bf6641bdb0e2050b76932cbb2e6034a0ddacc1d9bea82a6ba57f7cf"},"schema_version":"1.0","source":{"id":"1611.08152","kind":"arxiv","version":1}},"canonical_sha256":"caa9e3ced3843a7afadc944a006ab4e84336718c3b633481a22ab082ab69a1fc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"caa9e3ced3843a7afadc944a006ab4e84336718c3b633481a22ab082ab69a1fc","first_computed_at":"2026-05-18T00:56:44.205292Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:56:44.205292Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"v5qHE3tv4BLgTahR7zYAZqUgZtbeAcoWmFYvXRRizVs0XZ96/7pAlgc1vCotUy1PKEVKkE4tS1dxofNQphhvDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:56:44.206035Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.08152","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2c70e3c1a0373e784c974b575ef5dacf61e6ec030ca7783a7563e040fae2695a","sha256:d64988504231281e3644bf38251f4146286f388058301b3c60cde55ccaf2f889"],"state_sha256":"02e455ac6aa5f72b4707fe0b874d46f5c508c092cb0eaddd2931450aeec7fb97"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"M3eSv4goyS21VhnKFBvuEviyrVDXE+sxlN7Yar4h3Hz36HDwWnrZ+KYWG50fK7SDWamblo1n/+p7zncPKr/YAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T17:23:52.624975Z","bundle_sha256":"391822cb48e39251e32c73bf057fcc68339f59af0fb4074946f2d55466fd9c93"}}