{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:UEOM7TGTC57HD6TIPSFKHRDYAL","short_pith_number":"pith:UEOM7TGT","canonical_record":{"source":{"id":"1209.4267","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2012-09-19T14:51:32Z","cross_cats_sorted":[],"title_canon_sha256":"63a4cb701723c7dc4ce9dfd120f6c9cb8dc5171ec2bf7c62b75c65549da93b8e","abstract_canon_sha256":"e411b9b517c517a4b55fb642d77923490ce82ce9660e5764f7e3f2af28eb88c4"},"schema_version":"1.0"},"canonical_sha256":"a11ccfccd3177e71fa687c8aa3c47802f5b6ec56ad70ad96667750ea9f29d1c0","source":{"kind":"arxiv","id":"1209.4267","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.4267","created_at":"2026-05-18T01:23:21Z"},{"alias_kind":"arxiv_version","alias_value":"1209.4267v4","created_at":"2026-05-18T01:23:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.4267","created_at":"2026-05-18T01:23:21Z"},{"alias_kind":"pith_short_12","alias_value":"UEOM7TGTC57H","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"UEOM7TGTC57HD6TI","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"UEOM7TGT","created_at":"2026-05-18T12:27:23Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:UEOM7TGTC57HD6TIPSFKHRDYAL","target":"record","payload":{"canonical_record":{"source":{"id":"1209.4267","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2012-09-19T14:51:32Z","cross_cats_sorted":[],"title_canon_sha256":"63a4cb701723c7dc4ce9dfd120f6c9cb8dc5171ec2bf7c62b75c65549da93b8e","abstract_canon_sha256":"e411b9b517c517a4b55fb642d77923490ce82ce9660e5764f7e3f2af28eb88c4"},"schema_version":"1.0"},"canonical_sha256":"a11ccfccd3177e71fa687c8aa3c47802f5b6ec56ad70ad96667750ea9f29d1c0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:23:21.106837Z","signature_b64":"dsAqsNz62olkCMfh0xQFxBW9VdYT0mih/dbQHp5NrohfQ9S5Y0ABwaIRDNvgXlJOCEUZDkcGDtKFJb9eBwD3CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a11ccfccd3177e71fa687c8aa3c47802f5b6ec56ad70ad96667750ea9f29d1c0","last_reissued_at":"2026-05-18T01:23:21.106040Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:23:21.106040Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1209.4267","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:23:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"le+6g3uT80X4DtiWl1xqMLFakrPeILlT7CNd1/8gRgoGdgMSaWRSUwsriXF9ilEjRNwQdCeAE0Vq2zjwhvEyCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T10:22:06.041770Z"},"content_sha256":"a38a230d9c17441b56b0ea72f7887ce33673074ac90f0d66000242eadfd74f85","schema_version":"1.0","event_id":"sha256:a38a230d9c17441b56b0ea72f7887ce33673074ac90f0d66000242eadfd74f85"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:UEOM7TGTC57HD6TIPSFKHRDYAL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Transfinite inductions producing coanalytic sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Zolt\\'an Vidny\\'anszky","submitted_at":"2012-09-19T14:51:32Z","abstract_excerpt":"A. Miller proved the consistent existence of a coanalytic two-point set, Hamel basis and MAD family. In these cases the classical transfinite induction can be modified to produce a coanalytic set. We generalize his result formulating a condition which can be easily applied in such situations. We reprove the classical results and as a new application we show that in $V=L$ there exists an uncountable coanalytic subset of the plane that intersects every $C^1$ curve in a countable set."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.4267","kind":"arxiv","version":4},"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":"2026-05-18T01:23:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+0VBGSf436Gii7pcVuMRHIuO+LDVob/9ByDkiMuJtfSWnqADVyHvfbWBM6fLRxpyxpDvqyHqf8uOx36d4ifbDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T10:22:06.042112Z"},"content_sha256":"c004c499d8e7b239f94da8054b4c18f768d789fe054b69d2ef3e2b36f27e89e5","schema_version":"1.0","event_id":"sha256:c004c499d8e7b239f94da8054b4c18f768d789fe054b69d2ef3e2b36f27e89e5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UEOM7TGTC57HD6TIPSFKHRDYAL/bundle.json","state_url":"https://pith.science/pith/UEOM7TGTC57HD6TIPSFKHRDYAL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UEOM7TGTC57HD6TIPSFKHRDYAL/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":"2026-05-28T10:22:06Z","links":{"resolver":"https://pith.science/pith/UEOM7TGTC57HD6TIPSFKHRDYAL","bundle":"https://pith.science/pith/UEOM7TGTC57HD6TIPSFKHRDYAL/bundle.json","state":"https://pith.science/pith/UEOM7TGTC57HD6TIPSFKHRDYAL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UEOM7TGTC57HD6TIPSFKHRDYAL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:UEOM7TGTC57HD6TIPSFKHRDYAL","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":"e411b9b517c517a4b55fb642d77923490ce82ce9660e5764f7e3f2af28eb88c4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2012-09-19T14:51:32Z","title_canon_sha256":"63a4cb701723c7dc4ce9dfd120f6c9cb8dc5171ec2bf7c62b75c65549da93b8e"},"schema_version":"1.0","source":{"id":"1209.4267","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.4267","created_at":"2026-05-18T01:23:21Z"},{"alias_kind":"arxiv_version","alias_value":"1209.4267v4","created_at":"2026-05-18T01:23:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.4267","created_at":"2026-05-18T01:23:21Z"},{"alias_kind":"pith_short_12","alias_value":"UEOM7TGTC57H","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"UEOM7TGTC57HD6TI","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"UEOM7TGT","created_at":"2026-05-18T12:27:23Z"}],"graph_snapshots":[{"event_id":"sha256:c004c499d8e7b239f94da8054b4c18f768d789fe054b69d2ef3e2b36f27e89e5","target":"graph","created_at":"2026-05-18T01:23:21Z","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. Miller proved the consistent existence of a coanalytic two-point set, Hamel basis and MAD family. In these cases the classical transfinite induction can be modified to produce a coanalytic set. We generalize his result formulating a condition which can be easily applied in such situations. We reprove the classical results and as a new application we show that in $V=L$ there exists an uncountable coanalytic subset of the plane that intersects every $C^1$ curve in a countable set.","authors_text":"Zolt\\'an Vidny\\'anszky","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2012-09-19T14:51:32Z","title":"Transfinite inductions producing coanalytic sets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.4267","kind":"arxiv","version":4},"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:a38a230d9c17441b56b0ea72f7887ce33673074ac90f0d66000242eadfd74f85","target":"record","created_at":"2026-05-18T01:23:21Z","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":"e411b9b517c517a4b55fb642d77923490ce82ce9660e5764f7e3f2af28eb88c4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2012-09-19T14:51:32Z","title_canon_sha256":"63a4cb701723c7dc4ce9dfd120f6c9cb8dc5171ec2bf7c62b75c65549da93b8e"},"schema_version":"1.0","source":{"id":"1209.4267","kind":"arxiv","version":4}},"canonical_sha256":"a11ccfccd3177e71fa687c8aa3c47802f5b6ec56ad70ad96667750ea9f29d1c0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a11ccfccd3177e71fa687c8aa3c47802f5b6ec56ad70ad96667750ea9f29d1c0","first_computed_at":"2026-05-18T01:23:21.106040Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:23:21.106040Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dsAqsNz62olkCMfh0xQFxBW9VdYT0mih/dbQHp5NrohfQ9S5Y0ABwaIRDNvgXlJOCEUZDkcGDtKFJb9eBwD3CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:23:21.106837Z","signed_message":"canonical_sha256_bytes"},"source_id":"1209.4267","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a38a230d9c17441b56b0ea72f7887ce33673074ac90f0d66000242eadfd74f85","sha256:c004c499d8e7b239f94da8054b4c18f768d789fe054b69d2ef3e2b36f27e89e5"],"state_sha256":"5fa3da610fa1fa5011d8b7595efcb2d5040afba98d90beecff68468ae367303e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6SlP06152CR4eDRmqtBel8cAfCTcDaQpCeRhPNEm5sLNKcuZa5ZcVw+4/+P/NP0xpsXFqweNHozt3nbgncOrDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T10:22:06.043980Z","bundle_sha256":"1343919b391760d7eda2617bfbee336fc4bc2700ded62501b91337f9cae95c64"}}