{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:VXO5H42XCYEGSASKHIJWUECJK3","short_pith_number":"pith:VXO5H42X","canonical_record":{"source":{"id":"1808.04732","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.LO","submitted_at":"2018-08-14T15:01:08Z","cross_cats_sorted":[],"title_canon_sha256":"7f377a023b9f7c74945fadb7f58e2145e9b01b82b3ac07149b8f6513c825e261","abstract_canon_sha256":"29d6cf6e604a8fd3d3de613dd0ef781d82785b59be4a2c4a3c657e6e9a198718"},"schema_version":"1.0"},"canonical_sha256":"adddd3f357160869024a3a136a104956c4284184cc599687e1c56a29f3b603b3","source":{"kind":"arxiv","id":"1808.04732","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.04732","created_at":"2026-05-18T00:08:02Z"},{"alias_kind":"arxiv_version","alias_value":"1808.04732v2","created_at":"2026-05-18T00:08:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.04732","created_at":"2026-05-18T00:08:02Z"},{"alias_kind":"pith_short_12","alias_value":"VXO5H42XCYEG","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_16","alias_value":"VXO5H42XCYEGSASK","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_8","alias_value":"VXO5H42X","created_at":"2026-05-18T12:32:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:VXO5H42XCYEGSASKHIJWUECJK3","target":"record","payload":{"canonical_record":{"source":{"id":"1808.04732","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.LO","submitted_at":"2018-08-14T15:01:08Z","cross_cats_sorted":[],"title_canon_sha256":"7f377a023b9f7c74945fadb7f58e2145e9b01b82b3ac07149b8f6513c825e261","abstract_canon_sha256":"29d6cf6e604a8fd3d3de613dd0ef781d82785b59be4a2c4a3c657e6e9a198718"},"schema_version":"1.0"},"canonical_sha256":"adddd3f357160869024a3a136a104956c4284184cc599687e1c56a29f3b603b3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:08:02.468344Z","signature_b64":"8QgaLsYP8cMlaL4AHyCq/QpWY2HnWk+0xX8sjNi82SKkSi0r4eoRl6GlsTE8PwXQ3tcqHF82JLJ8cyIWLbPqBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"adddd3f357160869024a3a136a104956c4284184cc599687e1c56a29f3b603b3","last_reissued_at":"2026-05-18T00:08:02.467801Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:08:02.467801Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1808.04732","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:08:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FZpDVIhbcPEJaLFMfEtZJMx7Vpg1UZWlpefiOZl4BoElVehuCo2RvSJ2Crz+yZpPlNlIxtBrhqLe79wLpU7YBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T06:42:48.739172Z"},"content_sha256":"f6b69c614150dee6fab17f988393575bcf7247822b3dd31f8a20697bb99c4a61","schema_version":"1.0","event_id":"sha256:f6b69c614150dee6fab17f988393575bcf7247822b3dd31f8a20697bb99c4a61"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:VXO5H42XCYEGSASKHIJWUECJK3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A model of second-order arithmetic satisfying AC but not DC","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Sy-David Friedman, Victoria Gitman, Vladimir Kanovei","submitted_at":"2018-08-14T15:01:08Z","abstract_excerpt":"We show that there is a $\\beta$-model of second-order arithmetic in which the choice scheme holds, but the dependent choice scheme fails for a $\\Pi^1_2$-assertion, confirming a conjecture of Stephen Simpson. We obtain as a corollary that the Reflection Principle, stating that every formula reflects to a transitive set, can fail in models of ${\\rm ZFC}^-$. This work is a rediscovery by the first two authors of a result obtained by the third author."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.04732","kind":"arxiv","version":2},"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":"2026-05-18T00:08:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8X7anV5f5Mf2xIFJgmsGjvj4KcLQKNCpbAgGe0utJDvO5t70TogmxzMT5k9YyxSQ4IqLwmGPqPT5cm1ytwOvBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T06:42:48.739889Z"},"content_sha256":"6ae48555cfc9229e1bcb0259a1f85974e59b5db09fd3490563d4462f5499b4c4","schema_version":"1.0","event_id":"sha256:6ae48555cfc9229e1bcb0259a1f85974e59b5db09fd3490563d4462f5499b4c4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VXO5H42XCYEGSASKHIJWUECJK3/bundle.json","state_url":"https://pith.science/pith/VXO5H42XCYEGSASKHIJWUECJK3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VXO5H42XCYEGSASKHIJWUECJK3/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":"2026-06-09T06:42:48Z","links":{"resolver":"https://pith.science/pith/VXO5H42XCYEGSASKHIJWUECJK3","bundle":"https://pith.science/pith/VXO5H42XCYEGSASKHIJWUECJK3/bundle.json","state":"https://pith.science/pith/VXO5H42XCYEGSASKHIJWUECJK3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VXO5H42XCYEGSASKHIJWUECJK3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:VXO5H42XCYEGSASKHIJWUECJK3","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":"29d6cf6e604a8fd3d3de613dd0ef781d82785b59be4a2c4a3c657e6e9a198718","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.LO","submitted_at":"2018-08-14T15:01:08Z","title_canon_sha256":"7f377a023b9f7c74945fadb7f58e2145e9b01b82b3ac07149b8f6513c825e261"},"schema_version":"1.0","source":{"id":"1808.04732","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.04732","created_at":"2026-05-18T00:08:02Z"},{"alias_kind":"arxiv_version","alias_value":"1808.04732v2","created_at":"2026-05-18T00:08:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.04732","created_at":"2026-05-18T00:08:02Z"},{"alias_kind":"pith_short_12","alias_value":"VXO5H42XCYEG","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_16","alias_value":"VXO5H42XCYEGSASK","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_8","alias_value":"VXO5H42X","created_at":"2026-05-18T12:32:59Z"}],"graph_snapshots":[{"event_id":"sha256:6ae48555cfc9229e1bcb0259a1f85974e59b5db09fd3490563d4462f5499b4c4","target":"graph","created_at":"2026-05-18T00:08:02Z","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":"We show that there is a $\\beta$-model of second-order arithmetic in which the choice scheme holds, but the dependent choice scheme fails for a $\\Pi^1_2$-assertion, confirming a conjecture of Stephen Simpson. We obtain as a corollary that the Reflection Principle, stating that every formula reflects to a transitive set, can fail in models of ${\\rm ZFC}^-$. This work is a rediscovery by the first two authors of a result obtained by the third author.","authors_text":"Sy-David Friedman, Victoria Gitman, Vladimir Kanovei","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.LO","submitted_at":"2018-08-14T15:01:08Z","title":"A model of second-order arithmetic satisfying AC but not DC"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.04732","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:f6b69c614150dee6fab17f988393575bcf7247822b3dd31f8a20697bb99c4a61","target":"record","created_at":"2026-05-18T00:08:02Z","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":"29d6cf6e604a8fd3d3de613dd0ef781d82785b59be4a2c4a3c657e6e9a198718","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.LO","submitted_at":"2018-08-14T15:01:08Z","title_canon_sha256":"7f377a023b9f7c74945fadb7f58e2145e9b01b82b3ac07149b8f6513c825e261"},"schema_version":"1.0","source":{"id":"1808.04732","kind":"arxiv","version":2}},"canonical_sha256":"adddd3f357160869024a3a136a104956c4284184cc599687e1c56a29f3b603b3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"adddd3f357160869024a3a136a104956c4284184cc599687e1c56a29f3b603b3","first_computed_at":"2026-05-18T00:08:02.467801Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:08:02.467801Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8QgaLsYP8cMlaL4AHyCq/QpWY2HnWk+0xX8sjNi82SKkSi0r4eoRl6GlsTE8PwXQ3tcqHF82JLJ8cyIWLbPqBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:08:02.468344Z","signed_message":"canonical_sha256_bytes"},"source_id":"1808.04732","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f6b69c614150dee6fab17f988393575bcf7247822b3dd31f8a20697bb99c4a61","sha256:6ae48555cfc9229e1bcb0259a1f85974e59b5db09fd3490563d4462f5499b4c4"],"state_sha256":"002628c3d840b63c551047fb7b1fb7ae80177c801e7bda4fa6842033af741e99"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rdqOfECEHAcSkX5FyJ5oeLtCnMgmb0FCIXen/HVLDSOsBzeqYJeSebyJnN7qgn9S2LXNaykB797Shd4K++x8Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T06:42:48.743582Z","bundle_sha256":"ddbe7269d9ead39d14446b14b349ff755dd887c4a1ed838241d43708d52f32ef"}}