{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:Y5VOKYTIR5FXCFA4HLYNHJPTUM","short_pith_number":"pith:Y5VOKYTI","canonical_record":{"source":{"id":"1610.03985","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2016-10-13T09:06:21Z","cross_cats_sorted":[],"title_canon_sha256":"9cf96b2c29e68136358aef143627a3237ce4c8bcd3daf7743fd36e7e8b958bcd","abstract_canon_sha256":"1dd40a0c04af2e038b0528709ff150edcdcc8bfb7e6373f3ccaf34c6c1ab7a65"},"schema_version":"1.0"},"canonical_sha256":"c76ae562688f4b71141c3af0d3a5f3a32ca0b0913e4a017f7092cc4491ef0bb0","source":{"kind":"arxiv","id":"1610.03985","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.03985","created_at":"2026-05-18T00:16:09Z"},{"alias_kind":"arxiv_version","alias_value":"1610.03985v3","created_at":"2026-05-18T00:16:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.03985","created_at":"2026-05-18T00:16:09Z"},{"alias_kind":"pith_short_12","alias_value":"Y5VOKYTIR5FX","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_16","alias_value":"Y5VOKYTIR5FXCFA4","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_8","alias_value":"Y5VOKYTI","created_at":"2026-05-18T12:30:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:Y5VOKYTIR5FXCFA4HLYNHJPTUM","target":"record","payload":{"canonical_record":{"source":{"id":"1610.03985","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2016-10-13T09:06:21Z","cross_cats_sorted":[],"title_canon_sha256":"9cf96b2c29e68136358aef143627a3237ce4c8bcd3daf7743fd36e7e8b958bcd","abstract_canon_sha256":"1dd40a0c04af2e038b0528709ff150edcdcc8bfb7e6373f3ccaf34c6c1ab7a65"},"schema_version":"1.0"},"canonical_sha256":"c76ae562688f4b71141c3af0d3a5f3a32ca0b0913e4a017f7092cc4491ef0bb0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:16:09.531859Z","signature_b64":"RL9rydWNycr+9v2M7f+2zrMBGwVsKISi4UW+HcKRc2F8gzQDYSZUypUz7rsva+ZU0vQDoGuG8lo/klZP61SXAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c76ae562688f4b71141c3af0d3a5f3a32ca0b0913e4a017f7092cc4491ef0bb0","last_reissued_at":"2026-05-18T00:16:09.531144Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:16:09.531144Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1610.03985","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":"2026-05-18T00:16:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"K4sKJuPy93XGAkS9gMKfecEOIKTOG63CUUemdovme5sQ0T4hqr3fg7LM6EEAYx2Yy2EM1BhDF7X8R/mqtkLJDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T07:58:59.200952Z"},"content_sha256":"25ad4c01e8b9da46b8c262fe2e4690c5a601048b20ce2910520a37b3054f2932","schema_version":"1.0","event_id":"sha256:25ad4c01e8b9da46b8c262fe2e4690c5a601048b20ce2910520a37b3054f2932"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:Y5VOKYTIR5FXCFA4HLYNHJPTUM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Fodor's lemma can fail everywhere","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Asaf Karagila","submitted_at":"2016-10-13T09:06:21Z","abstract_excerpt":"We show that it is equiconsistent with $\\mathsf{ZF}$ that Fodor's lemma fails everywhere, and furthermore that the club filter on every regular cardinal is not even $\\sigma$-complete. Moreover, these failures can be controlled in a very precise manner."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.03985","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":"2026-05-18T00:16:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Iw5smZj5ClOvQ3qgyeFyaEMk3E8e202xAoxoWvOlxj7WJljkvwq+jYhcxEXYR8G0ZGNMlTrdiOeMl+ymrA/QDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T07:58:59.201536Z"},"content_sha256":"e56288183b2f72498bb202bdf95acf2c1be90ee9be6b0c04eeca06e241733f7e","schema_version":"1.0","event_id":"sha256:e56288183b2f72498bb202bdf95acf2c1be90ee9be6b0c04eeca06e241733f7e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Y5VOKYTIR5FXCFA4HLYNHJPTUM/bundle.json","state_url":"https://pith.science/pith/Y5VOKYTIR5FXCFA4HLYNHJPTUM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Y5VOKYTIR5FXCFA4HLYNHJPTUM/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":"2026-06-12T07:58:59Z","links":{"resolver":"https://pith.science/pith/Y5VOKYTIR5FXCFA4HLYNHJPTUM","bundle":"https://pith.science/pith/Y5VOKYTIR5FXCFA4HLYNHJPTUM/bundle.json","state":"https://pith.science/pith/Y5VOKYTIR5FXCFA4HLYNHJPTUM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Y5VOKYTIR5FXCFA4HLYNHJPTUM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:Y5VOKYTIR5FXCFA4HLYNHJPTUM","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":"1dd40a0c04af2e038b0528709ff150edcdcc8bfb7e6373f3ccaf34c6c1ab7a65","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2016-10-13T09:06:21Z","title_canon_sha256":"9cf96b2c29e68136358aef143627a3237ce4c8bcd3daf7743fd36e7e8b958bcd"},"schema_version":"1.0","source":{"id":"1610.03985","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.03985","created_at":"2026-05-18T00:16:09Z"},{"alias_kind":"arxiv_version","alias_value":"1610.03985v3","created_at":"2026-05-18T00:16:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.03985","created_at":"2026-05-18T00:16:09Z"},{"alias_kind":"pith_short_12","alias_value":"Y5VOKYTIR5FX","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_16","alias_value":"Y5VOKYTIR5FXCFA4","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_8","alias_value":"Y5VOKYTI","created_at":"2026-05-18T12:30:53Z"}],"graph_snapshots":[{"event_id":"sha256:e56288183b2f72498bb202bdf95acf2c1be90ee9be6b0c04eeca06e241733f7e","target":"graph","created_at":"2026-05-18T00:16:09Z","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 it is equiconsistent with $\\mathsf{ZF}$ that Fodor's lemma fails everywhere, and furthermore that the club filter on every regular cardinal is not even $\\sigma$-complete. Moreover, these failures can be controlled in a very precise manner.","authors_text":"Asaf Karagila","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2016-10-13T09:06:21Z","title":"Fodor's lemma can fail everywhere"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.03985","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":"sha256:25ad4c01e8b9da46b8c262fe2e4690c5a601048b20ce2910520a37b3054f2932","target":"record","created_at":"2026-05-18T00:16:09Z","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":"1dd40a0c04af2e038b0528709ff150edcdcc8bfb7e6373f3ccaf34c6c1ab7a65","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2016-10-13T09:06:21Z","title_canon_sha256":"9cf96b2c29e68136358aef143627a3237ce4c8bcd3daf7743fd36e7e8b958bcd"},"schema_version":"1.0","source":{"id":"1610.03985","kind":"arxiv","version":3}},"canonical_sha256":"c76ae562688f4b71141c3af0d3a5f3a32ca0b0913e4a017f7092cc4491ef0bb0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c76ae562688f4b71141c3af0d3a5f3a32ca0b0913e4a017f7092cc4491ef0bb0","first_computed_at":"2026-05-18T00:16:09.531144Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:16:09.531144Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RL9rydWNycr+9v2M7f+2zrMBGwVsKISi4UW+HcKRc2F8gzQDYSZUypUz7rsva+ZU0vQDoGuG8lo/klZP61SXAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:16:09.531859Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.03985","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:25ad4c01e8b9da46b8c262fe2e4690c5a601048b20ce2910520a37b3054f2932","sha256:e56288183b2f72498bb202bdf95acf2c1be90ee9be6b0c04eeca06e241733f7e"],"state_sha256":"2700d753b8fcb183fb4944136f1d5910812722b468cbd424db6f7767538aaf07"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tw8iXFvaXvTprE16eEd9ZwxVh2BH8YAzjTcGcvSJy6FCwbA1LiCJOTOdd9aOaUnrAb5mLlCSt2MSXGMnlM2LAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-12T07:58:59.203916Z","bundle_sha256":"61268c9d102982d76782c8a11d1d23dee2848901652d86c134840755e9772e10"}}