{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:O4QHERAHIH5XW3R65MMVLDSCK6","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":"9b7030a48a3a440d0f3b5fab09aacd351a7f0246a90cbfb60b6fde86304383db","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2019-10-24T10:51:14Z","title_canon_sha256":"f9a579c2421a1e0181218059429fc0a33ff0450fb4a8ed108935bdc707abfbc8"},"schema_version":"1.0","source":{"id":"1910.11025","kind":"arxiv","version":6}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1910.11025","created_at":"2026-07-05T02:19:14Z"},{"alias_kind":"arxiv_version","alias_value":"1910.11025v6","created_at":"2026-07-05T02:19:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1910.11025","created_at":"2026-07-05T02:19:14Z"},{"alias_kind":"pith_short_12","alias_value":"O4QHERAHIH5X","created_at":"2026-07-05T02:19:14Z"},{"alias_kind":"pith_short_16","alias_value":"O4QHERAHIH5XW3R6","created_at":"2026-07-05T02:19:14Z"},{"alias_kind":"pith_short_8","alias_value":"O4QHERAH","created_at":"2026-07-05T02:19:14Z"}],"graph_snapshots":[{"event_id":"sha256:b388c0dda2f95d3fdc498825f477d1f28dd64fe2c70903cf8f7c4996569809de","target":"graph","created_at":"2026-07-05T02:19:14Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1910.11025/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We investigate infinite sets that witness the failure of certain Ramsey-theoretic statements, such as Ramsey's or (appropriately phrased) Hindman's theorem; such sets may exist if one does not assume the Axiom of Choice. We obtain very precise information as to where such sets are located within the hierarchy of infinite Dedekind-finite sets.","authors_text":"David Fern\\'andez-Bret\\'on, Joshua Brot, Mengyang Cao","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2019-10-24T10:51:14Z","title":"Finiteness classes arising from Ramsey-theoretic statements in set theory without choice"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1910.11025","kind":"arxiv","version":6},"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":"sha256:3a43a16fd928f8bccfab5d58f610d0015f61fdcb4ac5366cce69e4f40ea09587","target":"record","created_at":"2026-07-05T02:19:14Z","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":"9b7030a48a3a440d0f3b5fab09aacd351a7f0246a90cbfb60b6fde86304383db","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2019-10-24T10:51:14Z","title_canon_sha256":"f9a579c2421a1e0181218059429fc0a33ff0450fb4a8ed108935bdc707abfbc8"},"schema_version":"1.0","source":{"id":"1910.11025","kind":"arxiv","version":6}},"canonical_sha256":"772072440741fb7b6e3eeb19558e4257b2019adcbb3c7dfeb9713bd917a780b7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"772072440741fb7b6e3eeb19558e4257b2019adcbb3c7dfeb9713bd917a780b7","first_computed_at":"2026-07-05T02:19:14.559072Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:19:14.559072Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"H5cfm0jqOF52zOENtqFCaIcLEQW1snM4rrUYbfIJ05nVYsyC6Q6qMAQuDm4VoGt0nHYDergKNpIs/mtUVNFUCw==","signature_status":"signed_v1","signed_at":"2026-07-05T02:19:14.559635Z","signed_message":"canonical_sha256_bytes"},"source_id":"1910.11025","source_kind":"arxiv","source_version":6}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3a43a16fd928f8bccfab5d58f610d0015f61fdcb4ac5366cce69e4f40ea09587","sha256:b388c0dda2f95d3fdc498825f477d1f28dd64fe2c70903cf8f7c4996569809de"],"state_sha256":"0905032ed0a89043a9ebb44ff4d9335373ea6240d2a3c4bbe869044a10bd77a1"}