{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:YS2PJYOMEXQ2CTBKIBU4GU3ZXL","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":"5f22b6be0e6ab08b02e6cfb4c648c659fae6e1c5bbeccd1440ee6380d055d662","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2012-01-09T09:12:51Z","title_canon_sha256":"77f24c43f990fb3a07302ddf3381001721062a09942d23e9fca9f8715ae6a55a"},"schema_version":"1.0","source":{"id":"1201.1713","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.1713","created_at":"2026-05-18T03:41:20Z"},{"alias_kind":"arxiv_version","alias_value":"1201.1713v2","created_at":"2026-05-18T03:41:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.1713","created_at":"2026-05-18T03:41:20Z"},{"alias_kind":"pith_short_12","alias_value":"YS2PJYOMEXQ2","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"YS2PJYOMEXQ2CTBK","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"YS2PJYOM","created_at":"2026-05-18T12:27:30Z"}],"graph_snapshots":[{"event_id":"sha256:8e41313269e5a15f8039c0af86e5a2928e162054a4341ea1679654e941b65613","target":"graph","created_at":"2026-05-18T03:41:20Z","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 prove the consistency of a singular cardinal $\\lambda$ with small value of the ultrafilter number $u_\\lambda$, and arbitrarily large value of $2^\\lambda$.","authors_text":"Saharon Shelah, Shimon Garti","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2012-01-09T09:12:51Z","title":"The ultrafilter number for singular cardinals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.1713","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":"sha256:6caaab540fbe612e03ca5609acfa5da63cd953ed561441dd43dd5b2d57f5d72b","target":"record","created_at":"2026-05-18T03:41:20Z","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":"5f22b6be0e6ab08b02e6cfb4c648c659fae6e1c5bbeccd1440ee6380d055d662","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2012-01-09T09:12:51Z","title_canon_sha256":"77f24c43f990fb3a07302ddf3381001721062a09942d23e9fca9f8715ae6a55a"},"schema_version":"1.0","source":{"id":"1201.1713","kind":"arxiv","version":2}},"canonical_sha256":"c4b4f4e1cc25e1a14c2a4069c35379bac0ec43694af67698bae0093e6c6f64ef","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c4b4f4e1cc25e1a14c2a4069c35379bac0ec43694af67698bae0093e6c6f64ef","first_computed_at":"2026-05-18T03:41:20.303393Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:41:20.303393Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QMiO5vT46mKKfjqkhucvWfaUs6nboTtHjHhiIgRLW3I8BAQVTG30qsgvfEALpORedSRXLAN15SpPqQrOoMFSCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:41:20.304053Z","signed_message":"canonical_sha256_bytes"},"source_id":"1201.1713","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6caaab540fbe612e03ca5609acfa5da63cd953ed561441dd43dd5b2d57f5d72b","sha256:8e41313269e5a15f8039c0af86e5a2928e162054a4341ea1679654e941b65613"],"state_sha256":"6a8ae1be3818ed8b839480398462ae37a9034d023e5b97ff9e6511cf03f1850b"}