{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1997:C27RGIT3VYJKMY4AU4ETUOUJM2","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":"a61d67413a8a6dd48f8118e65cf8cd0c6b5c127e09f5be9d3971498c8f7cf018","cross_cats_sorted":[],"license":"","primary_cat":"math.LO","submitted_at":"1997-07-16T00:00:00Z","title_canon_sha256":"9054474a92efd94519e711cd09db5368b358921d8027d8bdf30db2777aa34960"},"schema_version":"1.0","source":{"id":"math/9707202","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/9707202","created_at":"2026-05-18T01:05:35Z"},{"alias_kind":"arxiv_version","alias_value":"math/9707202v1","created_at":"2026-05-18T01:05:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9707202","created_at":"2026-05-18T01:05:35Z"},{"alias_kind":"pith_short_12","alias_value":"C27RGIT3VYJK","created_at":"2026-05-18T12:25:48Z"},{"alias_kind":"pith_short_16","alias_value":"C27RGIT3VYJKMY4A","created_at":"2026-05-18T12:25:48Z"},{"alias_kind":"pith_short_8","alias_value":"C27RGIT3","created_at":"2026-05-18T12:25:48Z"}],"graph_snapshots":[{"event_id":"sha256:9ba20b8063cd6a9459a9440b4df18e1a69fc519f39c63467b3619b48ef330337","target":"graph","created_at":"2026-05-18T01:05:35Z","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":"It is consistent that there is a partial order (P,<) of size aleph_1 such that every monotone (unary) function from P to P is first order definable in (P,<).\n  The partial order is constructed in an extension obtained by finite support iteration of Cohen forcing.\n  The main points is that (1) all monotone functions from P to P will (essentially) have countable range (this uses a Delta-system argument) and (2) that all countable subsets of P will be first order definable, so we have to code these countable sets into the partial order.  Amalgamation of finite structures plays an essential role.","authors_text":"Martin Goldstern, Saharon Shelah","cross_cats":[],"headline":"","license":"","primary_cat":"math.LO","submitted_at":"1997-07-16T00:00:00Z","title":"A Partial Order Where All Monotone Maps Are Definable"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9707202","kind":"arxiv","version":1},"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":"sha256:70adc8e341d7944e8f261063fbbd071f4fd923b7b7d60a1a1b2c1614dacc3bf5","target":"record","created_at":"2026-05-18T01:05:35Z","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":"a61d67413a8a6dd48f8118e65cf8cd0c6b5c127e09f5be9d3971498c8f7cf018","cross_cats_sorted":[],"license":"","primary_cat":"math.LO","submitted_at":"1997-07-16T00:00:00Z","title_canon_sha256":"9054474a92efd94519e711cd09db5368b358921d8027d8bdf30db2777aa34960"},"schema_version":"1.0","source":{"id":"math/9707202","kind":"arxiv","version":1}},"canonical_sha256":"16bf13227bae12a66380a7093a3a89668316982e78711df3eeff9eaea44947e0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"16bf13227bae12a66380a7093a3a89668316982e78711df3eeff9eaea44947e0","first_computed_at":"2026-05-18T01:05:35.099588Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:05:35.099588Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XKrw4OevjreMFs74QQYD6+xfLO6YpAKHci0lRvltCKIg+Ya+/r5Q439Lufzj+PgnkOLM/f253p9GjDtY/RQGDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:05:35.100352Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/9707202","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:70adc8e341d7944e8f261063fbbd071f4fd923b7b7d60a1a1b2c1614dacc3bf5","sha256:9ba20b8063cd6a9459a9440b4df18e1a69fc519f39c63467b3619b48ef330337"],"state_sha256":"64a1e7f07ffd6eba7849476816ccbf4340c3b9f3862a8d2bef6bc0adcd4b8a08"}