{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:EUSTXZFRTEBHNEX5RF5JZRCP6U","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":"01e4f07d2e94683a7fe8ecfcddfd5438de298b51ba4dfed217e522d91b99f96d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2016-04-20T18:00:57Z","title_canon_sha256":"47962d1e880981ffda0917d775b2f2f74d3adb08bccd47701e42a5208e67bb22"},"schema_version":"1.0","source":{"id":"1604.06044","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.06044","created_at":"2026-05-18T00:27:53Z"},{"alias_kind":"arxiv_version","alias_value":"1604.06044v3","created_at":"2026-05-18T00:27:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.06044","created_at":"2026-05-18T00:27:53Z"},{"alias_kind":"pith_short_12","alias_value":"EUSTXZFRTEBH","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_16","alias_value":"EUSTXZFRTEBHNEX5","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_8","alias_value":"EUSTXZFR","created_at":"2026-05-18T12:30:15Z"}],"graph_snapshots":[{"event_id":"sha256:2210645c192abc3aba089e75360ebeb397267951d181cd43da26542e934fc578","target":"graph","created_at":"2026-05-18T00:27:53Z","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 continue our study of the class $\\mathscr{C}(D)$, where $D$ is a uniform ultrafilter on a cardinal $\\kappa$ and $\\mathscr{C}(D)$ is the class of all pairs $(\\theta_1, \\theta_2),$ where $(\\theta_1, \\theta_2)$ is the cofinality of a cut in $J^\\kappa /D$ and $J$ is some $(\\theta_1+\\theta_2)^+$-saturated dense linear order. We give a combinatorial characterization of the class $\\mathscr{C}(D)$. We also show that if $(\\theta_1, \\theta_2) \\in \\mathscr{C}(D)$ and $D$ is $\\aleph_1$-complete or $\\theta_1 + \\theta_2 > 2^\\kappa,$ then $\\theta_1=\\theta_2.$","authors_text":"Mohammad Golshani, Saharon Shelah","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2016-04-20T18:00:57Z","title":"On cuts in ultraproducts of linear orders II"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.06044","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:da7903f4c06adcaa9d5547768e3cc98146ae27081a666cca13724c4517ccc901","target":"record","created_at":"2026-05-18T00:27:53Z","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":"01e4f07d2e94683a7fe8ecfcddfd5438de298b51ba4dfed217e522d91b99f96d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2016-04-20T18:00:57Z","title_canon_sha256":"47962d1e880981ffda0917d775b2f2f74d3adb08bccd47701e42a5208e67bb22"},"schema_version":"1.0","source":{"id":"1604.06044","kind":"arxiv","version":3}},"canonical_sha256":"25253be4b199027692fd897a9cc44ff51a30c19aac0a9ec571a508e75cc58854","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"25253be4b199027692fd897a9cc44ff51a30c19aac0a9ec571a508e75cc58854","first_computed_at":"2026-05-18T00:27:53.314497Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:27:53.314497Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vQmwaF/OTt5oqCWtMV5sO/RUb3lNlaQ3XcMWBGSEWS+GTbySJ+om9T67mxfJS+M2TTDT3O0IQ/qXP3S5r/+kBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:27:53.315070Z","signed_message":"canonical_sha256_bytes"},"source_id":"1604.06044","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:da7903f4c06adcaa9d5547768e3cc98146ae27081a666cca13724c4517ccc901","sha256:2210645c192abc3aba089e75360ebeb397267951d181cd43da26542e934fc578"],"state_sha256":"a43541d01b6bae9ea87eb3547082994dd8e25b01852b2444241cf42e2ad9fb1d"}