{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1995:RSYTQJALLJ52OHKQKQMSCIJOWZ","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":"cd33443e18b23a661452f6aac1ab5f75e57263635449c926ff3370bbdb83c590","cross_cats_sorted":[],"license":"","primary_cat":"math.LO","submitted_at":"1995-07-18T00:00:00Z","title_canon_sha256":"13a9564fd42318f1dde56f8a117642654f041948532bf7c4d8a14fdb1a45f135"},"schema_version":"1.0","source":{"id":"math/9507211","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/9507211","created_at":"2026-05-18T01:05:48Z"},{"alias_kind":"arxiv_version","alias_value":"math/9507211v1","created_at":"2026-05-18T01:05:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9507211","created_at":"2026-05-18T01:05:48Z"},{"alias_kind":"pith_short_12","alias_value":"RSYTQJALLJ52","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_16","alias_value":"RSYTQJALLJ52OHKQ","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_8","alias_value":"RSYTQJAL","created_at":"2026-05-18T12:25:47Z"}],"graph_snapshots":[{"event_id":"sha256:51dbace0c73c428536aa452105ed12a5beafa8d4fc50332a292571ed21508954","target":"graph","created_at":"2026-05-18T01:05:48Z","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":"For every uncountable cardinal $\\lambda$, suitable negations of the Generalized Continuum Hypothesis imply:\n - For all infinite $\\alpha$ and $\\beta$, there is no universal $K_{\\alpha,\\beta}$-free graphs in $\\lambda$\n - For all $\\alpha\\ge 3$, there is no universal $K_\\alpha$-free graph in $\\lambda$\n  The instance $K_{\\omega,\\omega_1}$ for $\\lambda=\\aleph_1$ was settled by Komjath and Pach from the principle $\\diamondsuit(\\omega_1)$.","authors_text":"Menachem Kojman","cross_cats":[],"headline":"","license":"","primary_cat":"math.LO","submitted_at":"1995-07-18T00:00:00Z","title":"On universal graphs without cliques or withour large bipartite graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9507211","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":"sha256:59a0eda94599be43c65423a3aa4e36d8c4dbd86b1cb673722a433ab5316af404","target":"record","created_at":"2026-05-18T01:05:48Z","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":"cd33443e18b23a661452f6aac1ab5f75e57263635449c926ff3370bbdb83c590","cross_cats_sorted":[],"license":"","primary_cat":"math.LO","submitted_at":"1995-07-18T00:00:00Z","title_canon_sha256":"13a9564fd42318f1dde56f8a117642654f041948532bf7c4d8a14fdb1a45f135"},"schema_version":"1.0","source":{"id":"math/9507211","kind":"arxiv","version":1}},"canonical_sha256":"8cb138240b5a7ba71d50541921212eb656e2cc4cd2fe545b0774c053a3a3f1fa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8cb138240b5a7ba71d50541921212eb656e2cc4cd2fe545b0774c053a3a3f1fa","first_computed_at":"2026-05-18T01:05:48.509825Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:05:48.509825Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OghLoDHgKUbnCuVpdDIE6ZZ5MW0wldMz81Mwcs8ZEXTRRQ/NBFPxh/v6d8FKgN/qi80gdhBj72FMFezw/zB1AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:05:48.510272Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/9507211","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:59a0eda94599be43c65423a3aa4e36d8c4dbd86b1cb673722a433ab5316af404","sha256:51dbace0c73c428536aa452105ed12a5beafa8d4fc50332a292571ed21508954"],"state_sha256":"15b18a8879f66569d233984021da8b2f6ea5207d95f79539230c48389e714fe2"}