{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:E2KGQRHJUKQKNKOP3PCGUWONEV","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":"2b6442d934b3f2d3346f2fe454f8c59df9672b6b79592b4a94a5bfa06cd299db","cross_cats_sorted":["math.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2011-07-20T11:44:05Z","title_canon_sha256":"5ac822d84a760d8ce5e6bec6c31256fa9ab2394d8d7ee274576f855d26296ba5"},"schema_version":"1.0","source":{"id":"1107.3946","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.3946","created_at":"2026-05-18T04:09:46Z"},{"alias_kind":"arxiv_version","alias_value":"1107.3946v2","created_at":"2026-05-18T04:09:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.3946","created_at":"2026-05-18T04:09:46Z"},{"alias_kind":"pith_short_12","alias_value":"E2KGQRHJUKQK","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"E2KGQRHJUKQKNKOP","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"E2KGQRHJ","created_at":"2026-05-18T12:26:26Z"}],"graph_snapshots":[{"event_id":"sha256:b04f6155080583bf5df55d00d531f6800b3757dd08cc38a588fd08910d533132","target":"graph","created_at":"2026-05-18T04:09:46Z","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":"The set of all transformation monoids on a fixed set of infinite cardinality \\lambda, equipped with the order of inclusion, forms a complete algebraic lattice Mon(\\lambda) with 2^{\\lambda} compact elements. We show that this lattice is universal with respect to closed sublattices, i.e., the closed sublattices of Mon(\\lambda) are, up to isomorphism, precisely the complete algebraic lattices with at most 2^{\\lambda} compact elements.","authors_text":"Michael Pinsker, Saharon Shelah","cross_cats":["math.LO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2011-07-20T11:44:05Z","title":"Universality of the lattice of transformation monoids"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.3946","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:b996261fee46190a818cd82422b20ac5265a6373ea855a5c8437237bff0c4da2","target":"record","created_at":"2026-05-18T04:09:46Z","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":"2b6442d934b3f2d3346f2fe454f8c59df9672b6b79592b4a94a5bfa06cd299db","cross_cats_sorted":["math.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2011-07-20T11:44:05Z","title_canon_sha256":"5ac822d84a760d8ce5e6bec6c31256fa9ab2394d8d7ee274576f855d26296ba5"},"schema_version":"1.0","source":{"id":"1107.3946","kind":"arxiv","version":2}},"canonical_sha256":"26946844e9a2a0a6a9cfdbc46a59cd2569a5bb46c889d26a07a8622c6825093c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"26946844e9a2a0a6a9cfdbc46a59cd2569a5bb46c889d26a07a8622c6825093c","first_computed_at":"2026-05-18T04:09:46.797646Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:09:46.797646Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cU6j5grqXQWR51IAlf/TtxEKCPdDpC7bjs/HZVA0nZrsmrAI/VLLiu+kAaFxld6KHjCcI9o7Nec8Wlr3OQa8Cw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:09:46.798072Z","signed_message":"canonical_sha256_bytes"},"source_id":"1107.3946","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b996261fee46190a818cd82422b20ac5265a6373ea855a5c8437237bff0c4da2","sha256:b04f6155080583bf5df55d00d531f6800b3757dd08cc38a588fd08910d533132"],"state_sha256":"3eb3990c8af194c755be9a7d60c04845e0a1b5ac9eff2f5668fadbeee5ed678a"}