{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:32IANEKAPOEVZOPAN5BXJSSIIP","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":"060a291d425dfcfa647d2d370a766b17c27bc3d46cc940b363e9e50130c32161","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2018-10-09T07:49:58Z","title_canon_sha256":"4c6970503c3473e4388b672a9f615681e2c3af2979c2f76bb02b24f9e071b87c"},"schema_version":"1.0","source":{"id":"1810.06407","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.06407","created_at":"2026-05-18T00:03:20Z"},{"alias_kind":"arxiv_version","alias_value":"1810.06407v1","created_at":"2026-05-18T00:03:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.06407","created_at":"2026-05-18T00:03:20Z"},{"alias_kind":"pith_short_12","alias_value":"32IANEKAPOEV","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_16","alias_value":"32IANEKAPOEVZOPA","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_8","alias_value":"32IANEKA","created_at":"2026-05-18T12:32:02Z"}],"graph_snapshots":[{"event_id":"sha256:3a9ff3662756785897dfdd938fca08d05d8ec1cff0f3c619b2205c68db1a36d3","target":"graph","created_at":"2026-05-18T00:03:20Z","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":"Given a bounded lattice $L$ with bounds $0$ and $1$, it is well known that the set $\\mathsf{Pol}_{0,1}(L)$ of all $0,1$-preserving polynomials of $L$ forms a natural subclass of the set $\\mathsf{C}(L)$ of aggregation functions on $L$. The main aim of this paper is to characterize all finite lattices $L$ for which these two classes coincide, i.e. when the set $\\mathsf{C}(L)$ is as small as possible. These lattices are shown to be completely determined by their tolerances, also several sufficient purely lattice-theoretical conditions are presented. In particular, all simple relatively complement","authors_text":"Jozef P\\'ocs, Radom\\'ir Hala\\v{s}","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2018-10-09T07:49:58Z","title":"On lattices with a smallest set of aggregation functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.06407","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:fec4b8b850def4e356ee569812c439457196d114954803357f4294b24b58f2f0","target":"record","created_at":"2026-05-18T00:03:20Z","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":"060a291d425dfcfa647d2d370a766b17c27bc3d46cc940b363e9e50130c32161","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2018-10-09T07:49:58Z","title_canon_sha256":"4c6970503c3473e4388b672a9f615681e2c3af2979c2f76bb02b24f9e071b87c"},"schema_version":"1.0","source":{"id":"1810.06407","kind":"arxiv","version":1}},"canonical_sha256":"de900691407b895cb9e06f4374ca4843f50e269b0871a2a4255a8389c3e48b61","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"de900691407b895cb9e06f4374ca4843f50e269b0871a2a4255a8389c3e48b61","first_computed_at":"2026-05-18T00:03:20.569851Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:03:20.569851Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QRj2uvySunJQsiqdEO6Eez0UjzrZG1wy/zHLwJJ28Pafx7eya1Z4jjPJ7pAtx0V1spiDrKhFKMQPTGaFKP84Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:03:20.570292Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.06407","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fec4b8b850def4e356ee569812c439457196d114954803357f4294b24b58f2f0","sha256:3a9ff3662756785897dfdd938fca08d05d8ec1cff0f3c619b2205c68db1a36d3"],"state_sha256":"c9a7a63ec55f587a671e0715446e373f675508ebd1cc7ee6b5753ba2d9ab4765"}