{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:K5XN3WJLVT3IHJQBEPCIXO75RF","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":"fe2d29834d4d370555d2c7cf2762882d31cd261a0e3e33f4c1133d0b8c838181","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2011-10-09T09:17:23Z","title_canon_sha256":"6a18f11b44c8c4aab4fa50dfff9cfe38ade9de23fe84f68b992e2a88eef70316"},"schema_version":"1.0","source":{"id":"1110.1811","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.1811","created_at":"2026-05-18T04:11:19Z"},{"alias_kind":"arxiv_version","alias_value":"1110.1811v1","created_at":"2026-05-18T04:11:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.1811","created_at":"2026-05-18T04:11:19Z"},{"alias_kind":"pith_short_12","alias_value":"K5XN3WJLVT3I","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_16","alias_value":"K5XN3WJLVT3IHJQB","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_8","alias_value":"K5XN3WJL","created_at":"2026-05-18T12:26:32Z"}],"graph_snapshots":[{"event_id":"sha256:dcbbfc376269c6fcdfcef4084df5cb535d729eefa4b44f731dc33034461f9806","target":"graph","created_at":"2026-05-18T04:11:19Z","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":"In this paper we consider an aggregation model f: X1 x ... x Xn --> Y for arbitrary sets X1, ..., Xn and a finite distributive lattice Y, factorizable as f(x1, ..., xn) = p(u1(x1), ..., un(xn)), where p is an n-variable lattice polynomial function over Y, and each uk is a map from Xk to Y. The resulting functions are referred to as pseudo-polynomial functions. We present an axiomatization for this class of pseudo-polynomial functions which differs from the previous ones both in flavour and nature, and develop general tools which are then used to obtain all possible such factorizations of a giv","authors_text":"Miguel Couceiro, Tam\\'as Waldhauser","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2011-10-09T09:17:23Z","title":"Pseudo-polynomial functions over finite distributive lattices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.1811","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:d25fe87e22db3a1f7bdf98981035eb6f4002232c51a0d0a5dba4933fb0fa554d","target":"record","created_at":"2026-05-18T04:11:19Z","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":"fe2d29834d4d370555d2c7cf2762882d31cd261a0e3e33f4c1133d0b8c838181","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2011-10-09T09:17:23Z","title_canon_sha256":"6a18f11b44c8c4aab4fa50dfff9cfe38ade9de23fe84f68b992e2a88eef70316"},"schema_version":"1.0","source":{"id":"1110.1811","kind":"arxiv","version":1}},"canonical_sha256":"576eddd92bacf683a60123c48bbbfd897754a1d679c929cd6f153875197c4b52","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"576eddd92bacf683a60123c48bbbfd897754a1d679c929cd6f153875197c4b52","first_computed_at":"2026-05-18T04:11:19.579530Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:11:19.579530Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7o28FOVOsaTbSHjtcOjHCUI0zYPeJ25zSfFrLALLO0UNSNvTQFtxhMvz8e6t5vsViQImZK+dQAkrUweMFAE4CA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:11:19.579988Z","signed_message":"canonical_sha256_bytes"},"source_id":"1110.1811","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d25fe87e22db3a1f7bdf98981035eb6f4002232c51a0d0a5dba4933fb0fa554d","sha256:dcbbfc376269c6fcdfcef4084df5cb535d729eefa4b44f731dc33034461f9806"],"state_sha256":"8c0243b03ba220535af041c7ea0bfb6cf00d1589297117eec936a718cb597a4c"}