{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:5L2U3DOQMRN245KN4M7ZKXKYNN","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":"a9e140533d0ac87ea4ba6691c864bf03a7dbe47fbfc403d11fc4549348ee957a","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2010-03-10T20:31:42Z","title_canon_sha256":"6b5b40a804bf85dfaadd56fbd1798fbadc8a2bdbb3e487b1ac99642112d6a972"},"schema_version":"1.0","source":{"id":"1003.2192","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1003.2192","created_at":"2026-05-18T00:57:38Z"},{"alias_kind":"arxiv_version","alias_value":"1003.2192v3","created_at":"2026-05-18T00:57:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1003.2192","created_at":"2026-05-18T00:57:38Z"},{"alias_kind":"pith_short_12","alias_value":"5L2U3DOQMRN2","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"5L2U3DOQMRN245KN","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"5L2U3DOQ","created_at":"2026-05-18T12:26:04Z"}],"graph_snapshots":[{"event_id":"sha256:84aa003ddfec092b66e1e3e9811ff88959a9ef0e65c925c48171984913bee6eb","target":"graph","created_at":"2026-05-18T00:57:38Z","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 aim of this paper is to classify order-preserving functions according to their arity gap. Noteworthy examples of order-preserving functions are so-called aggregation functions. We first explicitly classify the Lov\\'asz extensions of pseudo-Boolean functions according to their arity gap. Then we consider the class of order-preserving functions between partially ordered sets, and establish a similar explicit classification for this function class.","authors_text":"Erkko Lehtonen, Miguel Couceiro, Tam\\'as Waldhauser","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2010-03-10T20:31:42Z","title":"The arity gap of order-preserving functions and extensions of pseudo-Boolean functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.2192","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":"sha256:4c19869831056e7e48577ef71b673b72719d569024f481939e7d6ab60641be00","target":"record","created_at":"2026-05-18T00:57:38Z","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":"a9e140533d0ac87ea4ba6691c864bf03a7dbe47fbfc403d11fc4549348ee957a","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2010-03-10T20:31:42Z","title_canon_sha256":"6b5b40a804bf85dfaadd56fbd1798fbadc8a2bdbb3e487b1ac99642112d6a972"},"schema_version":"1.0","source":{"id":"1003.2192","kind":"arxiv","version":3}},"canonical_sha256":"eaf54d8dd0645bae754de33f955d586b7249db39b250b7f0fce0fca2e6dedafb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eaf54d8dd0645bae754de33f955d586b7249db39b250b7f0fce0fca2e6dedafb","first_computed_at":"2026-05-18T00:57:38.736530Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:57:38.736530Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ccR+l6PA9gwd8xSG+BFvjHm9d18PRfluQpMZ/VkhVvqJGYz+bxOuuH4WZyzRkZHCO4qeHCzBRYT8kvQ7v+JVAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:57:38.737148Z","signed_message":"canonical_sha256_bytes"},"source_id":"1003.2192","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4c19869831056e7e48577ef71b673b72719d569024f481939e7d6ab60641be00","sha256:84aa003ddfec092b66e1e3e9811ff88959a9ef0e65c925c48171984913bee6eb"],"state_sha256":"76e63c3fdc56829106b43f29bb1dcc9c23f9135f38954e338a4814f4c47988ad"}