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We prove that a (v,0)-semilattice $S$ is flat if and only if it is distributive."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"math/0501431","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.GM","submitted_at":"2005-01-25T08:24:15Z","cross_cats_sorted":[],"title_canon_sha256":"726462b6c2b92894677b3b573322a759c7cce3a24994b20de9a8392fbdb24878","abstract_canon_sha256":"b82765452776e01087377210573fa90e289f0566fffe9124bdb7510c7a661521"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:08:51.379178Z","signature_b64":"qYdGugzv8Uz7G7s8CH2x86t3q1FZgy2R5z3a6BuLVTeXIQU3+zS6QIpyEk7aGx1BwZscVNkr/1smgorFEQ6WAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1e6511ac332e4e031bfa88a422f1c07a449c4e19fc6ae07bd409a6b2fc88044e","last_reissued_at":"2026-05-18T01:08:51.378650Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:08:51.378650Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Flat semilattices","license":"","headline":"","cross_cats":[],"primary_cat":"math.GM","authors_text":"Friedrich Wehrung (LMNO), George Gr\\\"atzer","submitted_at":"2005-01-25T08:24:15Z","abstract_excerpt":"Let $A$, $B$, and $S$ be (v,0)-semilattices and let $f: A\\to B$ be a (v,0)-embedding. Then the canonical map, $f \\otimes \\id\\_S$, of the tensor product $A \\otimes S$ into the tensor product $B \\otimes S$ is not necessarily an embedding. The (v,0)-semilattice $S$ is flat, if for every embedding $f : A\\to B$, the canonical map $f\\otimes\\id$ is an embedding. 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