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For any two equivalence classes $[p]$ and $[q]$ of projections we write $[p]\\sqsubseteq [q]$ iff for every primitive ideal $\\mathfrak p$ of $A$ either $p/\\mathfrak p\\preceq q/\\mathfrak p\\preceq (1- q)/\\mathfrak p$ or $p/\\mathfrak p\\succeq q/\\mathfrak p \\succeq (1-q)/\\mathfrak p.$ We prove that $p$ is central iff $[p]$ is $\\sqsubseteq$-minimal iff $[p]$ is a characteristic element in $K_0(A)$. If, in addition, $A$ is liminary, then each extremal state of $K_0(A)$ is discrete, $K_0(A)$ has general comparab"},"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":"1806.03970","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2018-06-11T13:42:51Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"61ea7f08143a99a895f364b28284b7c093cc6f746bb5ec5acf9cd644e5aac311","abstract_canon_sha256":"2c667a4ee3af3f33a8d4acbe3e3f4599dadbdfe34c0f5aa3ba92fa900f229729"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:13:41.311148Z","signature_b64":"dsyn16ZkEH7MwGxg4Bo3IDN9UMlcefN5tHhpK/WiJaKmzfYsTyKZOpEbsvR3e4H6RwoNuWHOvIrIcAiXt8e7DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4747e7f5b22b26e3fefd891b630a40c7c3af45a4570e970da27126f9b32d46aa","last_reissued_at":"2026-05-18T00:13:41.310272Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:13:41.310272Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Approaching central projections in AF-algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.OA","authors_text":"Daniele Mundici","submitted_at":"2018-06-11T13:42:51Z","abstract_excerpt":"Let $A$ be a unital AF-algebra whose Murray-von Neumann order of projections is a lattice. For any two equivalence classes $[p]$ and $[q]$ of projections we write $[p]\\sqsubseteq [q]$ iff for every primitive ideal $\\mathfrak p$ of $A$ either $p/\\mathfrak p\\preceq q/\\mathfrak p\\preceq (1- q)/\\mathfrak p$ or $p/\\mathfrak p\\succeq q/\\mathfrak p \\succeq (1-q)/\\mathfrak p.$ We prove that $p$ is central iff $[p]$ is $\\sqsubseteq$-minimal iff $[p]$ is a characteristic element in $K_0(A)$. 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