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Furthermore, we show that any infinite-dimensional sublattice of $C[0,1]$ is either lattice isomorphic to $c_0$ or contains a sublattice isomorphic to $C[0,1]$. As a consequence, it is proved that for a separable Banach lattice $X$ the following conditions are equivalent:\n  (1) $X$ is linearly embeddable in a Banach lattice if and only if it is "},"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":"2109.00832","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2021-09-02T10:32:27Z","cross_cats_sorted":[],"title_canon_sha256":"32b1b9392119c575d24e185a4d797b280b4aec40ebb6268d8d62f8d94b0e8815","abstract_canon_sha256":"a70259c94a87c8e71b7b2be7a3fb953c5fb8136b6025b9711bee5782f22ce9e2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:10:58.886120Z","signature_b64":"oCwqOk3dCJFrusi9lsLi4PPYa6nPkhttTSTWC1AdrIjEFilsHPFxYmIxSUVABN2OiSvdWO9IZb+N9MDbsO79AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f7fa323fca8e63e383411ff11e2a3b981140d58b8bce79bf2545bf16d4db4ed2","last_reissued_at":"2026-07-05T03:10:58.885766Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:10:58.885766Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Linear versus lattice embeddings between Banach lattices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Abraham Rueda Zoca, Antonio Avil\\'es, Gonzalo Mart\\'inez-Cervantes, Pedro Tradacete","submitted_at":"2021-09-02T10:32:27Z","abstract_excerpt":"A well-known classical result states that $c_0$ is linearly embeddable in a Banach lattice if and only if it is lattice embeddable. 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