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We show that for any $A \\subseteq \\mathbb{Z}$, if $|A+A| \\le K|A|$, then there exists a subset $A' \\subseteq A$ such that the following holds: $|A'| \\gg_K |A|$ and there exists an order-preserving Freiman 2-isomorphism $\\phi: A' \\rightarrow [-c|A|,c|A|] \\cap \\mathbb{Z}$ where $c$ depends only on $K$. 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We show that for any $A \\subseteq \\mathbb{Z}$, if $|A+A| \\le K|A|$, then there exists a subset $A' \\subseteq A$ such that the following holds: $|A'| \\gg_K |A|$ and there exists an order-preserving Freiman 2-isomorphism $\\phi: A' \\rightarrow [-c|A|,c|A|] \\cap \\mathbb{Z}$ where $c$ depends only on $K$. 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