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[ "<thought>\nThe text is mid-sentence, having just introduced the efficiency gains of focusing on $O(k)$ coordinates. The next few tokens will logically continue this sentence, likely by elaborating on the benefits or consequences of this reduction in focus. The grammar suggests a clause beginning with \"Furthermore...
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[ "<thought>\nThe word \"We\" at the cut suggests the beginning of a new sentence, likely introducing a claim, result, or argument. Given the context of comparing recovery schemes and their measurement requirements, the next few tokens will most likely be \"show\" or \"prove\" followed by a statement about the number...
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[ "<thought>\nThe cut occurs mid-sentence, in the phrase “as well as for the setting where additional side information on the input vector $\\fl{x}$” — the sentence is clearly introducing a new condition or structure on $\\fl{x}$. The next few tokens will likely name or define the type of side information, possibly a...
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[ "<thought>\nThe text is mid-definition, inside a removed block, and the next tokens will continue the formal definition of $(\\epsilon, \\beta)$-approximate vector recovery. The next few tokens will likely complete the phrase “Fix any $0” by specifying the domain or constraint on $\\epsilon$ and $\\beta$, such as “...
[ 0 ]
[ false ]
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[ "<thought>\nThe text is mid-way through a definition, specifically the label and title line of a definition environment. The line begins with “\\begin{defn}[$(\\epsilon, \\beta)-$approximate vector recovery]\\label{def:approx_vector}” and cuts off at the comma following “$\\beta)-$approximate vector recovery”. The ...
[ 0 ]
[ false ]
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[ -63.38993835449219 ]
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false
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