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The phrase "approximates most closely" is correct and usable in written English.
It can be used when discussing how one thing is similar to or nearly matches another in a specific context.
Example: "The model approximates most closely the actual data observed in the experiment."
Alternatives: "is most similar to" or "is closest to".
Exact(2)
(You can boost your argument by pointing to the declining support for Alternative für Deutschland, the German party that approximates most closely to the National Front).
We use this definition throughout the article, since it approximates most closely the way 'community empowerment' is operationalised by Ashodaya (which, to our knowledge, has not explicitly developed a definition of its own).
Similar(58)
SIVmac251 and SIVmac239 infection of naive pigtail macaques resulted in a gradual decline in peripheral CD4+ T cells in the setting of high levels of viremia, approximating most closely human infection of HIV-1.
The Jelliffe formulae (I and II) [ 15, 16] have been shown to approximate most closely low values of GFR when compared with the inulin clearance [ 17].
The proportionality and scaling constants in our modified equation for emPAI were approximated to provide values for the three reference proteins that approximate most closely the reported or predicted values.
A2780 and CH1 approximated C5 tumours most closely, as both expressed low levels of Let-7 alleles, and high levels of HMGA2 and LIN28B (Figure S4A, S4B).
Harris et al. used the T12-S1 cadaveric spine to reveal that axial rotation increased at the segment of a TLIF stand-alone cage, UPSF further increased stiffness, and BPSF approximated axial rotation most closely to the intact specimen [ 40].
This method most closely approximates the legendary no-limit game.
The proposal issued today most closely approximates the bottom two options.
As a type of artist, Twombly most closely approximates the classic dandy: provoking and impenetrable.
"The goal of all us is to have a market that most closely approximates the normal environment," he said.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com