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The phrase "The smallest difference" is correct and usable in written English.
You can use it when discussing minimal variations or distinctions between two or more items, concepts, or situations. Example: "In the experiment, we observed the smallest difference in temperature between the two samples."
Exact(60)
The smallest difference, $100,000, belonged to Scott Hatteberg ($1.1 million) and the Boston Red Sox ($1 million).
The smallest difference in medians was found within poorly represented classes, in which all orders have medians less than 20.
The smallest difference was in the chest compression.
The smallest difference between the horizontal and vertical exposures is obtained for the haze.
The smallest difference obtained between the adaptive and the 10-iteration schemes occurs for the video "Claire".
The smallest difference between the two modalities occurred in the alcohol use domain.
The smallest difference between the two estimates was for the Neanderthals (<1%), while a 25% discrepancy was identified for the Au.
The smallest difference was observed in the Northland sample.
The smallest difference observed was for male gender (-1.0%).
The smallest difference outside the 95% range is called the smallest detectable difference.
The smallest difference was between the two Red Holstein base groups (0.49).
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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