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The phrase "and the only variation" is correct and usable in written English.
It can be used when discussing a specific difference or change among a set of items or options.
Example: "In this experiment, we tested several samples, and the only variation was the temperature at which they were stored."
Alternatives: "and the sole difference" or "and the unique variation".
Exact(4)
The timepiece's chronometry is measured with absolute precision by the Fleuritest machine and the only variation in rate tolerated falls within 0 and +5 seconds per day, making it one of the most demanding devices that exists.
To ensure a valid comparison, the sequence of random seeds is the same and the only variation is the choice of parameters.
Similar gas-phase conditions were obtained for both experiments and the only variation between the two experiments was the different sulfate seed aerosol acidities.
If everybody in the present model has the same genome, then their genetic death ages all agree, and the only variation would come from the Verhulst deaths (if these are not restricted to newborns).
Similar(56)
And the only variations they like are Bach's Goldberg ones.
A closer examination of these two haplotypes (WH4 and WH5) showed that the only variation present on WH4 is the c.-242-110delAGTA variant, which on its own shows a significant difference in frequency between both groups.
This experiment reproduced the variables manipulated in Experiment 3 (valence of the words, type of offer and uncertainty of the blocks), with the only variation being the instructions given to participants.
A federacy is the only variation between unitary states and federal states.
The only variation was a red lip.
The only variation is how the knuckleball is dancing.
The only variation is whether we have bananas or not.
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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