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'for the explanation' is a perfectly correct and usable phrase in written English.
You can use it in situations where you are giving an explanation for any given topic. For example, "I always appreciate your help - thank you for the explanation!".
Exact(60)
Thanks for the explanation Donald.
Thank you for the explanation.
but often leave the reader still searching for the explanation.
Please refer to the methods section for the explanation of the different p- and α-values.
Must the assumptions of an explanation be true for the explanation to be correct?
These solutions might be imperative and significant for the explanation of some practical physical phenomena.
This solution may be useful for the explanation of some practical physical problems.
The acidity of the support is considered for the explanation of the activity sequence.
This original technique is highly promising for the explanation of dispersion mechanisms in porous media.
The results demonstrate the importance of crack closure for the explanation of the LCF behaviour.
The trouble is, some of the visitors are too unsettled to linger long enough for the explanation.
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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