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The phrase "are valid only" is correct and usable in written English.
It can be used to specify that something is true or applicable in a limited context or under certain conditions.
Example: "These results are valid only for the specified time period."
Alternatives: "are applicable solely" or "are true exclusively".
Exact(59)
These findings are valid only for unchoked micro channel flows.
However, they are valid only in their own specific situations.
(Editor's note: the opinions expressed here are valid only until 1 30 Saturday afternoon.
Comparisons may be performed on Int, String, and Bool types, while arithmetic operators are valid only on Ints, and boolean operations are valid only on Bools.
The marriages are valid only in Spain and in other countries that accept same-sex marriages.
(NOTE: The comments about support are valid only through 30 June 2011).
Cancellation requests are valid only upon Stanford confirming receipt of your request.
The calculated capacities are valid only for a certain failure pattern.
However, they are not general because they are valid only for some model cases.
Unfortunately, these methods are valid only for the view-sun directions for which they are designed.
Tickets, which cost $18 on weekdays and $20 on weekends, are valid only for a specific time and date.
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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