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The phrase 'rigid to' is correct and usable in written English
You can use it to describe a situation that is resistant to change or unwilling to make concessions. For example, "The country's laws were rigid to any reform attempts."
Exact(59)
Thus, resin composites should have good rigidity (to achieve adequate mechanical properties), but should not be too rigid (to minimize stresses) [29].
We Germans are too rigid to compete".
Mr. Fiennes's performance, in any case, is too rigid to admit such undercurrents.
"More rigid to eliminate all the vibrations of the system," he said.
This self-important young woman was too rigid to achieve what she wanted.
Some blame a labour market that is too rigid to create sufficient jobs.
The Indian government may be too rigid to respond to it adequately.
It's strangely rigid to say that we stop being "literary" when we ask them.
And I think it would be too rigid to say everybody needs a four-year-college degree.
"At the consular stage, there's definitely some confusion coming down from the Administration about how rigid to be," he said.
This model is too rigid to bend to the winds of change -- and yet it seems clear that change is inevitable.
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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