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The phrase "a form that does not exist" is correct and usable in written English.
It can be used to describe something that is theoretical, imaginary, or not currently available in reality.
Example: "In the realm of mathematics, we often discuss a form that does not exist, such as a perfect circle in a digital environment."
Alternatives: "a non-existent form" or "an imaginary form".
Exact(1)
It's stale and inauthentic — a form that does not exist outside of the classroom.
Similar(59)
Kurdish authors use stylistic forms that do not exist in any other language.
That's the charm that does not exist in a concrete form building".
Today, that doesn't exist anymore.
In civilian life, that doesn't exist".
Today that doesn't exist.
Others want help that doesn't exist.
The design of the qualitative study assumed a form of collaboration among physicians that did not exist.
This form creates problems of equilibrium that do not exist in lintels.
This has had spin-off benefits in the form of creating new virtual communities that did not exist before.
"While there is a perception in some quarters that some form of control exists, that does not exist," he says.
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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