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The phrase "are unchangeable" is correct and usable in written English.
It can be used to describe something that cannot be altered or modified.
Example: "The rules of the game are unchangeable, so all players must adhere to them."
Alternatives: "cannot be altered" or "are immutable".
Dictionary
are unchangeable
noun
Something that cannot be changed.
Exact(26)
But there are unchangeable facts about Vaughn.
Unhealthy perfectionism is associated with a fixed mindset (the belief that your basic abilities are unchangeable).
"I'm just realistic," said Arrivabene. "Nobody has the magic to change things when things are unchangeable.
There's nothing about the color assignations which are unchangeable, of course.
Fear is at the heart of the problem: I think the fear that social and cultural norms are unchangeable is the beginning of the problem.
In the SSPP a Liner Service Provider (LSP) only revises one of its many operational strings, and it is assumed that the other strings are unchangeable.
Similar(34)
She simply was; unchangeable, unchanging, in her tweed skirt, her blouse, her Shetland cardigan, her suit for Sunday church, worn with chenille turban, her felt hat for shopping in Minehead.
No cue is unchangeable.
It is unchangeable, immutable.
toward this issue is unchangeable.
And their predilections were unchangeable.
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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