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"broken through" is correct and usable in written English.
You can use this phrase to describe someone or something overcoming an obstacle or successfully penetrating a barrier. For example, "The daring musician broke through all the preconceived notions about the genre and created a unique sound."
Exact(58)
Those who have broken through have varying reports.
And those that have broken through have come from pop acts that emulate secular recording artists.
Pacino had broken through.
We've broken through.
Not even Mariano Rivera has broken through.
The wah-wah had finally broken through.
But advertising has not broken through.
Agents had broken through his front window.
I wouldn't say I've broken through yet.
"They have broken through their denial".
Consumer cameras have broken through another barrier.
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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