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The phrase "the difference persists" is correct and usable in written English.
You can use it when you want to refer to an ongoing or continuous difference between two things. For example: "Even after the two companies merged, the difference in their corporate cultures persists."
Exact(7)
More than a century later, the difference persists in almost the same magnitude.
And the difference persists well beyond the years when women might be taking care of young children: it is actually greater among older, better-qualified workers.
So the difference persists, with the only people who own Palm being those who hope for a quick trade before the distribution or don't understand what is about to happen.
The breasts usually even out over time, but in some girls the difference persists after puberty.
The difference persists throughout the injection.
It remains unknown on whether the difference persists with age.
Similar(53)
The difference persisted in the long term.
The difference persisted even a month after the treatment stopped.
The difference persisted after controlling for CD32 and CD16 polymorphisms.
And the difference persisted over time: the results were not simply a consequence of workers' misunderstanding of the system.
The difference persisted even after controlling for age, race, sex, economic status, educational level, general health and other factors.
More suggestions(2)
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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