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Discover LudwigThe phrase "the assertion" is correct and usable in written English.
You can use it when you want to refer to a statement that is made to be accepted as true. For example, "The assertion that the world is round is now widely accepted."
Dictionary
the assertion
noun
The act of asserting, or that which is asserted; positive declaration or averment; affirmation; statement asserted; position advanced.
Exact(56)
The assertion has resonance.
The rebels denied the assertion.
Z then repeated the assertion.
The assertion shocked me.
Russell denied the assertion.
Republicans rejected the assertion.
The assertion could not be verified independently.
"It is the assertion of a promise.
The assertion seemed just as dubious.
The assertion, though conspiratorial, seemed plausible.
Politifact rated the assertion "mostly false".
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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