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The phrase "a decisive assertion" is correct and usable in written English
It can be used when you want to describe a statement or claim that is clear, firm, and likely to influence a decision or opinion. Example: "The speaker made a decisive assertion about the importance of climate change action, leaving no room for doubt."
Exact(1)
Noriega's overthrow was a decisive assertion of U.S. military force for a new American President in a moment of global tumult.
Similar(59)
Two years later, a pugnacious columnist from Baltimore, who was obsessed with language, boldly made the decisive assertion of linguistic independence that had been implicit in American life and letters since 1776.
The clue of the proof of Theorem 1(b) is the following decisive assertion, which is deduced from the strong law of large numbers.
She made a decisive decision.
Despite sharing this assertion, it is believed, however, that a decisive contribution to the reduction of information asymmetries results from the fact that business angels base their funding decisions mainly on qualitative information regarding the project, being aware of the scarcity of quantitative information related to innovation.
But the rise of the idea of the individual artist as auteur – with the concomitant assertion of personal ownership through copyright – marked a decisive breach with the notion of a shared, commonly owned lyrical tradition.
Brims are a decisive feature.
He won a decisive mandate.
"They want a decisive leader".
Is this a decisive argument?
A decisive moment approaches.
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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