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The phrase "a certain minimum" is correct and usable in written English.
It can be used when referring to a specific but unspecified lower limit or threshold in various contexts, such as requirements or standards.
Example: "To qualify for the scholarship, applicants must meet a certain minimum GPA."
Alternatives: "a specific minimum" or "a defined minimum".
Exact(59)
Our issue is we guarantee a certain minimum amount per team that goes to the players.
It is government policy that radio stations must play a certain minimum amount of French music.
One requires parents to certify that they have spent a certain minimum amount of time practicing driving with their children.
There's a mountain of research showing that, once over a certain minimum, increased income isn't reliably associated with increased happiness.
If a gypsy could not prove he had a certain minimum income, he would not get one.
In the interest of tax simplification, the tax credit should apply only to donations above a certain minimum.
Single-lens reflex cameras need a certain minimum lens-to-film distance to accommodate the swinging mirror.
When it comes to experience goods, price can be useful to reject anything below a certain minimum.
Update: Sotheby's was in fact itself the guarantor on this particular lot: it guaranteed the seller a certain minimum, regardless of what happened in the auction room.
The bonus is earned if the funds under management yield a return above a certain minimum level (e.g., full preservation of invested capital plus 8 percent).
There is a certain minimum level of spending required for core services like national defence, law and order, and basic education.
More suggestions(19)
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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