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Discover Ludwig"hard numbers" is a correct and usable phrase in written English.
It refers to specific and verifiable numerical data or statistics. You can use "hard numbers" when you want to emphasize the concrete numerical evidence supporting a statement or argument. Example: "While some may argue that the new policy is beneficial, the hard numbers show a decline in profits and customer satisfaction."
Exact(60)
(There are no hard numbers).
Hard numbers tell the story.
Those are the hard numbers.
Japanese doctors like the hard numbers.
Those are hard numbers to overcome.
Of course, these are not hard numbers.
So let's start with the hard numbers.
But elections are won with hard numbers.
Actual votes are fixed, hard numbers.
What does that mean in hard numbers?
"Some hard numbers on science's leadership problems". Nature.
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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