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The phrase "empirically proven" is correct and usable in written English.
It is typically used to describe something that has been demonstrated or validated through experimentation or observation. Example: The effectiveness of the new medication was empirically proven through a series of carefully controlled trials.
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I have empirically proven this during innumerable picnics.
Doctors could then be protected from negligence claims by showing they used an empirically proven course of treatment.
Then, add empirically proven design features to them, making it easier for workers to make good choices.
But I don't care, because in yesterday's independently-adjudicated time trials, it was empirically proven that I can type "The quick brown fox jumps over the lazy dog" faster than any of them.
Even just a couple of years ago, the suggestion that a rape allegation could stick to beloved frozen pudding magnate Bill Cosby was laughable (and empirically proven to be untrue – no one did believe them).
With empirically proven cognitive-behavior therapy, children can learn to reinterpret their overprotective brains and their unreliable first-reaction data and, in doing so, outsmart the worry and not let their amygdalas ruin their days.
Direct-air capture — deliberate extraction of CO2 from our atmosphere using empirically proven technologies — may turn out to be more expensive than carbon capture at the emission source, but it has several important possible advantages.
But you may be surprised to learn that, despite this decade's worth of empirically proven mediocrity, Marsh has managed to play 61 international matches for Australia, including seven Test matches, over the past five years.
Most of the activity on the left revolves around the Analyst Institute, a firm quietly founded in 2007 by A.F.L.-C.I.O. officials and liberal allies, whichseeks to establish a set of empirically proven "best practices" for interacting with voters.
"Experts" in magazines or on websites are always telling us to consume less caffeine, not to use a bar of chocolate to get over the mid-afternoon slump, to beat a work-endangering hangover with a bit of water and some vitamin C rather than the empirically proven solution of a ham and cheese croissant.
As a result, the literature lacks an empirically proven and systematic perspective on OC distribution structures.
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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