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The phrase "acknowledged this fact" is correct and usable in written English.
You can use it when referring to the recognition or acceptance of a particular piece of information or truth.
Example: "During the meeting, she acknowledged this fact and emphasized its importance for the project."
Alternatives: "recognized this fact" or "accepted this fact."
Exact(14)
The passage of the Federal Aviation Administration FAAA) Modernization and Reform Act in 2012 acknowledged this fact, and has since prompted expedited research and development for civilian sUAS.
Molière acknowledged this fact by saying: "My friend Corneille has a familiar who inspires him with the finest verses in the world.
This week, addressing the "Access Hollywood" videotape for the first time, Ivanka told Fast Company magazine, "My father's comments were clearly inappropriate and offensive, and I'm glad that he acknowledged this fact with an immediate apology to my family and the American people".
They even acknowledged this fact by creating Mac mini Servers with dual hard drives and no optical disc drive.
Google tacitly acknowledged this fact earlier this month, when it made a change to the way it measures Android version adoption on its Developers site.
Obama acknowledged this fact after the Charleston shooting in July.
Similar(46)
The U.A.W. acknowledges this fact.
Even Lewis acknowledges this fact.
Just acknowledging this fact helped exorcise Groomzilla.
The Romney campaign, however, has yet to acknowledge this fact.
Over time, Democratic politicians and economists have been forced to acknowledge this fact.
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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