"demonstrably known" is a correct and usable phrase in written English.
You can use "demonstrably known" when you want to emphasize that something is indisputably or clearly recognized or understood by others. Example: The scientist's theory was demonstrably known to be true after multiple experiments and peer-reviewed studies.
Mr. Van Taylor and Mr. Lichtenstein demonstrably know how to do just that.
Allowing these practices to propagate unregulated may have something to do with certain corporate values, which this administration demonstrably knows something about.
But Trump also straight-up lies on occasion, even if it's relatively rare to find a case where he said something he demonstrably knew to be untrue in an effort to deceive someone.
He had never known anyone demonstrably less busy.
He was out, completely and demonstrably, and he knew it as well as any of his outraged opponents.
Ignorance is bliss, or so they say, but it can also be perfidious; especially so when accompanied by the mindless arrogance and puffed-up smugness of the know-it-all who demonstrably does not know it all.
It only occurs to me when I'm back on the ground that the war on terror may not be a good blueprint - it having been, you know, demonstrably counterproductive.
Advocates for the disadvantaged must also highlight and capitalize on the many demonstrably effective antipoverty solutions already well known to the academic, research and nonprofit communities.
Those laundering money had to be shown to be doing so deliberately, not accidentally, and the money had to be demonstrably obtained from criminal acts, not simply deposited by a known criminal.
Polyaenus collected many snippets of information on warfare in his Strategems; some are known from other sources to be reliable, while others are demonstrably false.
