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The phrase "premised on how" is correct and usable in written English
It can be used when discussing the basis or foundation of an argument, theory, or idea, particularly in relation to a specific method or approach. Example: "The research findings are premised on how effectively the new teaching method engages students."
Exact(2)
It's a comedy that's premised on how wealthy and powerful Qataris are, but delivered with charm and a sense that he knows how arrogant, absurd even, the power and wealth might seem.
At the same time, his entire defence was precisely and explicitly premised on how much Trayvon Martin "looked like" a big, black "thug", and how reasonable it was to be suspicious and alarmed when Trayvon – doing nothing more than walking toward his father's house – resembled someone who "might be" a "predator" engaged in a "rash" or a "spree" of crime.
Similar(58)
That approval was "premised on a flawed depiction" of how the program operated, Bates wrote, "buttressed by repeated inaccurate statements in the government's submissions" to the court.
"It has finally come to light that the F.I.S.C.'s authorizations of this vast collection program have been premised on a flawed depiction of how the N.S.A. uses" the phone call data.
He writes that in 2009 the court concluded that its initial decision to authorise the phone-record collection "had been premised on a flawed depiction of how the NSA uses [the acquired] metadata…buttressed by repeated inaccurate statements made in the government's submissions".
3 EBCD is premised on developing deep understanding of how users perceive and experience the look, feel, processes and structures of services, all the aspects of organisations that users interact with.
This is premised on a belief that inequalities in service provision can be addressed by finding ways of improving how services are delivered [ 3, 45].
Was DOMA premised on discrimination?
Jihadi culture is premised on such anachronisms.
It's not premised on optimal conditions.
It is premised on an ingenious conceit.
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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