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The phrase 'based on an assumption' is correct and usable in written English.
You can use this phrase to indicate that something is inferred from a certain premise that may or may not be true. For example: "Our plans for the weekend are based on an assumption that the weather will be good."
Exact(60)
The technique is based on an assumption that the items appearing in one sensitive itemset will not appear in another.
"Consumers are making decisions based on an assumption that they are helping Australian farmers," Godfrey said.
The figure is based on an assumption of a static number of about 190,000 commencements.
THE relationship between writers and their readers is based on an assumption of intimacy.
"That was based on an assumption of 15 brigades in combat.
— based on an assumption that someone like me wouldn't have friends or a spouse.
Is it based on an assumption that men are inherently violent?
Scottish Widows' figures are based on an assumption that investments will grow at around 6% a year.
And, according to Corden himself, his character in Hollyoaks was based on an assumption that big people are unattractive people.
It's based on an assumption that servers at Asian restaurants are passing judgment on her choice of flatware.
To this end we apply a method of homogenization based on an assumption of perfect mix.
More suggestions(17)
based on presumptions
is founded on an assumption
based on the presumption
basis of an assumption
the basis of an assumption
based on the supposition
is predicated on an assumption
based on an industry
based on an investigation
based on an agreement
based on an examination
based on an adaptation
based on an interpolation
based on an integer
based on an area
based on an image
based on an action
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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