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"based on the assumption" is a valid phrase that can be used in written English.
You can use it when you are referring to a particular hypothesis or theory that you are taking as a starting point in order to explain something. For example, "Based on the assumption that the moon is made of cheese, we can explain why it affects the ocean tides."
Exact(60)
The indictment is based on the assumption — a prudent one — that money pays for image.
After all, this whole policy is based on the assumption that it will save money".
That was based on the assumption (unconfirmed) that David Laws was going to education.
The political case for universal coverage is based on the assumption that voters want it.
"They're based on the assumption that you can make up for the destruction after the fact.
"And that's based on the assumption you're going to get paid at all," Mr. Jacobs added.
This, too, is problematic, because it is based on the assumption that memory is infallible.
She escapes handily: her promise was based on the assumption that Al Gore would be president.
The move was based on the assumption that the endowment would keep growing.
Britain's responses to the phenomenon are based on the assumption that it is a local problem.
Arguments, such as this, are based on the assumption that truths can be arrived at.
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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