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"on this assumption" is correct and usable in written English
You can use it when introducing an idea or proposition that you are taking as a given, or when referring to a possible supposition or premise. For example: "On this assumption, we can make predictions about the future of the industry."
Exact(59)
"On this assumption, the resource assessment estimates up to 4,000 additional prison places may be needed.
On this assumption, the history of historical thinking and writing is itself an interesting subject.
On this assumption, how would its action express disrespect to those whose views were disfavored?
On this assumption, why not raise as much as possible and go as hard as possible at every startup?
On this assumption, Noah's approach to people parallels his approach to animals.
However, why should one insist on this assumption?
Based on this assumption, piles of hotels and commercial complexes are being built.
There have even been experiments on this assumption, and they have not met with success.
Based on this assumption, they used the serial numbers of captured tanks to estimate the total.
We cast doubt on this assumption.
"I made my comments on this assumption," he says.
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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