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"on this assumption" is correct and usable in written English
You can use this phrase to talk about a supposition that you are making and using to make a decision or a conclusion. For example, "Based on this assumption, I think the best course of action is..."
Exact(59)
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.
"On this assumption, the resource assessment estimates up to 4,000 additional prison places may be needed.
We cast doubt on this assumption.
"I made my comments on this assumption," he says.
If it does, reductionists can challenge mechanists on this assumption.
First-hit means were computed on this assumption.
But many of the value techniques used by investors build on this assumption, he says.
In fact, they have a special derogatory word for anyone who acts on this assumption: "populist".
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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