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Discover Ludwig"presumably by" is correct and can be used in written English.
You can use it when you are speculating or making an assumption about something. For example: "The dog must have escaped, presumably by digging under the fence."
Exact(59)
Presumably, by the Fourth of July, we will know.
They are "connected by numbers," presumably by their weight.
Her bedside lamp lit up, presumably by her hand.
FADH2 is also formed from reduced riboflavin, presumably by sequential flavokinase and FAD synthetase action.
One's vocation is that to which one has been called – called presumably by God – to perform.
Addition of rumen fluid increased power production, presumably by providing growth factors to anode-respiring bacteria.
Smc/ScpAB promotes chromosome segregation in prokaryotes, presumably by compacting and resolving nascent sister chromosomes.
Presumably, by 2006, members of this cohort had already lowered their expectations.
The same year, his blog was shut down, presumably by the government.
He was assassinated last year, presumably by Al Qaeda operatives, in the days before Sept. 11.
Similar(1)
"Most were shot, and some appear to have been crushed to death, presumably by vehicles.
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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