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"a mere conjecture" is correct and usable in written English.
You can use it to refer to an assumption or guess that has not been confirmed. For example, "His statement seems to be based on a mere conjecture, as he has not provided any evidence to support it."
Exact(3)
But we don't have to leave this as a mere conjecture.
"Such a conspiracy theory must remain a mere conjecture, attractive only because alternative explanations are so unsatisfactory," Marshall Lee Miller said in his book "Bulgaria During the Second World War" (Stanford University Press, 1975).
One may make a mere conjecture that those patients had not been so serious from the viewpoint of the pathologic exam.
Similar(57)
Thus, British civil servants in charge of the investigation noted that "some external cause may (have) overwhelm ed) both man and machine," which inadvertently inspired a plethora of theories based upon mere conjecture by the common population.
But, as Flossie did not permit an autopsy, this last theory is mere conjecture.
The style, she says, is the man, "a reputable scientific gentleman, courteous, trustworthy and friendly... a champion of common sense... and scornful of mere conjecture".
Unfortunately its promise remains unfulfilled, leading Lee Smolin to conclude that string theory is unscientific; not only that, he regards it as mere conjecture and unworthy of being called a theory at all.______________________________________________Fiction and memoirs______________________________________________Suite Française By Irène Némirovsky.
As a market researcher, Dr. Fink said that perception about the state is mere conjecture unless you use statistical surveys to compare New Jersey with other states, using something marketers call a "competitive set".
The existence of such an intensity-dependent activation of the descending modulatory system is mere conjecture at this point.
Of course, this is mere conjecture.
But all of that was mere conjecture last Friday night.
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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