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"groundless assumption" is a correct and usable phrase in written English
It can be used to describe a belief or idea that is not based on facts or evidence. Example: The politician's argument was based on groundless assumptions rather than concrete data, making it difficult for voters to trust his claims.
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But the haste and confusion of the planning, the determination to keep grim forecasts out of public view, the groundless assumptions, the desire to do it on the cheap — all this left Erdmann and his colleagues poorly prepared for what awaited them when they finally reached Baghdad, on April 23rd.
A reminder of the consequences of approaching systemic risks, based on flimsy or groundless assumptions that things will turn out okay, is seen in the bland reassurances that came back in response to repeated warnings about the massive risks facing the banking system far in advance of the 2007-2008 crisis.
Making explicit groundless assumptions, exposing fallacious arguments, and distinguishing between statements that can and cannot be proven are among the skills students will possess from their first day in college.
Because, assuming for the point of discussion that such a proposal can be made to work (an enormous assumption that may prove very quickly to be groundless, I will fully admit), it does seem to be a rather elegant way out of the wilderness for just about all of the interested parties in the current crisis.
In a first phase of the results analysis, most of the assumptions involving certain possible psychological factors proved to be groundless in view of the patient's answers.
Engaging groundlessness is moving into the discomfort of being groundless and working with that instability.
"The accusations were groundless".
My fears were groundless.
Any worries were groundless.
It's groundless".
The fears proved groundless.
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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