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The phrase "are based on mere" is correct and usable in written English.
It can be used when discussing the foundation or reasoning behind a statement, idea, or argument, often implying that it is insufficient or trivial.
Example: "The conclusions drawn in the report are based on mere speculation and lack substantial evidence."
Alternatives: "are founded on nothing but" or "are grounded in mere".
Exact(1)
The main problem remains, as Jona Lendering points out, that most of the things we know about Aspasia are based on mere hypothesis.
Similar(59)
The trial, he wrote, had been based on mere fantasies and delusions.
In his ruling Monday, the judge said he couldn't approve a settlement that was based on "mere allegations".
In their appeal motion, defence lawyers were sharply critical of the verdict, maintaining it was based on mere hypotheses and saying that the motive was absent.
The development of these forecasts cannot be based on mere transfer of experience from other airports, particularly in the modern era of wide regulatory reforms, liberalization of the aviation market and increasing airport competition.
Nevertheless, when a jury verdict bankrupts a media company for what it has published, we ought to examine meticulously whether the company received due process, whether the court applied the correct 1st Amendment principles, whether the verdict was based on mere antipathy rather than law and fact, and whether the damages are proportionate to the alleged wrongdoing.
Knowledge is based on forgetting.
At present almost all the world's food crops are based on a mere nine species of plants, but in the future any of thousands of other species might prove invaluable.
Both are based on trust.
EXDOs are based on ASBOs.
Some analysts worry that if a surveyor's workload has fallen sharply, his judgment may be based on a mere handful of properties.
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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