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The phrase 'based on one' is correct and usable in written English.
You can use this phrase when talking about something that is based on one element or idea. For example: The success of the business is based on one simple philosophy: the customer is always right.
Exact(51)
Based on one photo.
All based on one hallucination?
The rates are based on one cyclist's riding solo.
We can't lose focus based on one night".
It was not based on one 45-minute telephone call.
Or you can lose based on one tiny mistake".
Similar(9)
"It's not based on one-off projects.
Action cannot be based on one-sided-facts or thoughts.
The very essence of the form, the jam session, is based on one-upmanship.
*p-values based on one-way ANOVA.
P values are based on one-tailed test statistics.
More suggestions(25)
based on annihilating
based expressly on
based on received sync
based on boatloads of
based on the ioc
based on the converse
based on one exam
based on one game
based on one mode
based on merely one
based on one climb
based on illuminated
based on one early
based on realised
based on synthesizer
based on negation
between wrestlers based on
based on one index
based on six servings
based on improper
based on one internal
based on one element
between VOCs based on
based on justifiable
based on men coming
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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