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The phrase "which was based on" is correct and usable in written English.
You can use it when referring to something that was established on a certain basis or when referring to an idea that was derived from something else. For example, "The novel's plot was derived from a series of short stories, which was based on historical events".
Exact(58)
New York's campus safety law, which was based on the one in California, was signed by Governor Pataki in April.
This eliminated the old system, which was based on geography.
The movement's credibility, which was based on running its own state, has been sapped.
Herzl's Zionism, which was based on creating security for an endangered people, dissipated.
Ditto in today's update, which was based on questioning completed on Wednesday.
He was "absolutely shattered" at his sacking, which was based on a "misunderstanding".
(He has appealed his recent suspension, which was based on these allegations).
The price was $89,000, which was based on the first two of our numbers.
This idea, which was based on actual experiments, was suggested by Fowler's daughter.
The CX-5 replaces the Tribute crossover, which was based on the Ford Escape.
That year he completed The Card Party, which was based on sketches of his fellow soldiers.
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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