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The phrase "based on the framework of" is correct and usable in written English.
It can be used to describe something that is done following the structure of an established system or process. For example, "The new educational policy was created based on the framework of the previous program."
Exact(60)
Based on the framework of older game Ingress, which also encourages players to visit real world locations, the addition of Pokémon turned a modest sideshow into a global phenomenon.
The potential output series he's using comes from the Congressional Budget Office, which describes its method (pdf): CBO's estimate of potential output is based on the framework of a textbook model of long-term economic growth, the Solow growth model.
"We are still hammering out the details of the bill based on the framework of an agreement that was announced in January," the spokesman, Dan Morris, said in an e-mail.
The proposed method is based on the framework of [22].
Our method is based on the framework of proximal point algorithm.
This model is based on the framework of thermoelasticity augmented with an internal variable.
The research is based on the framework of the theory of planned behaviour (TPB).
The system is designed based on the framework of collaborative filtering.
Based on the framework of Wiener filter, a Wiener filter preprocessing algorithm for ICI mitigation is proposed.
DeepTutor is the first ITS based on the framework of Learning Progressions (LPs; (Corcoran et al. 2009)).
The formulas of the transmission coefficients are derived based on the framework of the nonequilibrium Green's function technique.
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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