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"principally based" is correct and usable in written English.
Typically, it is used to describe something that is largely or mostly based on a certain principle. For example: "This study is principally based on the principle that everyone should have access to quality healthcare."
Exact(60)
Road pricing schemes are principally based on cordon-based pricing.
The study is principally based on the SIMION8 program.
The presentation of his case is principally based on publicly available sources.
"I am especially pleased to join an enterprise principally based on the West Coast".
The interest in applying gold nanoparticles is principally based on their monodispersity.
The first stage is principally based on linear time invariant autoregressive modelling.
The concept of a natural tracer is principally based on water rock interaction.
The Council has been in existence since 1967 and until recently was principally based in Berkeley, Cal., where Pickus lives with his family.
The SI is principally based on a system of base quantities, each associated with a unit and a realization.
In this study, several bonded solid lubricant coatings, principally based on PTFE or MoS2, were investigated by ball cratering and fretting tests.
Zeolite membranes possess a highly defined microporous structure which is capable of very unique separation principally based around molecular size exclusion, adsorption, and diffusion.
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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