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The phrase "are principally based" is correct and usable in written English.
It can be used to indicate the primary foundation or source of something, often in academic or formal contexts.
Example: "The conclusions of the study are principally based on the data collected over the past five years."
Alternatives: "are mainly founded" or "are primarily derived".
Exact(9)
Road pricing schemes are principally based on cordon-based pricing.
Engineering standards employed in the United States to design concrete waterway control structures for barge impact loading are principally based on data collected from full-scale experimental barge flotilla (barge tow) impact tests.
Chemical weathering indices are principally based on the basic assumption that distributions of chemical elements as well as loss on ignition (LOI) content along the profile are mainly regulated by the degree of weathering.
It is pertinent to observe that these attitudinal ratings are principally based on anecdotal evidence rather than systematic investigation of parents and professionals.
The measures to eradicate and control brucellosis outbreaks are principally based on an intensive test-and-slaughter policy [ 2, 3], in which effective technology to diagnose brucellosis plays an important role.
10 In Argentina, Chile and Uruguay, the available data on CVD risk factors come mainly from cross-sectional studies that are principally based on self-report or studies conducted with small convenience samples, which do not give reliable estimates.
Similar(51)
The presentation of his case is principally based on publicly available sources.
The Council has been in existence since 1967 and until recently was principally based in Berkeley, Cal., where Pickus lives with his family.
The following classification is principally based on that of American paleontologist George Gaylord Simpson, with alterations in the bovid subfamilies, in the placing of early relatives of giraffes and deer in a giraffoid subfamily Palaeomerycinae, and in the placing of hypertragulids and protoceratids with camels.
The study is principally based on the SIMION8 program.
The interest in applying gold nanoparticles is principally based on their monodispersity.
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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