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The phrase "a complete classification of" is correct and usable in written English.
You can use it when discussing the categorization or organization of items, concepts, or data in a thorough manner.
Example: "The study aims to provide a complete classification of all known species in the region."
Alternatives: "a thorough categorization of" or "an exhaustive classification of".
Exact(42)
A complete classification of the Manchu-Tungus family is hampered by many obstacles.
We give a complete classification of direct limits of full triangular matrix algebras with order preserving embeddings.
Using the "relative" flow of weights for subfactors, we then give a complete classification of strongly amenable subfactors of typeIII0.
We obtain a complete classification of designs with r=2λ−μ in case Γ has an eigenvalue −2.
A complete classification of solution loci in terms of the above characteristics multiplicity, stability, and bifurcation direction at Hopf bifurcation points—is presented for the parameter region investigated.
A complete classification of [100] tilt grain boundaries into the categories of special, vicinal and general resulting from measurements of grain boundary segregation in α-iron is presented.
Similar(18)
Under certain assumptions, we can, thanks to a result by Popa, give a complete classification for this family of factors.
Secondly, we give a complete classification for the existence of a blow-up solution and a global solution.
We adopted a complete classification list of professions which has been published elsewhere by Elmarsafawy et al. (2002).
A complete classification is obtained of continuous, translation invariant, Minkowski valuations on an m-dimensional complex vector space which are covariant under the complex special linear group.
The groups Fp× above have order p − 1. Mathematicians often strive for a complete classification (or list) of a mathematical notion.
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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