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The phrase "based on their proximity" is grammatically correct and commonly used in written English.
It is typically used to describe a situation where something is influenced or determined by the closeness or nearness of something else. Example: The students were assigned to work in groups based on their proximity to each other in the classroom. In this example, the students' grouping was determined by their physical location in the classroom.
Exact(60)
Consumers join the coalitions whose energy profile is more similar to theirs and also based on their proximity.
4. Citizens are ranked based on their proximity to dying for their country.
Half of the students will be chosen based on their proximity to the school; the other half will come from disadvantaged areas across the city.
But there's no compelling reason that we should decide which immigrants to welcome based on their proximity to our border, and their ability to slip across.
The cards are available at 10 stations around the city, which were selected based on their proximity to the flagship store and their high ridership.
The bulk of state schools in England and Wales admit pupils based on their proximity to the school, meaning that the closer a family lives to their preferred school, the more likely they are to gain entrance.
The GAP METROCARDS, designed in the chain's trademark blue, are available at 10 subway stations, which were selected based on their proximity to Gap's three-story flagship at 60 West 34th Street.
The Department of Defence said the countries were chosen based on their proximity to training ranges that would reduce the time and cost of transporting it for joint US exercises.
Before he became boss of the central bank last year, Raghuram Rajan worried publicly that India could start looking like an oligarchy along the lines seen in Russia: "too many people have got too rich based on their proximity to the government".In a recent poll 96% of Indians said corruption was holding their country back, and 92% thought it has got worse in the past five years.
Binding-site residues are then identified based on their proximity to the docked ligand.
The app then scours the database and lists the sexual offenders based on their proximity to the location you gave.
More suggestions(16)
based on their ninja
based on their lack
based on their success
based on their year
based on their position
based on their spec
based on their story
based on their gender
based on their judgement
based on their yield
based on their fitness
based on their counter-subversion
based on their performance
based on their complexity
based on their skin
based on their faith
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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