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The phrase "bound in" is a valid English phrase that can be used in written English.
It is usually used to describe the condition of something being enclosed, usually by a physical object. For example, "The book was bound in leather."
Exact(59)
Theorem 3 and Corollary 1 show that the bound in (3) is bigger than the bound in (2) and the bound in Corollary 1 of [6].
Genes that were TSS-bound in ESCs tended to be bound in NPCs as well.
Hence, the bound in (2.1) is sharper than the bound in (1.2).
Some are boxed, others bound in goatskin.
His fists, bound in wristbands, are clenched.
Made of metal, bound in black.
He was bound in duct tape.
The book is bound in rich leather.
The booklet is bound in hymnbook green.
These restrict your growth and keep you bound in".
Similar(1)
Kmeans CPU-bound in iteration, IO-bound in clustering.
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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