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The phrase "a very narrow initial" is correct and usable in written English.
It can be used when describing something that has a limited or restricted beginning or starting point, often in a specific context such as a project, analysis, or design.
Example: "The study began with a very narrow initial focus on the effects of climate change on local wildlife."
Alternatives: "a limited initial" or "a restricted initial".
Exact(1)
A virtual polymer PFM system with a very narrow initial molecular weight distribution and a commercial low density polyethylene triallyl cyanurate system have been used to demonstrate the application of this algorithm.
Similar(59)
So for a vaccine to work, you've got a very narrow window, probably really just preventing the initial infection.
Figure 9 gives an insight into the micromechanics of proppant settling in a very narrow fracture of 2 mm width for low initial proppant concentrations where c v = 0.1 (2.0 lbs/gal).
God you will still recognise by his initial cap, but he had a very narrow escape.
Similar to the initial total RNA profile, cRNA for sample 390 showed a very narrow distribution range and lacked fragments above ~500 nt.
The initial formation of many major structures of the human embryo takes place during a very narrow window of time in the first weeks after conception, often before a woman even knows she is pregnant.
But that is a very narrow part.
"He has a very narrow political base".
It is a very narrow gap.
But it was a very narrow squeeze.
"It was a very narrow escape.
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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