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The phrase "exactly coincide" is correct and usable in written English.
You can use it when two things are exactly the same, or in alignment with each other. For example, "The results of our calculations exactly coincided with the results of the experiement."
Exact(41)
Often the two do not exactly coincide.
The knife-edges of image and screen exactly coincide.
And anyway, the Sun and the galactic center will not exactly coincide even in 2012.
It won't always be the case that the readings will exactly coincide with where the lectures are at.
All these things sort of break down a social network and happen to exactly coincide with the growth in pet populations.
The damage identification results obtained in all three cases do not exactly coincide, but they are consistent with the concentration of structural damage observed at the bottom two stories of the building.
Similar(19)
It is pure coincidence that The Observer job exactly coincides with the making of our garden.
The 1861 public debut of one of his big showpieces, "The Icebergs," almost exactly coincided with the declaration of war.
Thus her early career almost exactly coincided with the war, which began in 1975 and ended in 1990.
In 1956, exactly coinciding with Hamilton's collage, the Design Centre opened in the Haymarket, a heaven for aspirational homemakers.
Alas, it is not new, since it exactly coincides with a full state feedback, linear time invariant proportional plus integral (PI) controller with a decaying additive disturbance.
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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