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Is there any significant difference between Correspond to and Correspond with?

I only mean in the sense of "matching", here, rather than "communication".

I've looked at a few sources, but I can't seem to find a good explanation that makes it clear in which context each form would be used. Some sources suggest that only Correspond to is used in the sense of "matching", whereas others suggest Correspond with can also be used in that sense (and sometimes also with slightly different meaning).

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Your question sent me on a pleasant search. A bit more here.

Correspond to is used when two things are analogous or similar

...all of which correspond to real numbers...

or agree in amount, position, etc.

figures and letters on the left in the list below correspond to similar figures and letters in the statement of differences...
...events A and B also correspond to positions A and B on the train...
During the night Lee moved his left up to make his line correspond to ours...*

Correspond with is used when it means to be in harmony or agreement

...a committee was appointed of some from each Quarterly Meeting, to correspond with the meeting for sufferers in London...**
The empires grew in size and range, and men's ideas grew likewise to correspond with these things...

*Personal Memoirs of Ulysses S. Grant (1885)

**from Considerations on the Payment of a Tax laid for Carrying on the War against the Indians (1757)

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    Correspond with also, of course, means exchange letters with. – Brad Dec 19 '13 at 9:01
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To avoid confusion, use 'correspond with' to indicate written communication with someone and use 'correspond to' to indicate agreement or harmony.

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    The way to avoid confusion is to properly understand what the differences are - which is the whole point of the question. (The question is also specifically not about communication). – ekhumoro Sep 18 '18 at 15:27

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