Is 9999 coins a hard limit?

Is 9999 coins a hard limit? - Brown Wooden Heart Shaped Ornament

I know 9999 coins maxes out the coins display, but do coins accrue beyond the 9999 even if they don't display? For example, if I have 9999 coins, find 10, and spend 10, will my display register as 9999 or 9989? Trying to determine whether I would immediately need to spend down the number or else risk wasting coins.

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