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are balls that pass through splitters supposed to have a lifetime of less than one square...?

The lifetime of a ball gets "split" when it passes through a splitter, yes. If it's a truplicate, it may be as low as 1 square. There's a skill tree option to increase this tho

is there a chance it also gets inverted? Because it seems the shorter it flew, the less it lives.

It's timing based, not distance based. So the lifetime is a float value that gets cut in half per splitter it passes through. There could certainly be an error, yes, I'm not sure