How to Find the Error for Spline Interpolation Without the Original Function?

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Most of the literature (e.g.: http://pages.cs.wisc.edu/~amos/412/lecture-notes/lecture11.pdf) I have consulted thus far indicates how one would determine the error of a cubic when the original function F is known. Suppose if I wanted to determine the maximum error bound of the interpolating function when the original function is unknown, what would this error be?