Bitcoin Core Development – PinSketch Why are sketches made up of sums of odd powers?

You can reorganize elements whenever you need them. 2c Continuous power sum for k=a to k=a+2c-1 (power sum S_K is X_One^K + x₂^K +…x_N^K) regardless of the element. all You begin.

However, PinSketch operates on feature-2 fields, so it maintains: (a + b)² =a² + rain² (Freshman’s dream) That is why I assert the following. S_{2 thousand} = S_K²That is, you can calculate the even power sum by squaring the half power sum. Therefore, having an odd power sum is k=1 and k=2c-1 (i.e. set a=1) is sufficient to reconstruct all power sums (including even numbers). k=2c do.

There’s a more detailed explanation in the Miniscript code documentation.