What Mark Points can be Made

In some rather special cases, it is possible for the matrices on some diagonals to have only polynomial eigencomponents, saying that the Holder continuity is infinite. This happens for the B-splines. 

By taking a high enough power of the scheme, any rational point can be determined as a mark point. The power needed is just the Euler function of the quotient when the denominator has all powers of 2 (in general of the arity) divided out. 

However, at the time of writing, What is the simplest scheme with a Holder-dominant denominator greater than 3 was still an open question. 

The first few powers and the denominators of the mark points that they can find are 

The powers noted by are those cheaply created by successive squaring. Clearly some powers are richer than others for covering many denominators. 

---