Auxiliary functions for extending the five-point certificate

Construct auxiliary functions d(m1,m2) that eliminate the forbidden Chebyshev frequencies while preserving nonnegativity of all coefficients of the certificate for the five-point Fibonacci lattice throughout the range 0 < p <= 24.

Background

The continuous LP method constructs a function beta lying below the transformed potential gamma, interpolating gamma at the relevant Fibonacci-lattice distances, and having nonnegative Chebyshev coefficients. For the five-point Fibonacci lattice, certain frequencies are forbidden and must be removed using explicitly constructed nonnegative auxiliary functions.

The certificate constructed in the paper proves optimality for the worst-case integration potential only up to p approximately 11.664. The authors observe that, for 0 < p <= 24, additional coefficients become negative and explicitly ask whether better auxiliary functions can extend the certificate across this larger parameter range.