Systematic criteria for five-point Fibonacci optimality

Establish systematic conditions on the potential γ, preferably expressed through nonnegativity under differential operators or convexity, that ensure the certificate-construction algorithm proves optimality of the five-point Fibonacci lattice.

Background

The paper reduces five-point Fibonacci optimality to finitely many inequalities involving Hermite-interpolation coefficients and auxiliary-function corrections. These inequalities can be checked for an individual potential, but the paper does not derive general hypotheses that guarantee them.

A general criterion would convert the case-specific certificate method into a systematic optimality theorem for broad classes of tensor-product and related potentials. The authors specifically point to differential inequalities such as the conditions involving (∂s−∂t)^kγ and to convexity as possible ingredients.