Determine the difference between attainable f- and g-growth rates

Determine the set differences between the asymptotically attainable growth-function classes for f and g.

Background

The paper notes that the constant-zero function belongs to both classes but does not determine whether other functions distinguish the two invariants.

References

Problem 10.7. Determine Af \Pg and Pg f.

— Monochromatic graph decompositions and monochromatic piercing inspired by anti-Ramsey colorings  (2501.09342 - Caro et al., 16 Jan 2025) in Problem 10.7, Section 10.1