‘Degenerate’ in this context means ‘indistinguishable’. I hate the use of this word in scientific contexts, as it’s never used in non-scientific contexts to mean this. You’ll find it in Degenerate Four-Wave Mixing, for example.

Hope I didn’t write that KB article 

Hi Mark,

    Does it mean either “tilt”or “decenter”is sufficient for the surface tolerances?

Yes. The bottom line is, for a spherical surface, use either tilt or decenters, but not both.

For a parabola, there is a single axis of rotation that you can separately decenter and tilt, and that’s generally true for rotationally-symmetric aspheres. But you can draw an many axes as you like through a sphere: there’s no single axis of rotation. Hence tilts and decenters are degenerate, indistinguishable, for a sphere.