Well, rethinking a bit (and a involving bit of latte makkiato 
) I feel, I should add one thought: why this all...
The speculation behind this is, to extract a functional relation between two u, say u and v, or more precise u_k and v_j, having the same NET b, and to consider the eigensystem-based formula for the powerseries-expansion of tetration. Is it -under this functional relation- *necessary*, that the powerseries, constructed by u_k and v_j give different results? Or can it be shown, that they must give the same result?
Maybe, maybe it is even likely, this is of no help. I think, a very basic reconsideration is needed for the focused problem.
Gottfried
) I feel, I should add one thought: why this all...The speculation behind this is, to extract a functional relation between two u, say u and v, or more precise u_k and v_j, having the same NET b, and to consider the eigensystem-based formula for the powerseries-expansion of tetration. Is it -under this functional relation- *necessary*, that the powerseries, constructed by u_k and v_j give different results? Or can it be shown, that they must give the same result?
Maybe, maybe it is even likely, this is of no help. I think, a very basic reconsideration is needed for the focused problem.
Gottfried
Gottfried Helms, Kassel