Universal $\pm 1$ Congruence Speed Invariant in Any Numeral System

A self-contained statement of a constant congruence speed identity characterizing tetration in numeral systems with radix r > 2. The central formula is:

V_b^[r]((k*r^(t+1) + r^(t - nu_r(c)) +/- 1)^c) = t

and it holds for all integers b > 1, c > 1, k >= 0, and t > nu_r(c) + 1, for every squarefree r > 2, and also for all non-squarefree r > 2 such that rad(r) does not divide c or r divides c. Here nu_r(c) denotes the largest integer m such that r^m divides c, and rad(r) is the product of the distinct prime factors of r.