Universal \(\pm 1\) Congruence Speed Invariant in Any Numeral System

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

\(V_b^{[r]}\left(\left(k \cdot r^{t + 1} + r^{t - \nu_r(c)} \pm 1 \right)^c\right) = t\) 

and it holds for all integers \(b > 1\), \(c > 1\), \(k \geq 0\), and \(t > \nu_r(c) + 1\), for every squarefree integer \(r > 2\), and also for most pairs \((r, c)\) with positive non-squarefree integer \(r\). Here \(\nu_r(c)\) denotes the largest integer \(m\) such that \(r^m \mid c\), and \(\mathrm{rad}(r)\) is the product of the distinct prime factors of \(r\).

A Python verification tool numerically confirming the stated (constant) congruence speed for the admissible parameter ranges is provided as a supplementary .py file (Version 3) in this Zenodo record:
https://doi.org/10.5281/zenodo.17982198