Fast Growing Hierarchy Calculator High Quality

from functools import lru_cache

Currently, the best resources are scattered: Koteitan’s ordinal calculator, various GitHub gists with Buchholz, and the Googology Wiki’s reference tables. But the demand is clear from the steady trickle of forum posts: "Does anyone have a working FGH calculator that goes past ε₀?" fast growing hierarchy calculator high quality

# If no closed form, iterate safely with memoization result = x for _ in range(x): result = self._f(alpha - 1, result) return result Growth there was not only fast; it was catalytic

But the Calculator revealed a third path: the fast-growing hybrid. It emerged when a hierarchy alternated—one layer enforced constraint and refinement, the next exploded breadth, then constraint again. Growth there was not only fast; it was catalytic. New capabilities appeared at the interface between compression and expansion, like sparks where two currents meet. Growth there was not only fast