ε = f(ε): the equation that solves itself — and the band it can never quite land on.
This is an illustrative dynamical system — a decreasing self-consistency map with one fixed point — not the real running-coupling calculation. Solving the α probe's ε = f(ε) needs a boundary condition the framework hasn't shown it can derive from within, so this shows only the shape of "an equation that fixes its own value," and the fuzzy band is the leakage-tolerance reframe, not a derivation of 137.