V.T124 — Profinite convergence

The boundary-character expansion Z_tau(alpha) = sum c_n alpha^n converges absolutely for |alpha| < 1 (and for physical alpha approx 1/137). The n-th coefficient satisfies |c_n| <= C^n for a constant C determined by the coherence kernel. Dyson's factorial-growth argument does not apply because the profinite tower has finitely many orbits at each level.