Sturmian external angles of primitive components in the Mandelbrot set

The paper’s Theorem A states precisely that for n ≥ 1 and rationals P/Q, a/b satisfying the 01-Hyp, the angle θ = θ01(P/Q, a/b, n) is periodic of exact period b and the parameter ray Rθ lands at the root of a primitive hyperbolic component of period b; the proof proceeds via an explicit computation of the conjugate angle and an analysis of kneading sequences, invoking Cor. 5.5 of [LS94] to conclude primitivity . The candidate solution reaches the same conclusion by a different route (global ray-landing/wake theory and orbit-portrait arguments). Aside from a minor conflation of dynamic vs parameter rays and a likely misstatement about ray-periods in the satellite case (the paper explicitly notes that the characteristic angles of a component of period m are m-periodic under doubling) , the model’s reasoning aligns with the paper’s outcome. The core ingredients used by the paper (broken-line construction, 01-Hyp, periodicity and minimal period b of θ01(P/Q,a/b,n)) are clearly stated and justified .