n=8 R=80.0: 3395 reachable points (51008 nodes); types: A0:1644, A1:481, A2:277, A3:235, A4:277, A5:481   [1.9s]
Lemma 1: K(gamma_B) == type of Def. 2.1 (mod n-2) for 3395 points: failures 0 (non-integer K: 0)   [5.1s]
Descent (Lemma 4b) + invariance of the type under tau_k, mu, rho (Thm 1a): 3395 points, 19054 twist steps (max 42 per point; 8706 landed in the neighbouring corner), every step: shorter, reachable, same type; end = diagonal X_0X_(k+1) with k = type: failures 0   [6.4s]
Conj 2.6: 10535 instances (point, l, eps) with both points inside the disc: failures 0; Conj 2.7 (exact length ratio) on the same pairs: failures 0; 6448 instances with the parallel point outside the disc
Conj 2.6/2.7 by exact ray tracing for all points with |B| <= 40.0: 4243 instances, no short trajectory in the predicted direction within 12|B|+5: 0, type failures 0, length-ratio failures 0   [9.5s]
pairs (u,v), |u|,|v| <= 40.0, det(u,v) = sin(2pi/n) exactly: 707   [9.6s]
   (type u, type v) distribution: {(0, 0): 237, (0, 5): 235, (1, 0): 235}; pairs outside the three classes of Step A: 0
Conj 2.3: reachable n-gons found: 237; with vertex types != (A0,A1,...,A(n-3),A0): 0
   Corollary 3.1 (pair of type (A0,A0) <=> spans a reachable n-gon): failures 0; Theorem 3 (v_1,v_2,v_(n-2),v_(n-1) reachable => reachable n-gon): failures 0; vertices outside the disc decided by exact ray tracing: 2146   [13.9s]
exact fallbacks 65531, mp calls 0
