n=9 R=80.0: 3399 reachable points (45809 nodes); types: A0:1603, A1:446, A2:250, A3:202, A4:202, A5:250, A6:446   [1.9s]
Lemma 1: K(gamma_B) == type of Def. 2.1 (mod n-2) for 3399 points: failures 0 (non-integer K: 0)   [5.0s]
Descent (Lemma 4b) + invariance of the type under tau_k, mu, rho (Thm 1a): 3399 points, 18179 twist steps (max 42 per point; 8289 landed in the neighbouring corner), every step: shorter, reachable, same type; end = diagonal X_0X_(k+1) with k = type: failures 0   [6.3s]
Conj 2.6: 24667 instances (point, l, eps) with both points inside the disc: failures 0; Conj 2.7 (exact length ratio) on the same pairs: failures 0; 19536 instances with the parallel point outside the disc
Conj 2.6/2.7 by exact ray tracing for all points with |B| <= 40.0: 10897 instances, no short trajectory in the predicted direction within 12|B|+5: 0, type failures 0, length-ratio failures 0   [14.5s]
pairs (u,v), |u|,|v| <= 40.0, det(u,v) = sin(2pi/n) exactly: 681   [14.5s]
   (type u, type v) distribution: {(0, 0): 229, (0, 6): 226, (1, 0): 226}; pairs outside the three classes of Step A: 0
Conj 2.3: reachable n-gons found: 229; 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: 2842   [21.7s]
exact fallbacks 78403, mp calls 0
