n=12 R=80.0: 3339 reachable points (36586 nodes); types: A0:1522, A1:409, A2:205, A3:139, A4:107, A5:97, A6:107, A7:139, A8:205, A9:409   [2.2s]
Lemma 1: K(gamma_B) == type of Def. 2.1 (mod n-2) for 3339 points: failures 0 (non-integer K: 0)   [6.1s]
Descent (Lemma 4b) + invariance of the type under tau_k, mu, rho (Thm 1a): 3339 points, 16178 twist steps (max 40 per point; 7329 landed in the neighbouring corner), every step: shorter, reachable, same type; end = diagonal X_0X_(k+1) with k = type: failures 0   [7.6s]
Conj 2.6: 14783 instances (point, l, eps) with both points inside the disc: failures 0; Conj 2.7 (exact length ratio) on the same pairs: failures 0; 15280 instances with the parallel point outside the disc
Conj 2.6/2.7 by exact ray tracing for all points with |B| <= 40.0: 7491 instances, no short trajectory in the predicted direction within 12|B|+5: 0, type failures 0, length-ratio failures 0   [15.3s]
pairs (u,v), |u|,|v| <= 40.0, det(u,v) = sin(2pi/n) exactly: 607   [15.4s]
   (type u, type v) distribution: {(0, 0): 207, (0, 9): 200, (1, 0): 200}; pairs outside the three classes of Step A: 0
Conj 2.3: reachable n-gons found: 207; 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: 4452   [33.9s]
exact fallbacks 75936, mp calls 0
