n=30 R=40.0: 787 reachable points (3720 nodes); types: A0:346, A1:95, A2:43, A3:19, A4:13, A5:13, A6:7, A7:7, A8:7, A9:3, A10:3, A11:3, A12:3, A13:3, A14:3, A15:3, A16:3, A17:3, A18:3, A19:3, A20:7, A21:7, A22:7, A23:13, A24:13, A25:19, A26:43, A27:95   [1.2s]
Lemma 1: K(gamma_B) == type of Def. 2.1 (mod n-2) for 787 points: failures 0 (non-integer K: 0)   [3.0s]
Descent (Lemma 4b) + invariance of the type under tau_k, mu, rho (Thm 1a): 787 points, 2280 twist steps (max 19 per point; 968 landed in the neighbouring corner), every step: shorter, reachable, same type; end = diagonal X_0X_(k+1) with k = type: failures 0   [4.3s]
Conj 2.6: 5459 instances (point, l, eps) with both points inside the disc: failures 0; Conj 2.7 (exact length ratio) on the same pairs: failures 0; 15820 instances with the parallel point outside the disc
Conj 2.6/2.7 by exact ray tracing for all points with |B| <= 20.0: 5295 instances, no short trajectory in the predicted direction within 12|B|+5: 0, type failures 0, length-ratio failures 0   [16.6s]
pairs (u,v), |u|,|v| <= 20.0, det(u,v) = sin(2pi/n) exactly: 127   [16.6s]
   (type u, type v) distribution: {(0, 0): 45, (0, 27): 41, (1, 0): 41}; pairs outside the three classes of Step A: 0
Conj 2.3: reachable n-gons found: 45; 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: 3224   [139.3s]
exact fallbacks 29277, mp calls 0
