n=5: reachable points with |B|<=30: 461 (0.0s); by type: {0: 269, 1: 96, 2: 96}
exact check X_j = a_j*eta + b_j*xi (j=1..n-1) and a_j, b_j >= 1 for 2<=j<=n-2: OK

=== Conjecture 2.4: named points ===
identity 2+3z+z^2 = (lam^4-lam^2-1)xi + (lam^2+1)eta = X_1 - X_{n-1} + lam^2 X_{n-2}: exact OK
X_2                    |w|=1.6180 coords(xi,eta)=(1.0000,1.6180) reachable: N=1 segments, type A_1 ; reachable n-gons with w=gX_j (2<=j<=n-2), exhaustive: 1 [(2, [0, 1, 2, 0])] ; as neighbour of O: 19 partners with det=S in the disc, 0 n-gons
X_{n-2}                |w|=1.6180 coords(xi,eta)=(1.6180,1.0000) reachable: N=1 segments, type A_2 ; reachable n-gons with w=gX_j (2<=j<=n-2), exhaustive: 1 [(3, [0, 1, 2, 0])] ; as neighbour of O: 19 partners with det=S in the disc, 0 n-gons
w_n = 2+3zeta+zeta^2   |w|=4.0406 coords(xi,eta)=(3.2361,3.6180) reachable: N=3 segments, type A_2 ; reachable n-gons with w=gX_j (2<=j<=n-2), exhaustive: 0 [] ; as neighbour of O: 7 partners with det=S in the disc, 0 n-gons
mirror(w_n)            |w|=4.0406 coords(xi,eta)=(3.6180,3.2361) reachable: N=3 segments, type A_1 ; reachable n-gons with w=gX_j (2<=j<=n-2), exhaustive: 0 [] ; as neighbour of O: 7 partners with det=S in the disc, 0 n-gons

=== Conjecture 2.4: all reachable points of type != A_0 with |w| <= 9 ===
number of points by number of reachable n-gons through them (exhaustive for the vertices gX_j, 2<=j<=n-2): {0: 6, 1: 10}
in every n-gon found the point is the vertex v_{k+1} and the vertex types are A_0,A_1,...,A_{n-3},A_0: True
   on no n-gon: |w|=4.04057 coords(xi,eta)=(3.23607, 3.61803) type A_2 N=3  [is w_n: True, is mirror(w_n): False]
   on no n-gon: |w|=4.04057 coords(xi,eta)=(3.61803, 3.23607) type A_1 N=3  [is w_n: False, is mirror(w_n): True]
   on no n-gon: |w|=6.61382 coords(xi,eta)=(6.23607, 4.85410) type A_1 N=5  [is w_n: False, is mirror(w_n): False]
   on no n-gon: |w|=6.61382 coords(xi,eta)=(4.85410, 6.23607) type A_2 N=5  [is w_n: False, is mirror(w_n): False]
type != A_0 points as a neighbour of O: 114 partners with det = S inside the disc of radius 30, reachable n-gons among them: 0

=== pairs (u,v) of reachable points with det(u,v) = S, both of radius <= 9 ===
pairs: 53 ; (type u, type v) histogram: {(0, 0): 19, (0, 2): 17, (1, 0): 17}
unitary pairs: 19 ; of these spanning a reachable n-gon with vertex types A_0,A_1,..,A_{n-3},A_0: 19 ; non-unitary pairs spanning a reachable n-gon: 0

=== Conjecture 2.5 on all unitary pairs above; lines u+tv and v+tu inside the disc of radius 30 ===
corrected statement (step lam^2, offset lam^2-1): {'lines': 38, 'on_line': 336, 'extra': 0, 'cand': 320, 'missing': 0, 'wrongtype': 0, 'lower_reach': 0, 'lower_tested': 344}
  = lines 38 ; reachable points found on them 336, of which NOT of the form u+m*lam^2*v or u+(m*lam^2-1)*v: 0 ; predicted points inside disc and on the admissible side: 320, of which not reachable: 0 ; wrong type: 0 ; predicted points on the wrong side that are reachable (other than xi, eta): 0 of 344

--- printed constants of Conjecture 2.5 (lam+1 and lam) ---
lam = 1.618033989, lam+1 = 2.618033989, lam^2 = 2.618033989, lam^2-1 = 1.618033989
exact test on all 19 unitary pairs, m = -3..3 (points in the open upper half-plane): {'a_tested': 60, 'a_reach': 60, 'a_typeok': 60, 'b_tested': 88, 'b_reach': 88, 'b_typeok': 88, 'c_viol': 0}
  printed (a), m != 0: 60 points tested, 60 reachable ; printed (b): 88 tested, 88 reachable ; pairs for which printed (c) fails (u+lam^2 v reachable, not of a printed form): 0
t-values found (kind A: t = m lam^2, kind B: t = m lam^2 - 1) -> number of points: {('A', -3): 2, ('A', -2): 4, ('A', -1): 8, ('A', 0): 38, ('A', 1): 36, ('A', 2): 22, ('A', 3): 14, ('A', 4): 10, ('A', 5): 8, ('A', 6): 8, ('A', 7): 8, ('A', 8): 8, ('A', 9): 6, ('A', 10): 4, ('A', 11): 2, ('B', -2): 2, ('B', -1): 4, ('B', 0): 18, ('B', 1): 38, ('B', 2): 24, ('B', 3): 16, ('B', 4): 12, ('B', 5): 8, ('B', 6): 8, ('B', 7): 8, ('B', 8): 8, ('B', 9): 6, ('B', 10): 4, ('B', 11): 2}

=== type A_0 points: number of unitary partners inside growing discs (illustration of 'infinitely many') ===
   w with |w|=1.0000 arg=1.8850: unitary partners u (w = v_1) with |u| <= R/4, R/2, R: [3, 6, 12]
   w with |w|=1.0000 arg=-0.0000: unitary partners u (w = v_1) with |u| <= R/4, R/2, R: [0, 0, 0]
   w with |w|=2.4972 arg=1.4942: unitary partners u (w = v_1) with |u| <= R/4, R/2, R: [1, 2, 4]
   w with |w|=2.4972 arg=0.3907: unitary partners u (w = v_1) with |u| <= R/4, R/2, R: [2, 3, 5]
   w with |w|=3.0777 arg=0.9425: unitary partners u (w = v_1) with |u| <= R/4, R/2, R: [1, 1, 3]
   w with |w|=4.0876 arg=1.4009: unitary partners u (w = v_1) with |u| <= R/4, R/2, R: [1, 1, 3]
exact (non-float) decisions used: 17156 ; total time 0.3s
