n=9: reachable points with |B|<=30: 489 (0.0s); by type: {0: 233, 1: 62, 2: 38, 3: 28, 4: 28, 5: 38, 6: 62}
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|=1.8794 coords(xi,eta)=(1.0000,2.5321) reachable: N=1 segments, type A_1 ; reachable n-gons with w=gX_j (2<=j<=n-2), exhaustive: 1 [(2, [0, 1, 2, 3, 4, 5, 6, 0])] ; as neighbour of O: 16 partners with det=S in the disc, 0 n-gons
X_{n-2}                |w|=1.8794 coords(xi,eta)=(2.5321,1.0000) reachable: N=1 segments, type A_6 ; reachable n-gons with w=gX_j (2<=j<=n-2), exhaustive: 1 [(7, [0, 1, 2, 3, 4, 5, 6, 0])] ; as neighbour of O: 16 partners with det=S in the disc, 0 n-gons
w_n = 2+3zeta+zeta^2   |w|=5.3370 coords(xi,eta)=(7.9436,4.5321) reachable: N=3 segments, type A_6 ; reachable n-gons with w=gX_j (2<=j<=n-2), exhaustive: 0 [] ; as neighbour of O: 5 partners with det=S in the disc, 0 n-gons
mirror(w_n)            |w|=5.3370 coords(xi,eta)=(4.5321,7.9436) reachable: N=3 segments, type A_1 ; reachable n-gons with w=gX_j (2<=j<=n-2), exhaustive: 0 [] ; as neighbour of O: 5 partners with det=S in the disc, 0 n-gons

=== Conjecture 2.4: all reachable points of type != A_0 with |w| <= 6 ===
number of points by number of reachable n-gons through them (exhaustive for the vertices gX_j, 2<=j<=n-2): {0: 2, 1: 8}
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|=5.33698 coords(xi,eta)=(7.94356, 4.53209) type A_6 N=3  [is w_n: True, is mirror(w_n): False]
   on no n-gon: |w|=5.33698 coords(xi,eta)=(4.53209, 7.94356) type A_1 N=3  [is w_n: False, is mirror(w_n): True]
type != A_0 points as a neighbour of O: 54 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 <= 6 ===
pairs: 15 ; (type u, type v) histogram: {(0, 0): 5, (0, 6): 5, (1, 0): 5}
unitary pairs: 5 ; of these spanning a reachable n-gon with vertex types A_0,A_1,..,A_{n-3},A_0: 5 ; 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': 10, 'on_line': 98, 'extra': 0, 'cand': 92, 'missing': 0, 'wrongtype': 0, 'lower_reach': 0, 'lower_tested': 100}
  = lines 10 ; reachable points found on them 98, 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: 92, of which not reachable: 0 ; wrong type: 0 ; predicted points on the wrong side that are reachable (other than xi, eta): 0 of 100

--- printed constants of Conjecture 2.5 (lam+1 and lam) ---
lam = 1.879385242, lam+1 = 2.879385242, lam^2 = 3.532088886, lam^2-1 = 2.532088886
exact test on all 5 unitary pairs, m = -3..3 (points in the open upper half-plane): {'a_tested': 16, 'a_reach': 0, 'a_typeok': 0, 'b_tested': 22, 'b_reach': 2, 'b_typeok': 2, 'c_viol': 5}
  printed (a), m != 0: 16 points tested, 0 reachable ; printed (b): 22 tested, 2 reachable ; pairs for which printed (c) fails (u+lam^2 v reachable, not of a printed form): 5
t-values found (kind A: t = m lam^2, kind B: t = m lam^2 - 1) -> number of points: {('A', -1): 2, ('A', 0): 10, ('A', 1): 10, ('A', 2): 8, ('A', 3): 4, ('A', 4): 4, ('A', 5): 4, ('A', 6): 4, ('A', 7): 4, ('A', 8): 2, ('B', 0): 4, ('B', 1): 10, ('B', 2): 8, ('B', 3): 6, ('B', 4): 4, ('B', 5): 4, ('B', 6): 4, ('B', 7): 4, ('B', 8): 2}

=== type A_0 points: number of unitary partners inside growing discs (illustration of 'infinitely many') ===
   w with |w|=1.0000 arg=2.4435: unitary partners u (w = v_1) with |u| <= R/4, R/2, R: [3, 5, 9]
   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|=2.8397 arg=2.2151: unitary partners u (w = v_1) with |u| <= R/4, R/2, R: [1, 2, 3]
   w with |w|=2.8397 arg=0.2283: unitary partners u (w = v_1) with |u| <= R/4, R/2, R: [1, 2, 3]
   w with |w|=4.3459 arg=0.5497: unitary partners u (w = v_1) with |u| <= R/4, R/2, R: [0, 1, 2]
   w with |w|=4.3459 arg=1.8938: unitary partners u (w = v_1) with |u| <= R/4, R/2, R: [0, 1, 2]
exact (non-float) decisions used: 5847 ; total time 0.2s
