n=10: reachable points with |B|<=30: 477 (0.0s); by type: {0: 228, 1: 61, 2: 33, 3: 21, 4: 19, 5: 21, 6: 33, 7: 61}
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|=1.9021 coords(xi,eta)=(1.0000,2.6180) reachable: N=1 segments, type A_1 ; reachable n-gons with w=gX_j (2<=j<=n-2), exhaustive: 1 [(2, [0, 1, 2, 3, 4, 5, 6, 7, 0])] ; as neighbour of O: 16 partners with det=S in the disc, 0 n-gons
X_{n-2}                |w|=1.9021 coords(xi,eta)=(2.6180,1.0000) reachable: N=1 segments, type A_7 ; reachable n-gons with w=gX_j (2<=j<=n-2), exhaustive: 1 [(8, [0, 1, 2, 3, 4, 5, 6, 7, 0])] ; as neighbour of O: 16 partners with det=S in the disc, 0 n-gons
w_n = 2+3zeta+zeta^2   |w|=5.4588 coords(xi,eta)=(8.4721,4.6180) reachable: N=3 segments, type A_7 ; 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|=5.4588 coords(xi,eta)=(4.6180,8.4721) 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: 9}
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|=5.45879 coords(xi,eta)=(8.47214, 4.61803) type A_7 N=3  [is w_n: True, is mirror(w_n): False]
   on no n-gon: |w|=5.45879 coords(xi,eta)=(4.61803, 8.47214) 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, 7): 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': 98}
  = 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 98

--- printed constants of Conjecture 2.5 (lam+1 and lam) ---
lam = 1.902113033, lam+1 = 2.902113033, lam^2 = 3.618033989, lam^2-1 = 2.618033989
n even: lam = 2cos(pi/n) is not in Q(zeta_n) (degree argument), so the printed points are not in Z[zeta_n];
  numerical illustration on up to 200 unitary pairs: minimal distance from a printed point u+m(lam+1)v, u+(lam+(m-1)(lam+1))v (m=1,2) to the set of reachable points: 0.284079
  u + lam^2 v reachable (type A_0) for 5 of 5 unitary pairs; lam^2 is not of a printed form m(lam+1) or lam+m(lam+1)
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=2.5133: 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|=2.8699 arg=0.2063: unitary partners u (w = v_1) with |u| <= R/4, R/2, R: [1, 2, 3]
   w with |w|=2.8699 arg=2.3070: unitary partners u (w = v_1) with |u| <= R/4, R/2, R: [1, 1, 3]
   w with |w|=4.4659 arg=0.4963: unitary partners u (w = v_1) with |u| <= R/4, R/2, R: [0, 0, 1]
   w with |w|=4.4659 arg=2.0170: unitary partners u (w = v_1) with |u| <= R/4, R/2, R: [0, 1, 2]
exact (non-float) decisions used: 5226 ; total time 0.2s
