== Part 1: the two constructions, Theorems A-C, Lemma 3.4, controls
   max Jacobi areas vs geometry (relative): 4.24e-32
   max Jacobi vertices vs geometry: 5.32e-34
   max Prop 3.2: |A_M - A_-M| and |A'_M - A'_-M| (even N, relative): 1.76e-35
   max ThmA spread of A*A_M (N=0 mod 4): 1.28e-35
   max ThmB spread of A_M/A (N=2 mod 4): 3.14e-45
   max ThmC spread of A'_M/A' (N=0 mod 4): 8.9e-36
   max closure: 5.38e-32
   max odd N: spread of A'*A'_O: 8.84e-33
   max odd N: spread of A*A_O: 4.89e-34
   max tangency: 1.74e-32
PASS closure and tangency of the geometric trajectories (50 digits; stars lose digits near the focal segment)
PASS least period and winding number tau
PASS Jacobi formulas of the note agree with the geometry
PASS Lemma 3.4: A, A', A_O, A'_O > 0 at every member (all N, stars included)
PASS Theorem A: A*A_M constant (N = 0 mod 4, 6 points M incl. complex)
PASS Theorem B: A_M/A constant (N = 2 mod 4)
PASS Theorem C: A'_M/A' constant (N = 0 mod 4)
PASS Proposition 3.2: A_-M = A_M and A'_-M = A'_M for even N
   odd N: min relative |A_M - A_-M| = 1.7e-5 (linear part present)
PASS odd N: A*A_O and A'*A'_O constant (k203,b; k303,b)
   controls: min spread of A_M/A (N=0 mod 4, N>4, M != O) = 4.46e-14; of A*A_M (N=2 mod 4) = 1.86e-10
   odd N, M != O: min spread of A*A_M = 8.13e-9; of A'*A'_M = 6.22e-6
PASS controls vary (ratio for N=0 mod 4, product for N=2 mod 4, odd-N products for M != O)
== Part 2: constants
PASS N = 4: A*A_M = 8a^4b^4/(a^2+b^2)^2 and A'_M = A'/2 for all M; lambda = a^2b^2/(a^2+b^2)
   a=2, b=1, (N,tau)=(8,1), M=(0.8,0.3): A*A_M = 33.4063768502875027135279705346
PASS reference value 33.4063768502875027135279705... (all 25 printed decimals)
   (10,3), a = 1.3, 2, 3.5: |M|^2 = -kappa0/kappa2 = ['3.0378941', '5.8229483', '15.415808']
PASS exceptional circles |M|^2 = 3.0379, 5.8229, 15.4158 to 4 decimals (kappa2 < 0 < kappa0)
   note: the first value is 3.03789..., i.e. 3.0379 after rounding; written with an ellipsis it should read 3.0378...
PASS (10,3): A_M = 0 on the exceptional circle at every member tested  1.28e-46
   max |A'_M/A'_O - (1 + delta M.M/(2F))| over all even families and members: 3.46e-36
PASS Kriebel's formula (1): A'_M = A'_O (2F + delta M.M)/(2F) for every even N
PASS Table 2: alpha = 1.77778, (N,tau) = (4,1): lambda and identities  max error 1.76e-46
PASS Table 2: alpha = 4.0, (N,tau) = (6,1): lambda and identities  max error 8.04e-47
PASS Table 2: alpha = 2.66667, (N,tau) = (8,1): lambda and identities  max error 1.94e-46
PASS Table 2: alpha = 1.18519, (N,tau) = (8,3): lambda and identities  max error 1.94e-45
PASS star: delta = -24/35, F = 68/63, delta/(2F) = -27/85, -2F/delta = 85/27
PASS star: A'_M = 0 on |M|^2 = 85/27 at ten members  5.63e-50
== Part 3: complex phases (Jacobi formulas of the note)
PASS (N,tau)=(4,1): A*A_M and A'_M/A' at complex phases equal their real values  3.02e-57
PASS (N,tau)=(4,1): Lemma 5.1, residue r_A on iK'+G' and -r_A on 3iK'+G'  4.56e-31
PASS (N,tau)=(4,1): Lemma 4.5 A_M(u0) = 0 at u0 = iK', Lemma 4.6 A(u1) = 0 at u1 = K+iK'-Delta  3.06e-61
PASS (N,tau)=(4,1): Lemma 4.3 eps*A_M(u1+eps) converges (simple pole)  1.22643
PASS (N,tau)=(4,1): Theorem C, Res A'_O/Res A' = kappa'_0 at two poles  2.31e-50
PASS (N,tau)=(8,1): A*A_M and A'_M/A' at complex phases equal their real values  6.02e-58
PASS (N,tau)=(8,1): Lemma 5.1, residue r_A on iK'+G' and -r_A on 3iK'+G'  2.69e-30
PASS (N,tau)=(8,1): Lemma 4.5 A_M(u0) = 0 at u0 = iK', Lemma 4.6 A(u1) = 0 at u1 = K+iK'-Delta  7.24e-61
PASS (N,tau)=(8,1): Lemma 4.3 eps*A_M(u1+eps) converges (simple pole)  1.97835
PASS (N,tau)=(8,1): Theorem C, Res A'_O/Res A' = kappa'_0 at two poles  2.91e-49
PASS (N,tau)=(12,5): A*A_M and A'_M/A' at complex phases equal their real values  1.65e-52
PASS (N,tau)=(12,5): Lemma 5.1, residue r_A on iK'+G' and -r_A on 3iK'+G'  5.25e-31
PASS (N,tau)=(12,5): Lemma 4.5 A_M(u0) = 0 at u0 = iK', Lemma 4.6 A(u1) = 0 at u1 = K+iK'-Delta  4.66e-60
PASS (N,tau)=(12,5): Lemma 4.3 eps*A_M(u1+eps) converges (simple pole)  0.461698
PASS (N,tau)=(12,5): Theorem C, Res A'_O/Res A' = kappa'_0 at two poles  1.44e-51
PASS (N,tau)=(16,3): A*A_M and A'_M/A' at complex phases equal their real values  7.03e-59
PASS (N,tau)=(16,3): Lemma 5.1, residue r_A on iK'+G' and -r_A on 3iK'+G'  9.34e-30
PASS (N,tau)=(16,3): Lemma 4.5 A_M(u0) = 0 at u0 = iK', Lemma 4.6 A(u1) = 0 at u1 = K+iK'-Delta  3.07e-60
PASS (N,tau)=(16,3): Lemma 4.3 eps*A_M(u1+eps) converges (simple pole)  1.87069
PASS (N,tau)=(16,3): Theorem C, Res A'_O/Res A' = kappa'_0 at two poles  1.44e-50
PASS (N,tau)=(6,1): A_M/A at complex phases equals its real value  1.67e-57
PASS (N,tau)=(6,1): Lemma 5.1, residue r_A on iK'+G' and -r_A on 3iK'+G'  1.39e-30
PASS (N,tau)=(6,1): Theorem B, Res A_O/Res A = kappa0, Res c2/Res A = kappa2 (two cosets)  2.05e-38
PASS (N,tau)=(10,3): A_M/A at complex phases equals its real value  1.17e-57
PASS (N,tau)=(10,3): Lemma 5.1, residue r_A on iK'+G' and -r_A on 3iK'+G'  1.99e-30
PASS (N,tau)=(10,3): Theorem B, Res A_O/Res A = kappa0, Res c2/Res A = kappa2 (two cosets)  2.46e-38
PASS (N,tau)=(5,2): Lemma 5.1, residue r_A on iK'+G' and -r_A on 3iK'+G'  5.25e-31
PASS (N,tau)=(5,2): odd N, A(u1) = 0 at u1 = K+iK'-Delta  2.2e-61
PASS (N,tau)=(7,3): Lemma 5.1, residue r_A on iK'+G' and -r_A on 3iK'+G'  5.25e-31
PASS (N,tau)=(7,3): odd N, A(u1) = 0 at u1 = K+iK'-Delta  5.83e-61

TOTAL failures: 0 []
