r2_chebyshev.py (verification run 2, AMR-022-4023)  NMAX=20 seed=2027  numpy 2.5.2 sympy 1.14.0 mpmath 1.3.0
(A) EXACT checks, n = 1..20 (explicit-sum Chebyshev polynomials, integer arithmetic)
  n  rec  lead=2^(n-1)  s^(n-1)=0  zeros(60d)  realset=[-1,1]  G_n>0 on (-1,1)  crit=+-1  2rho
   1  True True          True       True        True            True             True      1.0000000000
   2  True True          True       True        True            True             True      1.4142135624
   3  True True          True       True        True            True             True      1.5874010520
   4  True True          True       True        True            True             True      1.6817928305
   5  True True          True       True        True            True             True      1.7411011266
   6  True True          True       True        True            True             True      1.7817974363
   7  True True          True       True        True            True             True      1.8114473285
   8  True True          True       True        True            True             True      1.8340080864
   9  True True          True       True        True            True             True      1.8517494246
  10  True True          True       True        True            True             True      1.8660659831
  11  True True          True       True        True            True             True      1.8778618213
  12  True True          True       True        True            True             True      1.8877486254
  13  True True          True       True        True            True             True      1.8961550287
  14  True True          True       True        True            True             True      1.9033903060
  15  True True          True       True        True            True             True      1.9096832078
  16  True True          True       True        True            True             True      1.9152065614
  17  True True          True       True        True            True             True      1.9200933737
  18  True True          True       True        True            True             True      1.9244476738
  19  True True          True       True        True            True             True      1.9283519959
  20  True True          True       True        True            True             True      1.9318726578
  (A) ALL PASSED  (0.3 s)
(B) NUMERICAL in R^3 (no planar reduction): exit distances of rays from c = 0, n = 2..12
    (4002 rays in double precision; the 25 largest exits recomputed with mpmath at 40 digits)
  n   2rho            max(doubles)-2rho   max(40 digits)-2rho   |u_1| at the max   max rel |P(y) - |q(t+i|s|)||
   2  1.414213562373  +2.22e-16           +2.30e-41             1.000000000000     3.2e-41
   3  1.587401051968  +0.00e+00           -2.30e-41             1.000000000000     4.4e-41
   4  1.681792830507  -2.00e-15           -2.30e-41             1.000000000000     6.3e-41
   5  1.741101126592  +3.53e-14           +1.01e-38             1.000000000000     6.3e-41
   6  1.781797436281  +1.18e-14           +9.30e-39             1.000000000000     7.8e-41
   7  1.811447328528  +2.09e-12           +2.22e-37             1.000000000000     1.1e-40
   8  1.834008086409  +3.08e-13           -3.20e-38             1.000000000000     9.2e-41
   9  1.851749424575  +1.51e-11           +4.63e-36             1.000000000000     1.1e-40
  10  1.866065983074  +2.64e-10           -7.11e-37             1.000000000000     1.0e-40
  11  1.877861821323  +1.96e-10           +3.00e-36             1.000000000000     1.2e-40
  12  1.887748625363  +6.26e-08           +1.16e-33             1.000000000000     1.2e-40
  (B) ALL PASSED  (52.6 s)
TOTAL: ALL CHECKS PASSED  (52.6 s)
