== couplings at M_Z ==
  alpha_em^-1 = 127.951,  sin^2 = 0.23121
  alpha1^-1(GUT-norm) = 59.0205
  alpha2^-1           = 29.5836
  alpha3^-1           = 8.4818

== one-loop g1=g2 crossing (sin^2 = 3/8 by construction) ==
  t* = ln(mu/M_Z) = 25.453
  mu* = 1.033e+13 GeV

== one-loop sin^2 theta_W at canonical scales ==
  mu = 9.119e+01 GeV :  sin^2 = 0.23121
  mu = 1.000e+03 GeV :  sin^2 = 0.24330
  mu = 1.000e+06 GeV :  sin^2 = 0.27972
  mu = 1.000e+09 GeV :  sin^2 = 0.31862
  mu = 1.000e+12 GeV :  sin^2 = 0.36026
  mu = 1.000e+13 GeV :  sin^2 = 0.37479
  mu = 1.000e+14 GeV :  sin^2 = 0.38968
  mu = 1.000e+15 GeV :  sin^2 = 0.40493
  mu = 1.000e+16 GeV :  sin^2 = 0.42056
  mu = 1.000e+17 GeV :  sin^2 = 0.43658
  mu = 1.033e+13 GeV :  sin^2 = 0.37500

== two-loop g1=g2 crossing (sin^2 = 3/8) ==
  mu* = 1.089e+13 GeV
  sin^2 at mu*  = 0.37500  (should be 0.375)

== two-loop sin^2 theta_W at canonical scales ==
  mu = 9.119e+01 GeV :  sin^2 = 0.23121
  mu = 1.000e+03 GeV :  sin^2 = 0.24314
  mu = 1.000e+09 GeV :  sin^2 = 0.31815
  mu = 1.000e+13 GeV :  sin^2 = 0.37445
  mu = 1.000e+14 GeV :  sin^2 = 0.38940
  mu = 1.000e+15 GeV :  sin^2 = 0.40473
  mu = 1.000e+16 GeV :  sin^2 = 0.42045
  mu = 1.000e+17 GeV :  sin^2 = 0.43658

================================================================
VERDICT (panel criterion: mu* in GUT window 1e15 - 1e17 GeV)
================================================================
  1-loop: sin^2=3/8 reached at 1.033e+13 GeV  -> OUTSIDE [1e15,1e17]
  2-loop: sin^2=3/8 reached at 1.089e+13 GeV  -> OUTSIDE [1e15,1e17]

IR anchor 3/(4pi) = 0.238732414637843
UV anchor 3/8     = 0.375

== same test, MSSM beta functions (b1=33/5, b2=1) ==
  g1=g2 (sin^2=3/8) at mu* = 2.013e+16 GeV  -> INSIDE [1e15,1e17]
  => the crossing scale is dominated by the (unknown) BSM content, not by cube geometry.