Complete end-to-end SU(2) physicalized Galerkin witness

Model:
  K_1 = span{chi_0, chi_{1/2}, chi_1} in L^2(SU(2))^{Ad SU(2)}
  H_el = diag(0, 3/4, 2)
  V = 1 - (1/2) chi_{1/2} >= 0
  H_mag = P_1 M_V P_1

Verified quantities:
  E0                     = 0.7263771031953169
  P_vac                  = explicit rank-one 3x3 matrix
  sigma_vac              = 0.8786808705991026
  tau_capture            = 0.0711077474866026
  Gram G                 = 0.7670237606041791
  M_phys                 = 1.4016539436411070
  b_max                  = 0.5375509394586401
  chosen b               = 0.5
  c_IR                   = 0.9479076321456580
  c_UV                   = 1.2542663120526782
  epsilon_mix            = 0.4163096927652430
  determinant margin     = 1.0156148496476303
  kappa                  = 0.6574906798706553
  exact Galerkin gap     = 1.1084990457494466
  certified fraction     = 0.5931359908624293

Scope:
  This is an exact finite Peter-Weyl Galerkin realization of the complete
  comparison package. It does not claim persistence of the same constants
  for the untruncated class-function Hamiltonian.
