{
  "checks_completed": 501,
  "maximum_errors": {
    "joint completed square": 7.105427357601002e-15,
    "five-dimensional selected spectrum": 2.7755575615628914e-16,
    "bivector uniquely reconstructs ray": 2.2355819889017596e-16,
    "effective Hessian symmetry": 0.0,
    "six flat and four positive normal directions": 1.7934692766270394e-09,
    "induced bivector metric has two weights": 0.0,
    "nonzero projective Berry curvature": 0.0,
    "evolving spinor norm": 1.31117339208231e-13,
    "reciprocal energy conservation": 1.9115820037995945e-12,
    "nonlinear distance-to-family energy identity": 4.948992604614233e-14
  },
  "exact_identities": [
    "n.n=N^2",
    "b.b=2N^2",
    "B^2=-N^2 I+n n^T",
    "Bn=0",
    "S w=2N w",
    "S^2+2N S=8N w w^dagger"
  ],
  "effective_hessian_eigenvalues": [
    4.4836745427545566e-10,
    4.4836745427545566e-10,
    1.7934692766270394e-09,
    1.7934692766270394e-09,
    1.7934692766270394e-09,
    1.7934692766270394e-09,
    2.5999999999999996,
    2.5999999999999996,
    2.6000000000026002,
    2.6000000000026002
  ],
  "induced_metric_eigenvalues_in_FS_unit_tangents": [
    4.0,
    4.0,
    4.0,
    4.0,
    8.0,
    8.0
  ],
  "spectral_discriminator": "For a>=b>0: gaps are 2b,2a,2(a+b); three equal positive gaps impossible.",
  "minimum_energy": -0.18846153846153843
}