Recorded data and provenance for the associated calculation.
| checks_completed | 504 |
|---|---|
| spectral_discriminator | For a>=b>0: gaps are 2b,2a,2(a+b); three equal positive gaps impossible. |
| minimum_operator_norm_distance_to_singlet_triplet | Delta/4, allowing any scalar shift and spinor basis |
| minimum_energy | -0.18846153846153843 |
View complete data
{
"checks_completed": 504,
"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,
"sharp singlet-triplet spectral distance": 0.0,
"centrally symmetric spectral sum rule": 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_operator_norm_distance_to_singlet_triplet": "Delta/4, allowing any scalar shift and spinor basis",
"minimum_energy": -0.18846153846153843
}