Recorded data and provenance for the associated calculation.
| utc | 2026-10-01T05:07:43.504590+00:00 |
|---|---|
| scope | Representation, exact normal-texture zero modes, critical-bubble grading and conditional chiral coupling; no unified action, particle stability or selected masses. |
View complete data
{
"utc": "2026-10-01T05:07:43.504590+00:00",
"scope": "Representation, exact normal-texture zero modes, critical-bubble grading and conditional chiral coupling; no unified action, particle stability or selected masses.",
"checks": {
"helicity_identity_d3": true,
"grading_square_d3": true,
"massive_chiral_weight_d3_0": true,
"massive_chiral_weight_d3_1": true,
"massive_paired_helicity_d3": true,
"bubble_grading_integral_d3": true,
"helicity_identity_d4": true,
"grading_square_d4": true,
"normal_reverses_C_d4": true,
"paired_massless_helicity_d4": true,
"massive_chiral_weight_d4_0": true,
"massive_chiral_weight_d4_1": true,
"massive_paired_helicity_d4": true,
"bubble_grading_integral_d4": true,
"helicity_identity_d5": true,
"grading_square_d5": true,
"normal_reverses_C_d5": true,
"paired_massless_helicity_d5": true,
"massive_chiral_weight_d5_0": true,
"massive_chiral_weight_d5_1": true,
"massive_chiral_weight_d5_2": true,
"massive_chiral_weight_d5_3": true,
"massive_paired_helicity_d5": true,
"bubble_grading_integral_d5": true,
"helicity_identity_d6": true,
"grading_square_d6": true,
"normal_reverses_C_d6": true,
"paired_massless_helicity_d6": true,
"massive_chiral_weight_d6_0": true,
"massive_chiral_weight_d6_1": true,
"massive_chiral_weight_d6_2": true,
"massive_chiral_weight_d6_3": true,
"massive_paired_helicity_d6": true,
"bubble_grading_integral_d6": true,
"helicity_identity_d10": true,
"grading_square_d10": true,
"normal_reverses_C_d10": true,
"paired_massless_helicity_d10": true,
"massive_chiral_weight_d10_0": true,
"massive_chiral_weight_d10_1": true,
"massive_chiral_weight_d10_2": true,
"massive_chiral_weight_d10_3": true,
"massive_chiral_weight_d10_4": true,
"massive_chiral_weight_d10_5": true,
"massive_chiral_weight_d10_6": true,
"massive_chiral_weight_d10_7": true,
"massive_chiral_weight_d10_8": true,
"massive_chiral_weight_d10_9": true,
"massive_chiral_weight_d10_10": true,
"massive_chiral_weight_d10_11": true,
"massive_chiral_weight_d10_12": true,
"massive_chiral_weight_d10_13": true,
"massive_chiral_weight_d10_14": true,
"massive_chiral_weight_d10_15": true,
"massive_paired_helicity_d10": true,
"bubble_grading_integral_d10": true,
"d5_tangent_normal_chirality_identity": true,
"zero_mode_weyl_operator_-1_0": true,
"zero_mode_weyl_operator_-1_1": true,
"zero_mode_weyl_operator_-1_2": true,
"zero_mode_weyl_operator_1_0": true,
"zero_mode_weyl_operator_1_1": true,
"zero_mode_weyl_operator_1_2": true,
"berry_connection_k1": true,
"curvature_k1": true,
"orthogonal_frame_derivative_k1": true,
"geometric_energy_density_k1": true,
"flux_k1": true,
"zero_mode_equation_k1_m0": true,
"berry_connection_k2": true,
"curvature_k2": true,
"orthogonal_frame_derivative_k2": true,
"geometric_energy_density_k2": true,
"flux_k2": true,
"zero_mode_equation_k2_m0": true,
"zero_mode_norm_k2_m0": true,
"zero_mode_equation_k2_m1": true,
"berry_connection_k3": true,
"curvature_k3": true,
"orthogonal_frame_derivative_k3": true,
"geometric_energy_density_k3": true,
"flux_k3": true,
"zero_mode_equation_k3_m0": true,
"zero_mode_norm_k3_m0": true,
"zero_mode_equation_k3_m1": true,
"zero_mode_norm_k3_m1": true,
"zero_mode_equation_k3_m2": true,
"berry_connection_k4": true,
"curvature_k4": true,
"orthogonal_frame_derivative_k4": true,
"geometric_energy_density_k4": true,
"flux_k4": true,
"zero_mode_equation_k4_m0": true,
"zero_mode_norm_k4_m0": true,
"zero_mode_equation_k4_m1": true,
"zero_mode_norm_k4_m1": true,
"zero_mode_equation_k4_m2": true,
"zero_mode_norm_k4_m2": true,
"zero_mode_equation_k4_m3": true,
"mirror_texture_flips_connection": true,
"k2_norm_exact": true,
"weak_weight_ratio": true,
"rational_beta_example": true,
"massive_vector_helicities": true,
"transverse_vector_helicities": true,
"scalar_helicity_zero": true,
"inverse_chiral_acceptance": true,
"minimum_winding_with_a_normalizable_mode": true,
"minimum_gradient_energy_in_this_family": true
},
"depths": [
{
"d": 3,
"minimal_massless_rank": 2,
"positive_energy_helicity_minus_half": 0,
"positive_energy_helicity_plus_half": 1,
"bubble_C_retention": "1",
"massive_both_helicities": true
},
{
"d": 4,
"minimal_massless_rank": 4,
"positive_energy_helicity_minus_half": 1,
"positive_energy_helicity_plus_half": 1,
"bubble_C_retention": "2/3",
"massive_both_helicities": true
},
{
"d": 5,
"minimal_massless_rank": 4,
"positive_energy_helicity_minus_half": 1,
"positive_energy_helicity_plus_half": 1,
"bubble_C_retention": "1/2",
"massive_both_helicities": true
},
{
"d": 6,
"minimal_massless_rank": 8,
"positive_energy_helicity_minus_half": 2,
"positive_energy_helicity_plus_half": 2,
"bubble_C_retention": "2/5",
"massive_both_helicities": true
},
{
"d": 10,
"minimal_massless_rank": 32,
"positive_energy_helicity_minus_half": 8,
"positive_energy_helicity_plus_half": 8,
"bubble_C_retention": "2/9",
"massive_both_helicities": true
}
],
"texture_zero_modes": [
{
"winding": 1,
"flux_over_2pi": 1,
"normalizable_modes": 0,
"allowed_m": []
},
{
"winding": 2,
"flux_over_2pi": 2,
"normalizable_modes": 1,
"allowed_m": [
0
]
},
{
"winding": 3,
"flux_over_2pi": 3,
"normalizable_modes": 2,
"allowed_m": [
0,
1
]
},
{
"winding": 4,
"flux_over_2pi": 4,
"normalizable_modes": 3,
"allowed_m": [
0,
1,
2
]
}
],
"sources": {
"experiments/depth-helicity-checks.py": "1bc1fa429b6b0a8dc20253df2c444504e72f63a39e3553059451145d58f2c6ae"
}
}