{
    "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"
    }
}