Recorded data and provenance for the associated calculation.
| experiment | One-script geometry, charge and sector selection comparison |
|---|---|
| created_at | 2026-10-09T05:29:27.909763+00:00 |
View complete data
{
"experiment": "One-script geometry, charge and sector selection comparison",
"created_at": "2026-10-09T05:29:27.909763+00:00",
"sources": {
"experiments/charge-sector-geometry-checks.py": "88e9144a9eab6902765828a75be3dca62d88283f2b8ff2e62f989933dc03d19c"
},
"original_geometry": {
"representation": {
"integer_center_weights": [
0,
2,
2,
2,
-3,
-1,
-1,
-1
],
"normalized_charges": [
"0",
"2/3",
"2/3",
"2/3",
"-1",
"-1/3",
"-1/3",
"-1/3"
],
"factorization": "E=(1+Lambda^2 W) tensor (1+det(W)^-1)",
"induced_connection": "A_E=diag(A_F,A_F-Tr(A) I4)=diag(C_F,C_F)+Tr(A) Q",
"same_transition_line": "Hom(D^-1,1)=D",
"determinant": "det(E)=D^4 D^-4=1",
"twist_family": "E tensor D^k shifts every normalized charge by k; canonical untwisted construction is a carrier choice",
"circle_globality": "Q is center generator/3; its 2pi exponential equals the SU3 center action, and its standalone period is 6pi"
},
"ranks": [
{
"complex_normal_rank": 1,
"ordinary_normal_dimensions": 2,
"weights": [
{
"degree": 0,
"multiplicity": 1,
"weight": "0"
},
{
"degree": 1,
"multiplicity": 1,
"weight": "-1"
}
],
"integer_weight_trace": "-1"
},
{
"complex_normal_rank": 2,
"ordinary_normal_dimensions": 4,
"weights": [
{
"degree": 0,
"multiplicity": 1,
"weight": "0"
},
{
"degree": 1,
"multiplicity": 2,
"weight": "-1/2"
},
{
"degree": 2,
"multiplicity": 1,
"weight": "1"
}
],
"integer_weight_trace": "0"
},
{
"complex_normal_rank": 3,
"ordinary_normal_dimensions": 6,
"weights": [
{
"degree": 0,
"multiplicity": 1,
"weight": "0"
},
{
"degree": 1,
"multiplicity": 3,
"weight": "-1/3"
},
{
"degree": 2,
"multiplicity": 3,
"weight": "2/3"
},
{
"degree": 3,
"multiplicity": 1,
"weight": "-1"
}
],
"integer_weight_trace": "0"
},
{
"complex_normal_rank": 4,
"ordinary_normal_dimensions": 8,
"weights": [
{
"degree": 0,
"multiplicity": 1,
"weight": "0"
},
{
"degree": 1,
"multiplicity": 4,
"weight": "-1/4"
},
{
"degree": 2,
"multiplicity": 6,
"weight": "1/2"
},
{
"degree": 3,
"multiplicity": 4,
"weight": "-3/4"
},
{
"degree": 4,
"multiplicity": 1,
"weight": "1"
}
],
"integer_weight_trace": "0"
},
{
"complex_normal_rank": 5,
"ordinary_normal_dimensions": 10,
"weights": [
{
"degree": 0,
"multiplicity": 1,
"weight": "0"
},
{
"degree": 1,
"multiplicity": 5,
"weight": "-1/5"
},
{
"degree": 2,
"multiplicity": 10,
"weight": "2/5"
},
{
"degree": 3,
"multiplicity": 10,
"weight": "-3/5"
},
{
"degree": 4,
"multiplicity": 5,
"weight": "4/5"
},
{
"degree": 5,
"multiplicity": 1,
"weight": "-1"
}
],
"integer_weight_trace": "0"
},
{
"complex_normal_rank": 6,
"ordinary_normal_dimensions": 12,
"weights": [
{
"degree": 0,
"multiplicity": 1,
"weight": "0"
},
{
"degree": 1,
"multiplicity": 6,
"weight": "-1/6"
},
{
"degree": 2,
"multiplicity": 15,
"weight": "1/3"
},
{
"degree": 3,
"multiplicity": 20,
"weight": "-1/2"
},
{
"degree": 4,
"multiplicity": 15,
"weight": "2/3"
},
{
"degree": 5,
"multiplicity": 6,
"weight": "-5/6"
},
{
"degree": 6,
"multiplicity": 1,
"weight": "1"
}
],
"integer_weight_trace": "0"
}
],
"minimal_carrier": {
"family": "Exactly one copy of each degree 0,1,2,3, each positive degree either original or conjugate; no character twists or extra summands",
"cases": [
{
"conjugation_signs_degrees_1_2_3": [
-1,
-1,
-1
],
"integer_weights": [
0,
-1,
-2,
-3
],
"determinant_power": -4,
"matching_triplet_type": false
},
{
"conjugation_signs_degrees_1_2_3": [
-1,
-1,
1
],
"integer_weights": [
0,
-1,
-2,
3
],
"determinant_power": -2,
"matching_triplet_type": false
},
{
"conjugation_signs_degrees_1_2_3": [
-1,
1,
-1
],
"integer_weights": [
0,
-1,
2,
-3
],
"determinant_power": 0,
"matching_triplet_type": true
},
{
"conjugation_signs_degrees_1_2_3": [
-1,
1,
1
],
"integer_weights": [
0,
-1,
2,
3
],
"determinant_power": 2,
"matching_triplet_type": true
},
{
"conjugation_signs_degrees_1_2_3": [
1,
-1,
-1
],
"integer_weights": [
0,
1,
-2,
-3
],
"determinant_power": -2,
"matching_triplet_type": true
},
{
"conjugation_signs_degrees_1_2_3": [
1,
-1,
1
],
"integer_weights": [
0,
1,
-2,
3
],
"determinant_power": 0,
"matching_triplet_type": true
},
{
"conjugation_signs_degrees_1_2_3": [
1,
1,
-1
],
"integer_weights": [
0,
1,
2,
-3
],
"determinant_power": 2,
"matching_triplet_type": false
},
{
"conjugation_signs_degrees_1_2_3": [
1,
1,
1
],
"integer_weights": [
0,
1,
2,
3
],
"determinant_power": 4,
"matching_triplet_type": false
}
],
"determinant_trivial_choices": [
[
-1,
1,
-1
],
[
1,
-1,
1
]
],
"conclusion": "E and its full conjugate are the only determinant-trivial choices in this finite family; their triplet types match automatically",
"premise": "A preferred parallel complex volume on the carrier is an extra selection criterion, not a consequence of orienting the real spatial normal bundle"
},
"projective": {
"normal_bundle": "N_CP2/CP5=Hom(ell,C6/A)=O(1) tensor (C6/A)",
"carrier": "O + O(2)^3 + O(-1)^3 + O(-3), with constant quotient-space factors retained",
"total_chern_polynomial": "24*H**7 - 44*H**6 - 6*H**5 + 39*H**4 - 2*H**3 - 12*H**2 + 1",
"chern_character_degree_four": "12 H^2",
"pullback": "O_CP5(-3)|CP3=O_CP3(-3)",
"compatibility_status": "Valid partial/global associated-bundle example; not a complete maintained sector chain",
"odd_intermediate_obstructions": [
{
"lower_depth": 2,
"higher_depth": 4,
"excluded_intermediate_depth": 3,
"normal_euler_class": "H"
},
{
"lower_depth": 4,
"higher_depth": 6,
"excluded_intermediate_depth": 5,
"normal_euler_class": "H"
}
]
},
"compatible_metric": {
"ordinary_space": "R4_x times R6_y, all noncompact physical spatial coordinates",
"metric": "g=sum dx_mu^2 + |dy+omega J y|^2, omega=b/2 (x1 dx2-x2 dx1)",
"normal_connection": "omega J, or i omega I3 in complex notation",
"normal_curvature": "b J dx1 wedge dx2",
"full_nested_flag": {
"2": "span(x1,x2)",
"3": "span(x1,x2,x3)",
"4": "R4_x at y=0",
"5": "R4_x plus y1",
"6": "R4_x plus y1,y2",
"10": "all coordinates"
},
"metric_properties": "smooth, positive, determinant one; no boundary or compactification",
"premises": "Chosen metric and complex normal structure; an existence construction, not selected IDWT geometry",
"scope": "Normal connection need not preserve each intermediate real normal line; all listed submanifolds coexist"
}
},
"rank_and_depth_tests": {
"ranks": [
{
"complex_rank": 1,
"real_normal_dimension": 2,
"determinant_unit": [
{
"charge": "0",
"multiplicity": 1
},
{
"charge": "-1",
"multiplicity": 1
}
],
"fixed_three_plane_unit": [
{
"charge": "0",
"multiplicity": 1
},
{
"charge": "-1/3",
"multiplicity": 1
}
],
"full_target_match": false
},
{
"complex_rank": 2,
"real_normal_dimension": 4,
"determinant_unit": [
{
"charge": "0",
"multiplicity": 1
},
{
"charge": "-1/2",
"multiplicity": 2
},
{
"charge": "1",
"multiplicity": 1
}
],
"fixed_three_plane_unit": [
{
"charge": "0",
"multiplicity": 1
},
{
"charge": "-1/3",
"multiplicity": 2
},
{
"charge": "2/3",
"multiplicity": 1
}
],
"full_target_match": false
},
{
"complex_rank": 3,
"real_normal_dimension": 6,
"determinant_unit": [
{
"charge": "0",
"multiplicity": 1
},
{
"charge": "-1/3",
"multiplicity": 3
},
{
"charge": "2/3",
"multiplicity": 3
},
{
"charge": "-1",
"multiplicity": 1
}
],
"fixed_three_plane_unit": [
{
"charge": "0",
"multiplicity": 1
},
{
"charge": "-1/3",
"multiplicity": 3
},
{
"charge": "2/3",
"multiplicity": 3
},
{
"charge": "-1",
"multiplicity": 1
}
],
"full_target_match": true
},
{
"complex_rank": 4,
"real_normal_dimension": 8,
"determinant_unit": [
{
"charge": "0",
"multiplicity": 1
},
{
"charge": "-1/4",
"multiplicity": 4
},
{
"charge": "1/2",
"multiplicity": 6
},
{
"charge": "-3/4",
"multiplicity": 4
},
{
"charge": "1",
"multiplicity": 1
}
],
"fixed_three_plane_unit": [
{
"charge": "0",
"multiplicity": 1
},
{
"charge": "-1/3",
"multiplicity": 4
},
{
"charge": "2/3",
"multiplicity": 6
},
{
"charge": "-1",
"multiplicity": 4
},
{
"charge": "4/3",
"multiplicity": 1
}
],
"full_target_match": false
},
{
"complex_rank": 5,
"real_normal_dimension": 10,
"determinant_unit": [
{
"charge": "0",
"multiplicity": 1
},
{
"charge": "-1/5",
"multiplicity": 5
},
{
"charge": "2/5",
"multiplicity": 10
},
{
"charge": "-3/5",
"multiplicity": 10
},
{
"charge": "4/5",
"multiplicity": 5
},
{
"charge": "-1",
"multiplicity": 1
}
],
"fixed_three_plane_unit": [
{
"charge": "0",
"multiplicity": 1
},
{
"charge": "-1/3",
"multiplicity": 5
},
{
"charge": "2/3",
"multiplicity": 10
},
{
"charge": "-1",
"multiplicity": 10
},
{
"charge": "4/3",
"multiplicity": 5
},
{
"charge": "-5/3",
"multiplicity": 1
}
],
"full_target_match": false
},
{
"complex_rank": 6,
"real_normal_dimension": 12,
"determinant_unit": [
{
"charge": "0",
"multiplicity": 1
},
{
"charge": "-1/6",
"multiplicity": 6
},
{
"charge": "1/3",
"multiplicity": 15
},
{
"charge": "-1/2",
"multiplicity": 20
},
{
"charge": "2/3",
"multiplicity": 15
},
{
"charge": "-5/6",
"multiplicity": 6
},
{
"charge": "1",
"multiplicity": 1
}
],
"fixed_three_plane_unit": [
{
"charge": "0",
"multiplicity": 1
},
{
"charge": "-1/3",
"multiplicity": 6
},
{
"charge": "2/3",
"multiplicity": 15
},
{
"charge": "-1",
"multiplicity": 20
},
{
"charge": "4/3",
"multiplicity": 15
},
{
"charge": "-5/3",
"multiplicity": 6
},
{
"charge": "2",
"multiplicity": 1
}
],
"full_target_match": false
}
],
"all_maintained_pairs": [
{
"lower_depth": 2,
"upper_depth": 3,
"normal_dimension": 1,
"status": "odd real normal rank: whole-normal complex structure unavailable",
"full_target_match": false
},
{
"lower_depth": 2,
"upper_depth": 4,
"normal_dimension": 2,
"complex_rank": 1,
"full_target_match": false,
"status": "Hermitian normal bundle assumed; full exterior carrier compared"
},
{
"lower_depth": 2,
"upper_depth": 5,
"normal_dimension": 3,
"status": "odd real normal rank: whole-normal complex structure unavailable",
"full_target_match": false
},
{
"lower_depth": 2,
"upper_depth": 6,
"normal_dimension": 4,
"complex_rank": 2,
"full_target_match": false,
"status": "Hermitian normal bundle assumed; full exterior carrier compared"
},
{
"lower_depth": 2,
"upper_depth": 10,
"normal_dimension": 8,
"complex_rank": 4,
"full_target_match": false,
"status": "Hermitian normal bundle assumed; full exterior carrier compared"
},
{
"lower_depth": 3,
"upper_depth": 4,
"normal_dimension": 1,
"status": "odd real normal rank: whole-normal complex structure unavailable",
"full_target_match": false
},
{
"lower_depth": 3,
"upper_depth": 5,
"normal_dimension": 2,
"complex_rank": 1,
"full_target_match": false,
"status": "Hermitian normal bundle assumed; full exterior carrier compared"
},
{
"lower_depth": 3,
"upper_depth": 6,
"normal_dimension": 3,
"status": "odd real normal rank: whole-normal complex structure unavailable",
"full_target_match": false
},
{
"lower_depth": 3,
"upper_depth": 10,
"normal_dimension": 7,
"status": "odd real normal rank: whole-normal complex structure unavailable",
"full_target_match": false
},
{
"lower_depth": 4,
"upper_depth": 5,
"normal_dimension": 1,
"status": "odd real normal rank: whole-normal complex structure unavailable",
"full_target_match": false
},
{
"lower_depth": 4,
"upper_depth": 6,
"normal_dimension": 2,
"complex_rank": 1,
"full_target_match": false,
"status": "Hermitian normal bundle assumed; full exterior carrier compared"
},
{
"lower_depth": 4,
"upper_depth": 10,
"normal_dimension": 6,
"complex_rank": 3,
"full_target_match": true,
"status": "Hermitian normal bundle assumed; full exterior carrier compared"
},
{
"lower_depth": 5,
"upper_depth": 6,
"normal_dimension": 1,
"status": "odd real normal rank: whole-normal complex structure unavailable",
"full_target_match": false
},
{
"lower_depth": 5,
"upper_depth": 10,
"normal_dimension": 5,
"status": "odd real normal rank: whole-normal complex structure unavailable",
"full_target_match": false
},
{
"lower_depth": 6,
"upper_depth": 10,
"normal_dimension": 4,
"complex_rank": 2,
"full_target_match": false,
"status": "Hermitian normal bundle assumed; full exterior carrier compared"
}
],
"maintained_pair_matches": [
[
4,
10
]
],
"all_integer_depths_2_to_10_matches": [
[
2,
8
],
[
3,
9
],
[
4,
10
]
],
"changed_tangent_rule_fixed_unit": [
{
"depth": 2,
"paired_rank": 1,
"extra_odd_direction_choice_required": false,
"charges": [
{
"charge": "0",
"multiplicity": 1
},
{
"charge": "-1/3",
"multiplicity": 1
}
],
"matter_target": null,
"target_multiplicity": null,
"multiplicity_at_target": null,
"target_available": null
},
{
"depth": 3,
"paired_rank": 1,
"extra_odd_direction_choice_required": true,
"charges": [
{
"charge": "0",
"multiplicity": 1
},
{
"charge": "-1/3",
"multiplicity": 1
}
],
"matter_target": "-1/3",
"target_multiplicity": 3,
"multiplicity_at_target": 1,
"target_available": true
},
{
"depth": 4,
"paired_rank": 2,
"extra_odd_direction_choice_required": false,
"charges": [
{
"charge": "0",
"multiplicity": 1
},
{
"charge": "-1/3",
"multiplicity": 2
},
{
"charge": "2/3",
"multiplicity": 1
}
],
"matter_target": "2/3",
"target_multiplicity": 3,
"multiplicity_at_target": 1,
"target_available": true
},
{
"depth": 5,
"paired_rank": 2,
"extra_odd_direction_choice_required": true,
"charges": [
{
"charge": "0",
"multiplicity": 1
},
{
"charge": "-1/3",
"multiplicity": 2
},
{
"charge": "2/3",
"multiplicity": 1
}
],
"matter_target": "0",
"target_multiplicity": 1,
"multiplicity_at_target": 1,
"target_available": true
},
{
"depth": 6,
"paired_rank": 3,
"extra_odd_direction_choice_required": false,
"charges": [
{
"charge": "0",
"multiplicity": 1
},
{
"charge": "-1/3",
"multiplicity": 3
},
{
"charge": "2/3",
"multiplicity": 3
},
{
"charge": "-1",
"multiplicity": 1
}
],
"matter_target": "-1",
"target_multiplicity": 1,
"multiplicity_at_target": 1,
"target_available": true
},
{
"depth": 10,
"paired_rank": 5,
"extra_odd_direction_choice_required": false,
"charges": [
{
"charge": "0",
"multiplicity": 1
},
{
"charge": "-1/3",
"multiplicity": 5
},
{
"charge": "2/3",
"multiplicity": 10
},
{
"charge": "-1",
"multiplicity": 10
},
{
"charge": "4/3",
"multiplicity": 5
},
{
"charge": "-5/3",
"multiplicity": 1
}
],
"matter_target": "-1",
"target_multiplicity": 1,
"multiplicity_at_target": 10,
"target_available": true
}
]
},
"fixed_carrier_assignment_tests": {
"restriction_scope": "Same W/E extended by pullback from the depth-four base on the explicit R10 example",
"spectra_at_depths": {
"2": [
{
"charge": "0",
"multiplicity": 1
},
{
"charge": "2/3",
"multiplicity": 3
},
{
"charge": "-1",
"multiplicity": 1
},
{
"charge": "-1/3",
"multiplicity": 3
}
],
"3": [
{
"charge": "0",
"multiplicity": 1
},
{
"charge": "2/3",
"multiplicity": 3
},
{
"charge": "-1",
"multiplicity": 1
},
{
"charge": "-1/3",
"multiplicity": 3
}
],
"4": [
{
"charge": "0",
"multiplicity": 1
},
{
"charge": "2/3",
"multiplicity": 3
},
{
"charge": "-1",
"multiplicity": 1
},
{
"charge": "-1/3",
"multiplicity": 3
}
],
"5": [
{
"charge": "0",
"multiplicity": 1
},
{
"charge": "2/3",
"multiplicity": 3
},
{
"charge": "-1",
"multiplicity": 1
},
{
"charge": "-1/3",
"multiplicity": 3
}
],
"6": [
{
"charge": "0",
"multiplicity": 1
},
{
"charge": "2/3",
"multiplicity": 3
},
{
"charge": "-1",
"multiplicity": 1
},
{
"charge": "-1/3",
"multiplicity": 3
}
],
"10": [
{
"charge": "0",
"multiplicity": 1
},
{
"charge": "2/3",
"multiplicity": 3
},
{
"charge": "-1",
"multiplicity": 1
},
{
"charge": "-1/3",
"multiplicity": 3
}
]
},
"one_to_one_assignment_count": 24,
"type_preserving_assignments": [
{
"down_at_3": "2/3",
"up_at_4": "-1/3",
"neutral_at_5": "0",
"charged_at_6_and_10": "-1"
},
{
"down_at_3": "2/3",
"up_at_4": "-1/3",
"neutral_at_5": "-1",
"charged_at_6_and_10": "0"
},
{
"down_at_3": "-1/3",
"up_at_4": "2/3",
"neutral_at_5": "0",
"charged_at_6_and_10": "-1"
},
{
"down_at_3": "-1/3",
"up_at_4": "2/3",
"neutral_at_5": "-1",
"charged_at_6_and_10": "0"
}
],
"with_additional_named_channel_alignment": [
{
"down_at_3": "2/3",
"up_at_4": "-1/3",
"neutral_at_5": "-1",
"charged_at_6_and_10": "0"
},
{
"down_at_3": "-1/3",
"up_at_4": "2/3",
"neutral_at_5": "0",
"charged_at_6_and_10": "-1"
}
],
"with_named_forward_channels_fixed_to_D": [
{
"down_at_3": "-1/3",
"up_at_4": "2/3",
"neutral_at_5": "0",
"charged_at_6_and_10": "-1"
}
],
"assignment_qualification": "The 24 and 4 counts do not impose a map from physical named channels to D. Such a map reduces counts by extra assumptions; the depth numbers still do not enter Q.",
"warning": "These are permitted identifications, not derived physical states. No branch-to-depth selector is present."
},
"charge_twist_tests": {
"carrier_family": "1 + (Lambda2 W tensor D^a) + D^b + (W* tensor D^c)",
"general_solution_for_common_D_power_m": {
"a": "2*m/3 - 2/3",
"b": "-m",
"c": "1/3 - m/3"
},
"admissible_m": "m congruent 1 modulo 3; m is nonzero; all weights are m times original Q",
"bounded_twist_domain": "a,c in [-3,3]; b determined by exact determinant cancellation",
"cases": [
{
"a": -3,
"b": 17,
"c": -3,
"charges": [
"0",
"-7/3",
"17",
"-10/3"
],
"common_transition": false
},
{
"a": -3,
"b": 14,
"c": -2,
"charges": [
"0",
"-7/3",
"14",
"-7/3"
],
"common_transition": false
},
{
"a": -3,
"b": 11,
"c": -1,
"charges": [
"0",
"-7/3",
"11",
"-4/3"
],
"common_transition": false
},
{
"a": -3,
"b": 8,
"c": 0,
"charges": [
"0",
"-7/3",
"8",
"-1/3"
],
"common_transition": false
},
{
"a": -3,
"b": 5,
"c": 1,
"charges": [
"0",
"-7/3",
"5",
"2/3"
],
"common_transition": false
},
{
"a": -3,
"b": 2,
"c": 2,
"charges": [
"0",
"-7/3",
"2",
"5/3"
],
"common_transition": false
},
{
"a": -3,
"b": -1,
"c": 3,
"charges": [
"0",
"-7/3",
"-1",
"8/3"
],
"common_transition": false
},
{
"a": -2,
"b": 14,
"c": -3,
"charges": [
"0",
"-4/3",
"14",
"-10/3"
],
"common_transition": false
},
{
"a": -2,
"b": 11,
"c": -2,
"charges": [
"0",
"-4/3",
"11",
"-7/3"
],
"common_transition": false
},
{
"a": -2,
"b": 8,
"c": -1,
"charges": [
"0",
"-4/3",
"8",
"-4/3"
],
"common_transition": false
},
{
"a": -2,
"b": 5,
"c": 0,
"charges": [
"0",
"-4/3",
"5",
"-1/3"
],
"common_transition": false
},
{
"a": -2,
"b": 2,
"c": 1,
"charges": [
"0",
"-4/3",
"2",
"2/3"
],
"common_transition": true
},
{
"a": -2,
"b": -1,
"c": 2,
"charges": [
"0",
"-4/3",
"-1",
"5/3"
],
"common_transition": false
},
{
"a": -2,
"b": -4,
"c": 3,
"charges": [
"0",
"-4/3",
"-4",
"8/3"
],
"common_transition": false
},
{
"a": -1,
"b": 11,
"c": -3,
"charges": [
"0",
"-1/3",
"11",
"-10/3"
],
"common_transition": false
},
{
"a": -1,
"b": 8,
"c": -2,
"charges": [
"0",
"-1/3",
"8",
"-7/3"
],
"common_transition": false
},
{
"a": -1,
"b": 5,
"c": -1,
"charges": [
"0",
"-1/3",
"5",
"-4/3"
],
"common_transition": false
},
{
"a": -1,
"b": 2,
"c": 0,
"charges": [
"0",
"-1/3",
"2",
"-1/3"
],
"common_transition": false
},
{
"a": -1,
"b": -1,
"c": 1,
"charges": [
"0",
"-1/3",
"-1",
"2/3"
],
"common_transition": false
},
{
"a": -1,
"b": -4,
"c": 2,
"charges": [
"0",
"-1/3",
"-4",
"5/3"
],
"common_transition": false
},
{
"a": -1,
"b": -7,
"c": 3,
"charges": [
"0",
"-1/3",
"-7",
"8/3"
],
"common_transition": false
},
{
"a": 0,
"b": 8,
"c": -3,
"charges": [
"0",
"2/3",
"8",
"-10/3"
],
"common_transition": false
},
{
"a": 0,
"b": 5,
"c": -2,
"charges": [
"0",
"2/3",
"5",
"-7/3"
],
"common_transition": false
},
{
"a": 0,
"b": 2,
"c": -1,
"charges": [
"0",
"2/3",
"2",
"-4/3"
],
"common_transition": false
},
{
"a": 0,
"b": -1,
"c": 0,
"charges": [
"0",
"2/3",
"-1",
"-1/3"
],
"common_transition": true
},
{
"a": 0,
"b": -4,
"c": 1,
"charges": [
"0",
"2/3",
"-4",
"2/3"
],
"common_transition": false
},
{
"a": 0,
"b": -7,
"c": 2,
"charges": [
"0",
"2/3",
"-7",
"5/3"
],
"common_transition": false
},
{
"a": 0,
"b": -10,
"c": 3,
"charges": [
"0",
"2/3",
"-10",
"8/3"
],
"common_transition": false
},
{
"a": 1,
"b": 5,
"c": -3,
"charges": [
"0",
"5/3",
"5",
"-10/3"
],
"common_transition": false
},
{
"a": 1,
"b": 2,
"c": -2,
"charges": [
"0",
"5/3",
"2",
"-7/3"
],
"common_transition": false
},
{
"a": 1,
"b": -1,
"c": -1,
"charges": [
"0",
"5/3",
"-1",
"-4/3"
],
"common_transition": false
},
{
"a": 1,
"b": -4,
"c": 0,
"charges": [
"0",
"5/3",
"-4",
"-1/3"
],
"common_transition": false
},
{
"a": 1,
"b": -7,
"c": 1,
"charges": [
"0",
"5/3",
"-7",
"2/3"
],
"common_transition": false
},
{
"a": 1,
"b": -10,
"c": 2,
"charges": [
"0",
"5/3",
"-10",
"5/3"
],
"common_transition": false
},
{
"a": 1,
"b": -13,
"c": 3,
"charges": [
"0",
"5/3",
"-13",
"8/3"
],
"common_transition": false
},
{
"a": 2,
"b": 2,
"c": -3,
"charges": [
"0",
"8/3",
"2",
"-10/3"
],
"common_transition": false
},
{
"a": 2,
"b": -1,
"c": -2,
"charges": [
"0",
"8/3",
"-1",
"-7/3"
],
"common_transition": false
},
{
"a": 2,
"b": -4,
"c": -1,
"charges": [
"0",
"8/3",
"-4",
"-4/3"
],
"common_transition": true
},
{
"a": 2,
"b": -7,
"c": 0,
"charges": [
"0",
"8/3",
"-7",
"-1/3"
],
"common_transition": false
},
{
"a": 2,
"b": -10,
"c": 1,
"charges": [
"0",
"8/3",
"-10",
"2/3"
],
"common_transition": false
},
{
"a": 2,
"b": -13,
"c": 2,
"charges": [
"0",
"8/3",
"-13",
"5/3"
],
"common_transition": false
},
{
"a": 2,
"b": -16,
"c": 3,
"charges": [
"0",
"8/3",
"-16",
"8/3"
],
"common_transition": false
},
{
"a": 3,
"b": -1,
"c": -3,
"charges": [
"0",
"11/3",
"-1",
"-10/3"
],
"common_transition": false
},
{
"a": 3,
"b": -4,
"c": -2,
"charges": [
"0",
"11/3",
"-4",
"-7/3"
],
"common_transition": false
},
{
"a": 3,
"b": -7,
"c": -1,
"charges": [
"0",
"11/3",
"-7",
"-4/3"
],
"common_transition": false
},
{
"a": 3,
"b": -10,
"c": 0,
"charges": [
"0",
"11/3",
"-10",
"-1/3"
],
"common_transition": false
},
{
"a": 3,
"b": -13,
"c": 1,
"charges": [
"0",
"11/3",
"-13",
"2/3"
],
"common_transition": false
},
{
"a": 3,
"b": -16,
"c": 2,
"charges": [
"0",
"11/3",
"-16",
"5/3"
],
"common_transition": false
},
{
"a": 3,
"b": -19,
"c": 3,
"charges": [
"0",
"11/3",
"-19",
"8/3"
],
"common_transition": false
}
],
"relative_counterexample": {
"a": 1,
"b": -4,
"c": 0,
"charges_in_original_unit": [
"0",
"5/3",
"-4",
"-1/3"
],
"charged_singlet_normalized_to_minus_one": [
"0",
"5/12",
"-1",
"-1/12"
],
"lost_premise": "The singlet and triplet transition lines are D^4 and D^2, rather than the same D"
}
},
"integer_character_scan": {
"case_count": 39304,
"scope": "all eight degree conjugations; three independent integer twists in [-8,8]",
"solutions": [
{
"degree_signs": [
-1,
1,
-1
],
"twists": [
-2,
4,
-6
],
"m": 7
},
{
"degree_signs": [
-1,
1,
-1
],
"twists": [
-1,
2,
-3
],
"m": 4
},
{
"degree_signs": [
-1,
1,
-1
],
"twists": [
0,
0,
0
],
"m": 1
},
{
"degree_signs": [
-1,
1,
-1
],
"twists": [
1,
-2,
3
],
"m": -2
},
{
"degree_signs": [
-1,
1,
-1
],
"twists": [
2,
-4,
6
],
"m": -5
},
{
"degree_signs": [
-1,
1,
1
],
"twists": [
-2,
4,
-8
],
"m": 7
},
{
"degree_signs": [
-1,
1,
1
],
"twists": [
-1,
2,
-5
],
"m": 4
},
{
"degree_signs": [
-1,
1,
1
],
"twists": [
0,
0,
-2
],
"m": 1
},
{
"degree_signs": [
-1,
1,
1
],
"twists": [
1,
-2,
1
],
"m": -2
},
{
"degree_signs": [
-1,
1,
1
],
"twists": [
2,
-4,
4
],
"m": -5
},
{
"degree_signs": [
-1,
1,
1
],
"twists": [
3,
-6,
7
],
"m": -8
},
{
"degree_signs": [
1,
-1,
-1
],
"twists": [
-3,
6,
-7
],
"m": 8
},
{
"degree_signs": [
1,
-1,
-1
],
"twists": [
-2,
4,
-4
],
"m": 5
},
{
"degree_signs": [
1,
-1,
-1
],
"twists": [
-1,
2,
-1
],
"m": 2
},
{
"degree_signs": [
1,
-1,
-1
],
"twists": [
0,
0,
2
],
"m": -1
},
{
"degree_signs": [
1,
-1,
-1
],
"twists": [
1,
-2,
5
],
"m": -4
},
{
"degree_signs": [
1,
-1,
-1
],
"twists": [
2,
-4,
8
],
"m": -7
},
{
"degree_signs": [
1,
-1,
1
],
"twists": [
-2,
4,
-6
],
"m": 5
},
{
"degree_signs": [
1,
-1,
1
],
"twists": [
-1,
2,
-3
],
"m": 2
},
{
"degree_signs": [
1,
-1,
1
],
"twists": [
0,
0,
0
],
"m": -1
},
{
"degree_signs": [
1,
-1,
1
],
"twists": [
1,
-2,
3
],
"m": -4
},
{
"degree_signs": [
1,
-1,
1
],
"twists": [
2,
-4,
6
],
"m": -7
}
],
"interpretation": "Every accepted carrier is an overall charge rescaling, not a new relative-charge table"
},
"anisotropic_metric_test": {
"plane_rates": [
1,
1,
2
],
"determinant_unit": 4,
"complete_holonomy_response": [
"0",
"1/2",
"3/4",
"3/4",
"-1",
"-1/2",
"-1/4",
"-1/4"
],
"metric": "g=|dx|^2+|dy+omega J_lambda y|^2, omega=(x1 dx2-x2 dx1)/2",
"retained": [
"ordinary nested depths",
"compatible J",
"fixed exterior carrier",
"neutral singlet",
"trace zero",
"unit paired differences"
],
"changed": "Charge identified with complete anisotropic holonomy instead of the central determinant component; color scalar property is lost",
"qualification": "This does not change Q when electric charge is still defined by the determinant component. It tests a relaxed identification."
},
"sector_selector_tests": {
"scope": "Seven added uniform predicates, two complex-subspace policies, two compatible nested real flags",
"premise": "Only the intersection of each tangent sector with the fixed four-in-ten normal bundle enters the selector",
"predicates": {
"unrestricted": "all p,q",
"tangent-only": "q=0",
"normal-only": "p=0",
"saturated-tangent": "p=r",
"saturated-normal": "q=3-r",
"balanced-occupation": "p=q",
"fully-saturated": "p=r and q=3-r"
},
"rank_rows": [
{
"geometry": "aligned-flag",
"depth": 2,
"real_intersection_rank": 0,
"maximal_complex_rank": 0,
"minimal_closure_complex_rank": 0
},
{
"geometry": "aligned-flag",
"depth": 3,
"real_intersection_rank": 0,
"maximal_complex_rank": 0,
"minimal_closure_complex_rank": 0
},
{
"geometry": "aligned-flag",
"depth": 4,
"real_intersection_rank": 0,
"maximal_complex_rank": 0,
"minimal_closure_complex_rank": 0
},
{
"geometry": "aligned-flag",
"depth": 5,
"real_intersection_rank": 1,
"maximal_complex_rank": 0,
"minimal_closure_complex_rank": 1
},
{
"geometry": "aligned-flag",
"depth": 6,
"real_intersection_rank": 2,
"maximal_complex_rank": 1,
"minimal_closure_complex_rank": 1
},
{
"geometry": "aligned-flag",
"depth": 10,
"real_intersection_rank": 6,
"maximal_complex_rank": 3,
"minimal_closure_complex_rank": 3
},
{
"geometry": "tilted-flag",
"depth": 2,
"real_intersection_rank": 0,
"maximal_complex_rank": 0,
"minimal_closure_complex_rank": 0
},
{
"geometry": "tilted-flag",
"depth": 3,
"real_intersection_rank": 0,
"maximal_complex_rank": 0,
"minimal_closure_complex_rank": 0
},
{
"geometry": "tilted-flag",
"depth": 4,
"real_intersection_rank": 0,
"maximal_complex_rank": 0,
"minimal_closure_complex_rank": 0
},
{
"geometry": "tilted-flag",
"depth": 5,
"real_intersection_rank": 1,
"maximal_complex_rank": 0,
"minimal_closure_complex_rank": 1
},
{
"geometry": "tilted-flag",
"depth": 6,
"real_intersection_rank": 2,
"maximal_complex_rank": 0,
"minimal_closure_complex_rank": 2
},
{
"geometry": "tilted-flag",
"depth": 10,
"real_intersection_rank": 6,
"maximal_complex_rank": 3,
"minimal_closure_complex_rank": 3
}
],
"cases": [
{
"geometry": "aligned-flag",
"policy": "maximal-contained",
"rule": "unrestricted",
"depth": 2,
"complex_active_rank": 0,
"charges": [
{
"charge": "-1",
"multiplicity": 1
},
{
"charge": "-1/3",
"multiplicity": 3
},
{
"charge": "0",
"multiplicity": 1
},
{
"charge": "2/3",
"multiplicity": 3
}
],
"full_SU3_triplets_preserved": true,
"target_available": null,
"exact_target_multiplet": null
},
{
"geometry": "aligned-flag",
"policy": "maximal-contained",
"rule": "tangent-only",
"depth": 2,
"complex_active_rank": 0,
"charges": [
{
"charge": "0",
"multiplicity": 1
}
],
"full_SU3_triplets_preserved": true,
"target_available": null,
"exact_target_multiplet": null
},
{
"geometry": "aligned-flag",
"policy": "maximal-contained",
"rule": "normal-only",
"depth": 2,
"complex_active_rank": 0,
"charges": [
{
"charge": "-1",
"multiplicity": 1
},
{
"charge": "-1/3",
"multiplicity": 3
},
{
"charge": "0",
"multiplicity": 1
},
{
"charge": "2/3",
"multiplicity": 3
}
],
"full_SU3_triplets_preserved": true,
"target_available": null,
"exact_target_multiplet": null
},
{
"geometry": "aligned-flag",
"policy": "maximal-contained",
"rule": "saturated-tangent",
"depth": 2,
"complex_active_rank": 0,
"charges": [
{
"charge": "-1",
"multiplicity": 1
},
{
"charge": "-1/3",
"multiplicity": 3
},
{
"charge": "0",
"multiplicity": 1
},
{
"charge": "2/3",
"multiplicity": 3
}
],
"full_SU3_triplets_preserved": true,
"target_available": null,
"exact_target_multiplet": null
},
{
"geometry": "aligned-flag",
"policy": "maximal-contained",
"rule": "saturated-normal",
"depth": 2,
"complex_active_rank": 0,
"charges": [
{
"charge": "-1",
"multiplicity": 1
}
],
"full_SU3_triplets_preserved": true,
"target_available": null,
"exact_target_multiplet": null
},
{
"geometry": "aligned-flag",
"policy": "maximal-contained",
"rule": "balanced-occupation",
"depth": 2,
"complex_active_rank": 0,
"charges": [
{
"charge": "0",
"multiplicity": 1
}
],
"full_SU3_triplets_preserved": true,
"target_available": null,
"exact_target_multiplet": null
},
{
"geometry": "aligned-flag",
"policy": "maximal-contained",
"rule": "fully-saturated",
"depth": 2,
"complex_active_rank": 0,
"charges": [
{
"charge": "-1",
"multiplicity": 1
}
],
"full_SU3_triplets_preserved": true,
"target_available": null,
"exact_target_multiplet": null
},
{
"geometry": "aligned-flag",
"policy": "minimal-containing",
"rule": "unrestricted",
"depth": 2,
"complex_active_rank": 0,
"charges": [
{
"charge": "-1",
"multiplicity": 1
},
{
"charge": "-1/3",
"multiplicity": 3
},
{
"charge": "0",
"multiplicity": 1
},
{
"charge": "2/3",
"multiplicity": 3
}
],
"full_SU3_triplets_preserved": true,
"target_available": null,
"exact_target_multiplet": null
},
{
"geometry": "aligned-flag",
"policy": "minimal-containing",
"rule": "tangent-only",
"depth": 2,
"complex_active_rank": 0,
"charges": [
{
"charge": "0",
"multiplicity": 1
}
],
"full_SU3_triplets_preserved": true,
"target_available": null,
"exact_target_multiplet": null
},
{
"geometry": "aligned-flag",
"policy": "minimal-containing",
"rule": "normal-only",
"depth": 2,
"complex_active_rank": 0,
"charges": [
{
"charge": "-1",
"multiplicity": 1
},
{
"charge": "-1/3",
"multiplicity": 3
},
{
"charge": "0",
"multiplicity": 1
},
{
"charge": "2/3",
"multiplicity": 3
}
],
"full_SU3_triplets_preserved": true,
"target_available": null,
"exact_target_multiplet": null
},
{
"geometry": "aligned-flag",
"policy": "minimal-containing",
"rule": "saturated-tangent",
"depth": 2,
"complex_active_rank": 0,
"charges": [
{
"charge": "-1",
"multiplicity": 1
},
{
"charge": "-1/3",
"multiplicity": 3
},
{
"charge": "0",
"multiplicity": 1
},
{
"charge": "2/3",
"multiplicity": 3
}
],
"full_SU3_triplets_preserved": true,
"target_available": null,
"exact_target_multiplet": null
},
{
"geometry": "aligned-flag",
"policy": "minimal-containing",
"rule": "saturated-normal",
"depth": 2,
"complex_active_rank": 0,
"charges": [
{
"charge": "-1",
"multiplicity": 1
}
],
"full_SU3_triplets_preserved": true,
"target_available": null,
"exact_target_multiplet": null
},
{
"geometry": "aligned-flag",
"policy": "minimal-containing",
"rule": "balanced-occupation",
"depth": 2,
"complex_active_rank": 0,
"charges": [
{
"charge": "0",
"multiplicity": 1
}
],
"full_SU3_triplets_preserved": true,
"target_available": null,
"exact_target_multiplet": null
},
{
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"mismatched_depths": [
3,
4,
5,
6,
10
]
},
{
"geometry": "aligned-flag",
"policy": "minimal-containing",
"rule": "tangent-only",
"all_target_numbers_available": false,
"all_target_multiplets_selected": false,
"mismatched_depths": [
3,
4,
5,
6,
10
]
},
{
"geometry": "aligned-flag",
"policy": "minimal-containing",
"rule": "normal-only",
"all_target_numbers_available": false,
"all_target_multiplets_selected": false,
"mismatched_depths": [
3,
4,
5,
6,
10
]
},
{
"geometry": "aligned-flag",
"policy": "minimal-containing",
"rule": "saturated-tangent",
"all_target_numbers_available": false,
"all_target_multiplets_selected": false,
"mismatched_depths": [
3,
4,
5,
6
]
},
{
"geometry": "aligned-flag",
"policy": "minimal-containing",
"rule": "saturated-normal",
"all_target_numbers_available": false,
"all_target_multiplets_selected": false,
"mismatched_depths": [
3,
4,
5,
6,
10
]
},
{
"geometry": "aligned-flag",
"policy": "minimal-containing",
"rule": "balanced-occupation",
"all_target_numbers_available": false,
"all_target_multiplets_selected": false,
"mismatched_depths": [
3,
4,
5,
6,
10
]
},
{
"geometry": "aligned-flag",
"policy": "minimal-containing",
"rule": "fully-saturated",
"all_target_numbers_available": false,
"all_target_multiplets_selected": false,
"mismatched_depths": [
3,
4,
5
]
},
{
"geometry": "tilted-flag",
"policy": "maximal-contained",
"rule": "unrestricted",
"all_target_numbers_available": true,
"all_target_multiplets_selected": false,
"mismatched_depths": [
3,
4,
5,
6,
10
]
},
{
"geometry": "tilted-flag",
"policy": "maximal-contained",
"rule": "tangent-only",
"all_target_numbers_available": false,
"all_target_multiplets_selected": false,
"mismatched_depths": [
3,
4,
6,
10
]
},
{
"geometry": "tilted-flag",
"policy": "maximal-contained",
"rule": "normal-only",
"all_target_numbers_available": false,
"all_target_multiplets_selected": false,
"mismatched_depths": [
3,
4,
5,
6,
10
]
},
{
"geometry": "tilted-flag",
"policy": "maximal-contained",
"rule": "saturated-tangent",
"all_target_numbers_available": true,
"all_target_multiplets_selected": false,
"mismatched_depths": [
3,
4,
5,
6
]
},
{
"geometry": "tilted-flag",
"policy": "maximal-contained",
"rule": "saturated-normal",
"all_target_numbers_available": false,
"all_target_multiplets_selected": false,
"mismatched_depths": [
3,
4,
5,
10
]
},
{
"geometry": "tilted-flag",
"policy": "maximal-contained",
"rule": "balanced-occupation",
"all_target_numbers_available": false,
"all_target_multiplets_selected": false,
"mismatched_depths": [
3,
4,
6,
10
]
},
{
"geometry": "tilted-flag",
"policy": "maximal-contained",
"rule": "fully-saturated",
"all_target_numbers_available": false,
"all_target_multiplets_selected": false,
"mismatched_depths": [
3,
4,
5
]
},
{
"geometry": "tilted-flag",
"policy": "minimal-containing",
"rule": "unrestricted",
"all_target_numbers_available": true,
"all_target_multiplets_selected": false,
"mismatched_depths": [
3,
4,
5,
6,
10
]
},
{
"geometry": "tilted-flag",
"policy": "minimal-containing",
"rule": "tangent-only",
"all_target_numbers_available": false,
"all_target_multiplets_selected": false,
"mismatched_depths": [
3,
4,
5,
6,
10
]
},
{
"geometry": "tilted-flag",
"policy": "minimal-containing",
"rule": "normal-only",
"all_target_numbers_available": false,
"all_target_multiplets_selected": false,
"mismatched_depths": [
3,
4,
5,
6,
10
]
},
{
"geometry": "tilted-flag",
"policy": "minimal-containing",
"rule": "saturated-tangent",
"all_target_numbers_available": false,
"all_target_multiplets_selected": false,
"mismatched_depths": [
3,
4,
5,
6
]
},
{
"geometry": "tilted-flag",
"policy": "minimal-containing",
"rule": "saturated-normal",
"all_target_numbers_available": false,
"all_target_multiplets_selected": false,
"mismatched_depths": [
3,
4,
5,
6,
10
]
},
{
"geometry": "tilted-flag",
"policy": "minimal-containing",
"rule": "balanced-occupation",
"all_target_numbers_available": false,
"all_target_multiplets_selected": false,
"mismatched_depths": [
3,
4,
5,
6,
10
]
},
{
"geometry": "tilted-flag",
"policy": "minimal-containing",
"rule": "fully-saturated",
"all_target_numbers_available": false,
"all_target_multiplets_selected": false,
"mismatched_depths": [
3,
4,
5
]
}
],
"number_only_matches": [
{
"geometry": "aligned-flag",
"policy": "maximal-contained",
"rule": "unrestricted",
"all_target_numbers_available": true,
"all_target_multiplets_selected": false,
"mismatched_depths": [
3,
4,
5,
6,
10
]
},
{
"geometry": "aligned-flag",
"policy": "maximal-contained",
"rule": "saturated-tangent",
"all_target_numbers_available": true,
"all_target_multiplets_selected": false,
"mismatched_depths": [
3,
4,
5,
6
]
},
{
"geometry": "aligned-flag",
"policy": "minimal-containing",
"rule": "unrestricted",
"all_target_numbers_available": true,
"all_target_multiplets_selected": false,
"mismatched_depths": [
3,
4,
5,
6,
10
]
},
{
"geometry": "tilted-flag",
"policy": "maximal-contained",
"rule": "unrestricted",
"all_target_numbers_available": true,
"all_target_multiplets_selected": false,
"mismatched_depths": [
3,
4,
5,
6,
10
]
},
{
"geometry": "tilted-flag",
"policy": "maximal-contained",
"rule": "saturated-tangent",
"all_target_numbers_available": true,
"all_target_multiplets_selected": false,
"mismatched_depths": [
3,
4,
5,
6
]
},
{
"geometry": "tilted-flag",
"policy": "minimal-containing",
"rule": "unrestricted",
"all_target_numbers_available": true,
"all_target_multiplets_selected": false,
"mismatched_depths": [
3,
4,
5,
6,
10
]
}
],
"complete_assignment_matches": [],
"no_separation_reason": "S_3=S_4=0. Every uniform function of this intersection and J alone gives the same retained spectrum at both depths.",
"scope_limit": "No exclusion of rules using additional base-tangent, embedding, curvature or physical branch data. Complex intersections define subbundles only on constant-rank regions."
},
"checks": [
{
"name": "Hodge reordering is unitary",
"passed": true
},
{
"name": "g unitary",
"passed": true
},
{
"name": "g global determinant factorization",
"passed": true
},
{
"name": "g carrier determinant one",
"passed": true
},
{
"name": "h unitary",
"passed": true
},
{
"name": "h global determinant factorization",
"passed": true
},
{
"name": "h carrier determinant one",
"passed": true
},
{
"name": "gh unitary",
"passed": true
},
{
"name": "gh global determinant factorization",
"passed": true
},
{
"name": "gh carrier determinant one",
"passed": true
},
{
"name": "representation composition on noncommuting unitary elements",
"passed": true
},
{
"name": "test matrices do not commute",
"passed": true
},
{
"name": "general u3 connection factorization",
"passed": true
},
{
"name": "induced connection has zero trace",
"passed": true
},
{
"name": "single determinant connection gives all relative charges",
"passed": true
},
{
"name": "charge generator parallel for induced unitary connection",
"passed": true
},
{
"name": "charge trace zero",
"passed": true
},
{
"name": "same unit transition on singlet and triplet",
"passed": true
},
{
"name": "transition is a section of determinant line",
"passed": true
},
{
"name": "color generator 1 commutes with charge",
"passed": true
},
{
"name": "color generator 2 commutes with charge",
"passed": true
},
{
"name": "color generator 3 commutes with charge",
"passed": true
},
{
"name": "color generator 4 commutes with charge",
"passed": true
},
{
"name": "color generator 5 commutes with charge",
"passed": true
},
{
"name": "color generator 6 commutes with charge",
"passed": true
},
{
"name": "color generator 7 commutes with charge",
"passed": true
},
{
"name": "color generator 8 commutes with charge",
"passed": true
},
{
"name": "both triplets have fundamental Casimir",
"passed": true
},
{
"name": "old parity-number shortcut fails the unchanged wedge product",
"passed": true
},
{
"name": "determinant twist changes trace",
"passed": true
},
{
"name": "rank 2 alternating binomial trace",
"passed": true
},
{
"name": "rank 3 alternating binomial trace",
"passed": true
},
{
"name": "rank 4 alternating binomial trace",
"passed": true
},
{
"name": "rank 5 alternating binomial trace",
"passed": true
},
{
"name": "rank 6 alternating binomial trace",
"passed": true
},
{
"name": "rank three has exact multiplicities 1,3,3,1",
"passed": true
},
{
"name": "all eight minimal exterior choices classified",
"passed": true
},
{
"name": "trivial complex determinant forces matching triplets in this family",
"passed": true
},
{
"name": "projective carrier c1 vanishes",
"passed": true
},
{
"name": "projective carrier c2",
"passed": true
},
{
"name": "projective carrier ch2",
"passed": true
},
{
"name": "lepton transition exponent",
"passed": true
},
{
"name": "triplet transition exponent",
"passed": true
},
{
"name": "CP1 to CP2 normal Euler class nonzero",
"passed": true
},
{
"name": "CP2 to CP3 normal Euler class nonzero",
"passed": true
},
{
"name": "metric Schur complement identity",
"passed": true
},
{
"name": "normal connection equals prescribed geometric one-form 1",
"passed": true
},
{
"name": "normal connection equals prescribed geometric one-form 2",
"passed": true
},
{
"name": "normal connection equals prescribed geometric one-form 3",
"passed": true
},
{
"name": "normal connection equals prescribed geometric one-form 4",
"passed": true
},
{
"name": "normal curvature is nonzero central U3 curvature",
"passed": true
},
{
"name": "zero section is totally geodesic",
"passed": true
},
{
"name": "rank 1 exterior total dimension",
"passed": true
},
{
"name": "rank 2 exterior total dimension",
"passed": true
},
{
"name": "rank 3 exterior total dimension",
"passed": true
},
{
"name": "rank 4 exterior total dimension",
"passed": true
},
{
"name": "rank 5 exterior total dimension",
"passed": true
},
{
"name": "rank 6 exterior total dimension",
"passed": true
},
{
"name": "only rank three gives the complete target spectrum in ranks 1..6",
"passed": true
},
{
"name": "only maintained pair 4-in-10 has full rank-three table",
"passed": true
},
{
"name": "rank criterion is a gap criterion, not absolute depth selection",
"passed": true
},
{
"name": "changed tangent rule contains all target numbers with fixed unit",
"passed": true
},
{
"name": "changed tangent rule fails target multiplet ranks at depths 3,4,10",
"passed": true
},
{
"name": "depth 2 pulled-back connection preserves Q",
"passed": true
},
{
"name": "depth 3 pulled-back connection preserves Q",
"passed": true
},
{
"name": "depth 4 pulled-back connection preserves Q",
"passed": true
},
{
"name": "depth 5 pulled-back connection preserves Q",
"passed": true
},
{
"name": "depth 6 pulled-back connection preserves Q",
"passed": true
},
{
"name": "depth 10 pulled-back connection preserves Q",
"passed": true
},
{
"name": "every one-to-one branch assignment retains trace",
"passed": true
},
{
"name": "24 permutations allowed by fibre construction",
"passed": true
},
{
"name": "four assignments remain after singlet/triplet grouping",
"passed": true
},
{
"name": "quark-depth swap remains geometrically allowed",
"passed": true
},
{
"name": "naming the same oriented physical channels leaves two assignments",
"passed": true
},
{
"name": "naming physical forward channels as D leaves one assignment",
"passed": true
},
{
"name": "common-transition character solution",
"passed": true
},
{
"name": "exact determinant transition fixes all twists",
"passed": true
},
{
"name": "twist (-3,-3) full trace",
"passed": true
},
{
"name": "twist (-3,-2) full trace",
"passed": true
},
{
"name": "twist (-3,-1) full trace",
"passed": true
},
{
"name": "twist (-3,0) full trace",
"passed": true
},
{
"name": "twist (-3,1) full trace",
"passed": true
},
{
"name": "twist (-3,2) full trace",
"passed": true
},
{
"name": "twist (-3,3) full trace",
"passed": true
},
{
"name": "twist (-2,-3) full trace",
"passed": true
},
{
"name": "twist (-2,-2) full trace",
"passed": true
},
{
"name": "twist (-2,-1) full trace",
"passed": true
},
{
"name": "twist (-2,0) full trace",
"passed": true
},
{
"name": "twist (-2,1) full trace",
"passed": true
},
{
"name": "common twist (-2,1) is only an overall scale",
"passed": true
},
{
"name": "common twist (-2,1) U3 globality",
"passed": true
},
{
"name": "twist (-2,2) full trace",
"passed": true
},
{
"name": "twist (-2,3) full trace",
"passed": true
},
{
"name": "twist (-1,-3) full trace",
"passed": true
},
{
"name": "twist (-1,-2) full trace",
"passed": true
},
{
"name": "twist (-1,-1) full trace",
"passed": true
},
{
"name": "twist (-1,0) full trace",
"passed": true
},
{
"name": "twist (-1,1) full trace",
"passed": true
},
{
"name": "twist (-1,2) full trace",
"passed": true
},
{
"name": "twist (-1,3) full trace",
"passed": true
},
{
"name": "twist (0,-3) full trace",
"passed": true
},
{
"name": "twist (0,-2) full trace",
"passed": true
},
{
"name": "twist (0,-1) full trace",
"passed": true
},
{
"name": "twist (0,0) full trace",
"passed": true
},
{
"name": "common twist (0,0) is only an overall scale",
"passed": true
},
{
"name": "common twist (0,0) U3 globality",
"passed": true
},
{
"name": "twist (0,1) full trace",
"passed": true
},
{
"name": "twist (0,2) full trace",
"passed": true
},
{
"name": "twist (0,3) full trace",
"passed": true
},
{
"name": "twist (1,-3) full trace",
"passed": true
},
{
"name": "twist (1,-2) full trace",
"passed": true
},
{
"name": "twist (1,-1) full trace",
"passed": true
},
{
"name": "twist (1,0) full trace",
"passed": true
},
{
"name": "twist (1,1) full trace",
"passed": true
},
{
"name": "twist (1,2) full trace",
"passed": true
},
{
"name": "twist (1,3) full trace",
"passed": true
},
{
"name": "twist (2,-3) full trace",
"passed": true
},
{
"name": "twist (2,-2) full trace",
"passed": true
},
{
"name": "twist (2,-1) full trace",
"passed": true
},
{
"name": "common twist (2,-1) is only an overall scale",
"passed": true
},
{
"name": "common twist (2,-1) U3 globality",
"passed": true
},
{
"name": "twist (2,0) full trace",
"passed": true
},
{
"name": "twist (2,1) full trace",
"passed": true
},
{
"name": "twist (2,2) full trace",
"passed": true
},
{
"name": "twist (2,3) full trace",
"passed": true
},
{
"name": "twist (3,-3) full trace",
"passed": true
},
{
"name": "twist (3,-2) full trace",
"passed": true
},
{
"name": "twist (3,-1) full trace",
"passed": true
},
{
"name": "twist (3,0) full trace",
"passed": true
},
{
"name": "twist (3,1) full trace",
"passed": true
},
{
"name": "twist (3,2) full trace",
"passed": true
},
{
"name": "twist (3,3) full trace",
"passed": true
},
{
"name": "relative-charge counterexample keeps neutrality and determinant cancellation",
"passed": true
},
{
"name": "counterexample is not a unit change",
"passed": true
},
{
"name": "counterexample loses common transition",
"passed": true
},
{
"name": "block-scalar neutral trace common-unit constraints fix relative weights",
"passed": true
},
{
"name": "integer family solution 1",
"passed": true
},
{
"name": "integer family solution 2",
"passed": true
},
{
"name": "integer family solution 3",
"passed": true
},
{
"name": "integer family solution 4",
"passed": true
},
{
"name": "integer family solution 5",
"passed": true
},
{
"name": "integer family solution 6",
"passed": true
},
{
"name": "integer family solution 7",
"passed": true
},
{
"name": "integer family solution 8",
"passed": true
},
{
"name": "integer family solution 9",
"passed": true
},
{
"name": "integer family solution 10",
"passed": true
},
{
"name": "integer family solution 11",
"passed": true
},
{
"name": "integer family solution 12",
"passed": true
},
{
"name": "integer family solution 13",
"passed": true
},
{
"name": "integer family solution 14",
"passed": true
},
{
"name": "integer family solution 15",
"passed": true
},
{
"name": "integer family solution 16",
"passed": true
},
{
"name": "integer family solution 17",
"passed": true
},
{
"name": "integer family solution 18",
"passed": true
},
{
"name": "integer family solution 19",
"passed": true
},
{
"name": "integer family solution 20",
"passed": true
},
{
"name": "integer family solution 21",
"passed": true
},
{
"name": "integer family solution 22",
"passed": true
},
{
"name": "integer scan includes even m4",
"passed": true
},
{
"name": "general plane rates have traceless carrier generator",
"passed": true
},
{
"name": "general plane rates retain same singlet and pair transition",
"passed": true
},
{
"name": "anisotropic response is not color scalar",
"passed": true
},
{
"name": "equal triplet weights force equal plane rates",
"passed": true
},
{
"name": "determinant part remains original Q even for anisotropic rates",
"passed": true
},
{
"name": "all three independent plane rates preserve the same complex structure",
"passed": true
},
{
"name": "anisotropic metric remains positive by Schur complement",
"passed": true
},
{
"name": "anisotropic normal connection follows from the actual metric",
"passed": true
},
{
"name": "normal flag tilt is an exact orthogonal rotation",
"passed": true
},
{
"name": "relative normal flag tilt changes J alignment",
"passed": true
},
{
"name": "aligned-flag depth 2 common rotation covariance",
"passed": true
},
{
"name": "aligned-flag depth 2 complex core/closure dimension identity",
"passed": true
},
{
"name": "aligned-flag depth 2 maximal-contained is J-invariant",
"passed": true
},
{
"name": "aligned-flag depth 2 maximal-contained is Hermitian projector",
"passed": true
},
{
"name": "selector projector 1 unrestricted is an orthogonal projector",
"passed": true
},
{
"name": "selector projector 1 unrestricted retains charge eigenbranches",
"passed": true
},
{
"name": "selector projector 1 unrestricted matches binomial branching",
"passed": true
},
{
"name": "selector projector 2 tangent-only is an orthogonal projector",
"passed": true
},
{
"name": "selector projector 2 tangent-only retains charge eigenbranches",
"passed": true
},
{
"name": "selector projector 2 tangent-only matches binomial branching",
"passed": true
},
{
"name": "selector projector 3 normal-only is an orthogonal projector",
"passed": true
},
{
"name": "selector projector 3 normal-only retains charge eigenbranches",
"passed": true
},
{
"name": "selector projector 3 normal-only matches binomial branching",
"passed": true
},
{
"name": "selector projector 4 saturated-tangent is an orthogonal projector",
"passed": true
},
{
"name": "selector projector 4 saturated-tangent retains charge eigenbranches",
"passed": true
},
{
"name": "selector projector 4 saturated-tangent matches binomial branching",
"passed": true
},
{
"name": "selector projector 5 saturated-normal is an orthogonal projector",
"passed": true
},
{
"name": "selector projector 5 saturated-normal retains charge eigenbranches",
"passed": true
},
{
"name": "selector projector 5 saturated-normal matches binomial branching",
"passed": true
},
{
"name": "selector projector 6 balanced-occupation is an orthogonal projector",
"passed": true
},
{
"name": "selector projector 6 balanced-occupation retains charge eigenbranches",
"passed": true
},
{
"name": "selector projector 6 balanced-occupation matches binomial branching",
"passed": true
},
{
"name": "selector projector 7 fully-saturated is an orthogonal projector",
"passed": true
},
{
"name": "selector projector 7 fully-saturated retains charge eigenbranches",
"passed": true
},
{
"name": "selector projector 7 fully-saturated matches binomial branching",
"passed": true
},
{
"name": "aligned-flag depth 2 minimal-containing is J-invariant",
"passed": true
},
{
"name": "aligned-flag depth 2 minimal-containing is Hermitian projector",
"passed": true
},
{
"name": "aligned-flag depth 3 common rotation covariance",
"passed": true
},
{
"name": "aligned-flag depth 3 complex core/closure dimension identity",
"passed": true
},
{
"name": "aligned-flag depth 3 maximal-contained is J-invariant",
"passed": true
},
{
"name": "aligned-flag depth 3 maximal-contained is Hermitian projector",
"passed": true
},
{
"name": "aligned-flag depth 3 minimal-containing is J-invariant",
"passed": true
},
{
"name": "aligned-flag depth 3 minimal-containing is Hermitian projector",
"passed": true
},
{
"name": "aligned-flag depth 4 common rotation covariance",
"passed": true
},
{
"name": "aligned-flag depth 4 complex core/closure dimension identity",
"passed": true
},
{
"name": "aligned-flag depth 4 maximal-contained is J-invariant",
"passed": true
},
{
"name": "aligned-flag depth 4 maximal-contained is Hermitian projector",
"passed": true
},
{
"name": "aligned-flag depth 4 minimal-containing is J-invariant",
"passed": true
},
{
"name": "aligned-flag depth 4 minimal-containing is Hermitian projector",
"passed": true
},
{
"name": "aligned-flag depth 5 common rotation covariance",
"passed": true
},
{
"name": "aligned-flag depth 5 complex core/closure dimension identity",
"passed": true
},
{
"name": "aligned-flag depth 5 maximal-contained is J-invariant",
"passed": true
},
{
"name": "aligned-flag depth 5 maximal-contained is Hermitian projector",
"passed": true
},
{
"name": "aligned-flag depth 5 minimal-containing is J-invariant",
"passed": true
},
{
"name": "aligned-flag depth 5 minimal-containing is Hermitian projector",
"passed": true
},
{
"name": "selector projector 8 unrestricted is an orthogonal projector",
"passed": true
},
{
"name": "selector projector 8 unrestricted retains charge eigenbranches",
"passed": true
},
{
"name": "selector projector 8 unrestricted matches binomial branching",
"passed": true
},
{
"name": "selector projector 9 tangent-only is an orthogonal projector",
"passed": true
},
{
"name": "selector projector 9 tangent-only retains charge eigenbranches",
"passed": true
},
{
"name": "selector projector 9 tangent-only matches binomial branching",
"passed": true
},
{
"name": "selector projector 10 normal-only is an orthogonal projector",
"passed": true
},
{
"name": "selector projector 10 normal-only retains charge eigenbranches",
"passed": true
},
{
"name": "selector projector 10 normal-only matches binomial branching",
"passed": true
},
{
"name": "selector projector 11 saturated-tangent is an orthogonal projector",
"passed": true
},
{
"name": "selector projector 11 saturated-tangent retains charge eigenbranches",
"passed": true
},
{
"name": "selector projector 11 saturated-tangent matches binomial branching",
"passed": true
},
{
"name": "selector projector 12 saturated-normal is an orthogonal projector",
"passed": true
},
{
"name": "selector projector 12 saturated-normal retains charge eigenbranches",
"passed": true
},
{
"name": "selector projector 12 saturated-normal matches binomial branching",
"passed": true
},
{
"name": "selector projector 13 balanced-occupation is an orthogonal projector",
"passed": true
},
{
"name": "selector projector 13 balanced-occupation retains charge eigenbranches",
"passed": true
},
{
"name": "selector projector 13 balanced-occupation matches binomial branching",
"passed": true
},
{
"name": "selector projector 14 fully-saturated is an orthogonal projector",
"passed": true
},
{
"name": "selector projector 14 fully-saturated retains charge eigenbranches",
"passed": true
},
{
"name": "selector projector 14 fully-saturated matches binomial branching",
"passed": true
},
{
"name": "aligned-flag depth 6 common rotation covariance",
"passed": true
},
{
"name": "aligned-flag depth 6 complex core/closure dimension identity",
"passed": true
},
{
"name": "aligned-flag depth 6 maximal-contained is J-invariant",
"passed": true
},
{
"name": "aligned-flag depth 6 maximal-contained is Hermitian projector",
"passed": true
},
{
"name": "aligned-flag depth 6 minimal-containing is J-invariant",
"passed": true
},
{
"name": "aligned-flag depth 6 minimal-containing is Hermitian projector",
"passed": true
},
{
"name": "aligned-flag depth 10 common rotation covariance",
"passed": true
},
{
"name": "aligned-flag depth 10 complex core/closure dimension identity",
"passed": true
},
{
"name": "aligned-flag depth 10 maximal-contained is J-invariant",
"passed": true
},
{
"name": "aligned-flag depth 10 maximal-contained is Hermitian projector",
"passed": true
},
{
"name": "selector projector 15 unrestricted is an orthogonal projector",
"passed": true
},
{
"name": "selector projector 15 unrestricted retains charge eigenbranches",
"passed": true
},
{
"name": "selector projector 15 unrestricted matches binomial branching",
"passed": true
},
{
"name": "selector projector 16 tangent-only is an orthogonal projector",
"passed": true
},
{
"name": "selector projector 16 tangent-only retains charge eigenbranches",
"passed": true
},
{
"name": "selector projector 16 tangent-only matches binomial branching",
"passed": true
},
{
"name": "selector projector 17 normal-only is an orthogonal projector",
"passed": true
},
{
"name": "selector projector 17 normal-only retains charge eigenbranches",
"passed": true
},
{
"name": "selector projector 17 normal-only matches binomial branching",
"passed": true
},
{
"name": "selector projector 18 saturated-tangent is an orthogonal projector",
"passed": true
},
{
"name": "selector projector 18 saturated-tangent retains charge eigenbranches",
"passed": true
},
{
"name": "selector projector 18 saturated-tangent matches binomial branching",
"passed": true
},
{
"name": "selector projector 19 saturated-normal is an orthogonal projector",
"passed": true
},
{
"name": "selector projector 19 saturated-normal retains charge eigenbranches",
"passed": true
},
{
"name": "selector projector 19 saturated-normal matches binomial branching",
"passed": true
},
{
"name": "selector projector 20 balanced-occupation is an orthogonal projector",
"passed": true
},
{
"name": "selector projector 20 balanced-occupation retains charge eigenbranches",
"passed": true
},
{
"name": "selector projector 20 balanced-occupation matches binomial branching",
"passed": true
},
{
"name": "selector projector 21 fully-saturated is an orthogonal projector",
"passed": true
},
{
"name": "selector projector 21 fully-saturated retains charge eigenbranches",
"passed": true
},
{
"name": "selector projector 21 fully-saturated matches binomial branching",
"passed": true
},
{
"name": "aligned-flag depth 10 minimal-containing is J-invariant",
"passed": true
},
{
"name": "aligned-flag depth 10 minimal-containing is Hermitian projector",
"passed": true
},
{
"name": "tilted-flag depth 2 common rotation covariance",
"passed": true
},
{
"name": "tilted-flag depth 2 complex core/closure dimension identity",
"passed": true
},
{
"name": "tilted-flag depth 2 maximal-contained is J-invariant",
"passed": true
},
{
"name": "tilted-flag depth 2 maximal-contained is Hermitian projector",
"passed": true
},
{
"name": "tilted-flag depth 2 minimal-containing is J-invariant",
"passed": true
},
{
"name": "tilted-flag depth 2 minimal-containing is Hermitian projector",
"passed": true
},
{
"name": "tilted-flag depth 3 common rotation covariance",
"passed": true
},
{
"name": "tilted-flag depth 3 complex core/closure dimension identity",
"passed": true
},
{
"name": "tilted-flag depth 3 maximal-contained is J-invariant",
"passed": true
},
{
"name": "tilted-flag depth 3 maximal-contained is Hermitian projector",
"passed": true
},
{
"name": "tilted-flag depth 3 minimal-containing is J-invariant",
"passed": true
},
{
"name": "tilted-flag depth 3 minimal-containing is Hermitian projector",
"passed": true
},
{
"name": "tilted-flag depth 4 common rotation covariance",
"passed": true
},
{
"name": "tilted-flag depth 4 complex core/closure dimension identity",
"passed": true
},
{
"name": "tilted-flag depth 4 maximal-contained is J-invariant",
"passed": true
},
{
"name": "tilted-flag depth 4 maximal-contained is Hermitian projector",
"passed": true
},
{
"name": "tilted-flag depth 4 minimal-containing is J-invariant",
"passed": true
},
{
"name": "tilted-flag depth 4 minimal-containing is Hermitian projector",
"passed": true
},
{
"name": "tilted-flag depth 5 common rotation covariance",
"passed": true
},
{
"name": "tilted-flag depth 5 complex core/closure dimension identity",
"passed": true
},
{
"name": "tilted-flag depth 5 maximal-contained is J-invariant",
"passed": true
},
{
"name": "tilted-flag depth 5 maximal-contained is Hermitian projector",
"passed": true
},
{
"name": "tilted-flag depth 5 minimal-containing is J-invariant",
"passed": true
},
{
"name": "tilted-flag depth 5 minimal-containing is Hermitian projector",
"passed": true
},
{
"name": "tilted-flag depth 6 common rotation covariance",
"passed": true
},
{
"name": "tilted-flag depth 6 complex core/closure dimension identity",
"passed": true
},
{
"name": "tilted-flag depth 6 maximal-contained is J-invariant",
"passed": true
},
{
"name": "tilted-flag depth 6 maximal-contained is Hermitian projector",
"passed": true
},
{
"name": "tilted-flag depth 6 minimal-containing is J-invariant",
"passed": true
},
{
"name": "tilted-flag depth 6 minimal-containing is Hermitian projector",
"passed": true
},
{
"name": "selector projector 22 unrestricted is an orthogonal projector",
"passed": true
},
{
"name": "selector projector 22 unrestricted retains charge eigenbranches",
"passed": true
},
{
"name": "selector projector 22 unrestricted matches binomial branching",
"passed": true
},
{
"name": "selector projector 23 tangent-only is an orthogonal projector",
"passed": true
},
{
"name": "selector projector 23 tangent-only retains charge eigenbranches",
"passed": true
},
{
"name": "selector projector 23 tangent-only matches binomial branching",
"passed": true
},
{
"name": "selector projector 24 normal-only is an orthogonal projector",
"passed": true
},
{
"name": "selector projector 24 normal-only retains charge eigenbranches",
"passed": true
},
{
"name": "selector projector 24 normal-only matches binomial branching",
"passed": true
},
{
"name": "selector projector 25 saturated-tangent is an orthogonal projector",
"passed": true
},
{
"name": "selector projector 25 saturated-tangent retains charge eigenbranches",
"passed": true
},
{
"name": "selector projector 25 saturated-tangent matches binomial branching",
"passed": true
},
{
"name": "selector projector 26 saturated-normal is an orthogonal projector",
"passed": true
},
{
"name": "selector projector 26 saturated-normal retains charge eigenbranches",
"passed": true
},
{
"name": "selector projector 26 saturated-normal matches binomial branching",
"passed": true
},
{
"name": "selector projector 27 balanced-occupation is an orthogonal projector",
"passed": true
},
{
"name": "selector projector 27 balanced-occupation retains charge eigenbranches",
"passed": true
},
{
"name": "selector projector 27 balanced-occupation matches binomial branching",
"passed": true
},
{
"name": "selector projector 28 fully-saturated is an orthogonal projector",
"passed": true
},
{
"name": "selector projector 28 fully-saturated retains charge eigenbranches",
"passed": true
},
{
"name": "selector projector 28 fully-saturated matches binomial branching",
"passed": true
},
{
"name": "tilted-flag depth 10 common rotation covariance",
"passed": true
},
{
"name": "tilted-flag depth 10 complex core/closure dimension identity",
"passed": true
},
{
"name": "tilted-flag depth 10 maximal-contained is J-invariant",
"passed": true
},
{
"name": "tilted-flag depth 10 maximal-contained is Hermitian projector",
"passed": true
},
{
"name": "tilted-flag depth 10 minimal-containing is J-invariant",
"passed": true
},
{
"name": "tilted-flag depth 10 minimal-containing is Hermitian projector",
"passed": true
},
{
"name": "aligned-flag maximal-contained unrestricted cannot distinguish d3/d4",
"passed": true
},
{
"name": "aligned-flag maximal-contained tangent-only cannot distinguish d3/d4",
"passed": true
},
{
"name": "aligned-flag maximal-contained normal-only cannot distinguish d3/d4",
"passed": true
},
{
"name": "aligned-flag maximal-contained saturated-tangent cannot distinguish d3/d4",
"passed": true
},
{
"name": "aligned-flag maximal-contained saturated-normal cannot distinguish d3/d4",
"passed": true
},
{
"name": "aligned-flag maximal-contained balanced-occupation cannot distinguish d3/d4",
"passed": true
},
{
"name": "aligned-flag maximal-contained fully-saturated cannot distinguish d3/d4",
"passed": true
},
{
"name": "aligned-flag minimal-containing unrestricted cannot distinguish d3/d4",
"passed": true
},
{
"name": "aligned-flag minimal-containing tangent-only cannot distinguish d3/d4",
"passed": true
},
{
"name": "aligned-flag minimal-containing normal-only cannot distinguish d3/d4",
"passed": true
},
{
"name": "aligned-flag minimal-containing saturated-tangent cannot distinguish d3/d4",
"passed": true
},
{
"name": "aligned-flag minimal-containing saturated-normal cannot distinguish d3/d4",
"passed": true
},
{
"name": "aligned-flag minimal-containing balanced-occupation cannot distinguish d3/d4",
"passed": true
},
{
"name": "aligned-flag minimal-containing fully-saturated cannot distinguish d3/d4",
"passed": true
},
{
"name": "tilted-flag maximal-contained unrestricted cannot distinguish d3/d4",
"passed": true
},
{
"name": "tilted-flag maximal-contained tangent-only cannot distinguish d3/d4",
"passed": true
},
{
"name": "tilted-flag maximal-contained normal-only cannot distinguish d3/d4",
"passed": true
},
{
"name": "tilted-flag maximal-contained saturated-tangent cannot distinguish d3/d4",
"passed": true
},
{
"name": "tilted-flag maximal-contained saturated-normal cannot distinguish d3/d4",
"passed": true
},
{
"name": "tilted-flag maximal-contained balanced-occupation cannot distinguish d3/d4",
"passed": true
},
{
"name": "tilted-flag maximal-contained fully-saturated cannot distinguish d3/d4",
"passed": true
},
{
"name": "tilted-flag minimal-containing unrestricted cannot distinguish d3/d4",
"passed": true
},
{
"name": "tilted-flag minimal-containing tangent-only cannot distinguish d3/d4",
"passed": true
},
{
"name": "tilted-flag minimal-containing normal-only cannot distinguish d3/d4",
"passed": true
},
{
"name": "tilted-flag minimal-containing saturated-tangent cannot distinguish d3/d4",
"passed": true
},
{
"name": "tilted-flag minimal-containing saturated-normal cannot distinguish d3/d4",
"passed": true
},
{
"name": "tilted-flag minimal-containing balanced-occupation cannot distinguish d3/d4",
"passed": true
},
{
"name": "tilted-flag minimal-containing fully-saturated cannot distinguish d3/d4",
"passed": true
},
{
"name": "no tested uniform selector selects the complete assignment",
"passed": true
},
{
"name": "depth-six core rank changes under relative J alignment",
"passed": true
}
]
}