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"rotation_Casimir": 40, "multiplicity": 5148 }, { "blade_degree": 10, "rotation_Casimir": 30, "multiplicity": 1144 }, { "blade_degree": 12, "rotation_Casimir": 12, "multiplicity": 52 } ], "scope": "Full paired Dirac carrier without choosing a minimal rotation irrep" }, { "spatial_depth": 14, "maintained_paired_carrier_rank": 128, "lowest_positive_rotation_Casimir": 13, "lowest_positive_channel_rank": 28, "components": [ { "blade_degree": 0, "rotation_Casimir": 0, "multiplicity": 1 }, { "blade_degree": 1, "rotation_Casimir": 13, "multiplicity": 14 }, { "blade_degree": 2, "rotation_Casimir": 24, "multiplicity": 91 }, { "blade_degree": 3, "rotation_Casimir": 33, "multiplicity": 364 }, { "blade_degree": 4, "rotation_Casimir": 40, "multiplicity": 1001 }, { "blade_degree": 5, "rotation_Casimir": 45, "multiplicity": 2002 }, { "blade_degree": 6, "rotation_Casimir": 48, "multiplicity": 3003 }, { "blade_degree": 7, "rotation_Casimir": 49, "multiplicity": 3432 }, { "blade_degree": 8, "rotation_Casimir": 48, "multiplicity": 3003 }, { "blade_degree": 9, "rotation_Casimir": 45, "multiplicity": 2002 }, { "blade_degree": 10, "rotation_Casimir": 40, "multiplicity": 1001 }, { "blade_degree": 11, "rotation_Casimir": 33, "multiplicity": 364 }, { "blade_degree": 12, "rotation_Casimir": 24, "multiplicity": 91 }, { "blade_degree": 13, "rotation_Casimir": 13, "multiplicity": 14 }, { "blade_degree": 14, "rotation_Casimir": 0, "multiplicity": 1 } ], "scope": "Full paired Dirac carrier without choosing a minimal rotation irrep" }, { "spatial_depth": 15, "maintained_paired_carrier_rank": 256, "lowest_positive_rotation_Casimir": 14, "lowest_positive_channel_rank": 60, "components": [ { "blade_degree": 0, "rotation_Casimir": 0, "multiplicity": 4 }, { "blade_degree": 2, "rotation_Casimir": 26, "multiplicity": 420 }, { "blade_degree": 4, "rotation_Casimir": 44, "multiplicity": 5460 }, { "blade_degree": 6, "rotation_Casimir": 54, "multiplicity": 20020 }, { "blade_degree": 8, "rotation_Casimir": 56, "multiplicity": 25740 }, { "blade_degree": 10, "rotation_Casimir": 50, "multiplicity": 12012 }, { "blade_degree": 12, "rotation_Casimir": 36, "multiplicity": 1820 }, { "blade_degree": 14, "rotation_Casimir": 14, "multiplicity": 60 } ], "scope": "Full paired Dirac carrier without choosing a minimal rotation irrep" }, { "spatial_depth": 16, "maintained_paired_carrier_rank": 256, "lowest_positive_rotation_Casimir": 15, "lowest_positive_channel_rank": 32, "components": [ { "blade_degree": 0, "rotation_Casimir": 0, "multiplicity": 1 }, { "blade_degree": 1, "rotation_Casimir": 15, "multiplicity": 16 }, { "blade_degree": 2, "rotation_Casimir": 28, "multiplicity": 120 }, { "blade_degree": 3, "rotation_Casimir": 39, "multiplicity": 560 }, { "blade_degree": 4, "rotation_Casimir": 48, "multiplicity": 1820 }, { "blade_degree": 5, "rotation_Casimir": 55, "multiplicity": 4368 }, { "blade_degree": 6, "rotation_Casimir": 60, "multiplicity": 8008 }, { "blade_degree": 7, "rotation_Casimir": 63, "multiplicity": 11440 }, { "blade_degree": 8, "rotation_Casimir": 64, "multiplicity": 12870 }, { "blade_degree": 9, "rotation_Casimir": 63, "multiplicity": 11440 }, { "blade_degree": 10, "rotation_Casimir": 60, "multiplicity": 8008 }, { "blade_degree": 11, "rotation_Casimir": 55, "multiplicity": 4368 }, { "blade_degree": 12, "rotation_Casimir": 48, "multiplicity": 1820 }, { "blade_degree": 13, "rotation_Casimir": 39, "multiplicity": 560 }, { "blade_degree": 14, "rotation_Casimir": 28, "multiplicity": 120 }, { "blade_degree": 15, "rotation_Casimir": 15, "multiplicity": 16 }, { "blade_degree": 16, "rotation_Casimir": 0, "multiplicity": 1 } ], "scope": "Full paired Dirac carrier without choosing a minimal rotation irrep" } ], "neutrality_controls": { "unpolarized_triplet_mean_generators": "0", "unpolarized_triplet_Casimir": "4/3", "equal_component_pure_triplet_mean_square": "1/3", "meson_total_generators": "0", "baryon_total_generators": "0", "three_triplets_Casimir_spectrum": { "0": 1, "3": 16, "6": 10 }, "zero_triality_decuplet_Casimir": "6" }, "three_four_restriction": { "both_chiral_restrictions_rank": 3, "observer_actions_equal": true, "extra_rotation_actions_opposite": true, "rotation_commutant_complex_dimension": 1, "nonzero_color_rotation_commutators": 20, "eight_endomorphisms_rotation_Casimir": { "2": 3, "6": 5 } }, "relative_frame_completion": { "mixed_generator_checks": 24, "relative_amplitudes_are_rotation_invariant": true, "color_Casimir_preserved": "4/3", "separate_spin_half_and_color_actions_commute": true, "scope": "Requires a geometric moving frame and a justified equivalent-mode sector" }, "projected_mode_curvature": { "complex_variations_u3_span": 9, "traceless_complex_variations_su3_span": 8, "real_variations_so3_span": 3, "two_dimensional_pullback_holonomy_Lie_rank": 8, "same_pullback_extends_to_depths": [ 2, 16 ], "SO3_invariant_quartic_SU3_counterexample": [ 4, 0 ], "scope": "Availability if an actual geometric rank-three mode projector is derived" }, "sources": { "experiments/color-depth-algebra-checks.py": "3ab5b9bca1a6ec4a3f16dcc868396632a09f1a1981f3575098619ec68072498c" } }