s1216 — G-BULK-COLOR
receipts {'s380_arrays': 'c2ec54e078fdf22c', 'bein': '8075f28d77773d13', 'substrate': '43341215b5224b20', 's381_original': 'd0be03c3ea061389'}
  cartans {'b_min_norm_lift': [0.333333, 0.333333, 0.333333, -0.333333, -0.333333, -0.333333, -0.333333, 1.666667], 'trace_b': 1.333333333, 'uniform_part_on_16': 0.5, 'traceless_lift_miss': 0.585366, 'invisible_direction': 'e5 - e6', 'y_s377_lift': [0.333333, 0.333333, 0.333333, -0.5, -0.5, 1.0, -1.0, 0.0], 'colour_not_isolated_at_t': [-1.333333, 1.333333]}
  su8 {'dim_C_b': 25, 'expected_from_multiplicities_b': 25, 'mult_b': [4, 3, 1], 'dim_C_b_y': 15, 'mult_joint': [3, 2, 1, 1, 1]}
  split {'dim_C_b_sl8R': 25, 'colour_factor_trace_form_signature': (5, 3), 'compact_su3_trace_form_signature': (0, 8)}
  e7 {'imag_part_lt_1e-9': True, 'e7_span_residual_lt_1e-8': True, 'J0_commutator_lt_1e-8': True, 'trace_form_56_eigen_range': [-6.0, -6.0], 'bracket_homomorphism_lt_1e-8': True}
  h8 {'dim_centraliser_in_colour': 4, 'normalises_colour_lt_1e-9': True, 'D_minus_one_indices': [2, 6]}
  computed  PASS found_1a_Lambda3_map_has_one_invisible_direction_e5_minus_e6
  computed  PASS found_1b_s377_6Y8_is_an_exact_lift_of_Y16
  computed  PASS found_1c_B_minus_L_needs_a_uniform_part_outside_su8
  computed  PASS expectation_1b_B_minus_L_equals_X_plus_4Y_over_5_with_X_1_m3_5
  computed  PASS found_1d_colour_eigenspace_is_exactly_3_for_every_lift_but_two
  computed  PASS expectation_2a_colour_su3_in_su8_centraliser_of_b
  computed  PASS expectation_2b_unitary_class_3_plus_5x1_on_the_8
  computed  PASS expectation_2c_joint_centraliser_of_y_and_b_contains_su3_plus_su2
  computed  PASS expectation_3_split_colour_factor_is_sl3R_signature_5_3
  computed  PASS expectation_4_compact_colour_is_a_compact_subalgebra_of_e7_7
  computed  PASS expectation_5_h8_normalises_but_does_not_centralise_colour
  argument  ARG  charge_wall_cited_not_recomputed
  argument  ARG  reading

VERDICT B−L = su(8) Cartan + ½·1 on the 16 (uniform part outside e7(7)); colour-degenerate for every lift; C_su8(B−L) ⊇ unitary-class compact su(3) (dim 25); split form gives sl(3,ℝ) (5, 3); compact colour ⊂ e7(7) max-compact (trace form ≤ -6.00); h8 centralises only dim 4 of colour. foothold: bulk (ungauged) compact colour
RESULT_HASH 4b69afee696b47c1
s1216: 11 computed PASS-able, 2 argument, 0 failed
