s1309 — the ε² exclusion, proved
  Q1_grading                     {"D56 on 56": {"-6": 1, "-2": 27, "2": 27, "6": 1}, "e7 levels −4, 0, 4": [27, 79, 27], "e7₄ abelian, e7₋₄ abelian": ["<1e-12", "<1e-12"], "912 by weight 6, 2, −2, −6": [78, 378, 378, 78]}
  Q2_level_bookkeeping           {"basis tensors checked": 456, "max forbidden level component": "<1e-12", "levels seen per index weight h_M": {"-6": [], "-2": [4], "2": [0, 4], "6": [-4, 0]}, "number of indices M carrying a level −4 part": 1}
  Q3_hX_simple                   {"gauge algebra of X: dim, derived, Killing (+,−,0)": [28, 28, [12, 16, 0]], "commutant of ad (two generic elements)": 1}
  Q4_commutant_multiplicities    {"commutant of h_X in gl(56): dim, max |[c, g]| on all generators": [4, "<1e-12"], "eigenvalue multiplicities of 4 random commutant elements": [[28, 28], [28, 28], [28, 28], [28, 28]], "D56 multiplicities": [1, 1, 27, 27]}
  Q5_controls                    {"X₊ (the class member at λ = 0): gauge algebra dim, derived, Killing": [28, 27, [0, 16, 12]], "generic class tensor: fixed vectors": 0}
  receipt   PASS filed_d1414_house_frames_npz
  receipt   PASS s1288_results_machinery_grading_theta_tensor_P912
  computed  PASS Q1_D56_grades_the_56_as_1_27_27_1_and_e7_as_27_79_27_with_abelian_extreme_levels
  computed  PASS Q2_over_the_whole_class_the_generators_have_only_the_allowed_levels_and_only_the_singlet_index_carries_level_minus4
  computed  PASS Q3_the_gauge_algebra_of_X_is_simple_so62
  computed  PASS Q4_every_commutant_element_has_multiplicities_divisible_by_28_while_D56_has_1_27_27_1_so_no_D56_conjugate_commutes_with_h_X
  computed  PASS Q5_CONTROLS_the_class_member_on_the_line_has_a_non_semisimple_algebra_and_a_generic_class_tensor_fixes_no_vector
  argument  ARG  theorem
  argument  ARG  scope
VERDICT: no E7(7) frame puts X in the twist + 351 class (D56 weights 6, 2 only): such a frame would put the simple so(6,2) gauge algebra in the D56 parabolic, hence commuting with a conjugate of D56, but its commutant has eigenvalue multiplicities divisible by 28. The S388 sampled exclusion is now a proof (three standard theorems cited).
RESULT_HASH 127161db2f9706d1
s1309: 5 computed, 2 receipt, 2 argument, 0 failed
