s1277 — the 5D origin test
  Q1_gradings          {"D56": {"ad spectrum": {"-4.0": 27, "0.0": 79, "4.0": 27}, "Levi": [79, 78, [42, 36, 1]], "derived Levi dim": 78, "H on the 56": {"-6.0": 1, "-2.0": 27, "2.0": 27, "6.0": 1}, "27 invariant under the derived Levi": "<1e-12"}, "D_sol": {"ad spectrum": {"-4.0": 27, "0.0": 79, "4.0": 27}, "Levi": [79, 78, [42, 36, 1]], "derived Levi dim": 78, "H on the 56": {"-6.0": 1, "-2.0": 27, "2.0": 27, "6.0": 1}, "27 invariant under the derived Levi": "<1e-12"}, "so(5,5) ⊂ e6(6) of D56 (residual)": "<1e-10"}
  Q2_css_control       {"CSS D56-grade norm²": {"-4.0": 12.0, "0.0": 1.0, "4.0": 0.0}}
  Q3_both_sides        {"registered X": {"D56": [6.0, 6.0], "D_sol": [6.0, 6.0]}, "(6,2) odd 12 +π/4": {"D56": [6.0, 6.0], "D_sol": [6.0, 6.0]}, "(6,2) odd 12 −π/4": {"D56": [6.0, 6.0], "D_sol": [6.0, 6.0]}, "(8,0) +π/4": {"D56": [6.0, 6.0], "D_sol": [6.0, 6.0]}, "(8,0) −π/4": {"D56": [6.0, 6.0], "D_sol": [6.0, 6.0]}, "(4,4) +π/4": {"D56": [6.0, 6.0], "D_sol": [6.0, 6.0]}, "(4,4) −π/4": {"D56": [6.0, 6.0], "D_sol": [6.0, 6.0]}}
  Q4_d4_branching      {"the 10: signature of its invariant form": [5, 5], "D4 (dim, derived, Tr56 inertia)": [28, 28, [16, 12, 0]], "D4 ⊂ e6(6) (residual)": "<1e-10", "Casimir on the 27 (value: count)": {"0.0": 3, "0.583333": 24}, "commutant dimension on the 27": 12}
  Q5_spinor_reality    {"(8,0)": ["real", "real"], "(7,1)": ["complex", "complex"], "(6,2)": ["quaternionic", "quaternionic"], "(5,3)": ["complex", "complex"], "(4,4)": ["real", "real"]}
  receipt   PASS filed_d1414_house_frames_npz
  receipt   PASS filed_chatgpt_d1414_maps_npz
  computed  PASS Q1_both_5d_gradings_cut_e7_as_27_79_27_with_levi_e66_R_and_the_56_as_1_27_27_1
  computed  PASS Q2_positive_control_the_lanes_5d_css_algebra_lies_on_one_side_of_the_D56_grading
  computed  PASS Q3_the_registered_gauge_algebra_and_all_census_members_meet_both_sides_of_both_5d_gradings
  computed  PASS Q4_an_exhibited_so44_inside_e66_cuts_the_real_27_into_three_distinct_real_eights_and_three_singlets
  computed  PASS Q5_the_weyl_spinors_of_so62_are_quaternionic_so8_so44_real_so71_so53_complex
  argument  ARG  the_obstruction
  argument  ARG  combined_with_s1271
  argument  ARG  scope
VERDICT: both 5D gradings have Levi e6(6) ⊕ ℝ; the CSS control sits on one side, the registered so(6,2) on both; any D4 in e6(6) cuts the real 27 into three distinct real 8s + 3 singlets (computed for the exhibited so(4,4)), and so(6,2)'s spinors are quaternionic — so so(6,2) ⊄ e6(6): no circle origin in maximal 5D supergravity (so(8) excluded too, so(4,4) not). With s1271: no torus or circle origin in 5D or 6D. Algebraic; Dynkin's D4 ⊂ E6 uniqueness cited.
RESULT_HASH ae5fbb2d0b871977
s1277: 5 computed, 2 receipt, 3 argument, 0 failed
