  [PASS] G0 certified E7(7) 56: 133 independent generators, trace-form signature (70,63,0)  rank 133, sig (70, 63, 0)
  [PASS] G1 θ := −transpose preserves e7 (max proj. residual), is involutive and bracket-compatible; fixed set dim 63 with trace form NEGATIVE DEFINITE ⇒ Cartan involution, fixed = su(8)  res 1.9e-15, θ²−1 7.1e-15, aut 0.0e+00, dim 63, sig (0, 63, 0)
  [PASS] G2 σ := grading parity of the D_KK 3-grading (g_0 79 = C(H), g_{±4} 27+27) is an automorphism (bracket-compatible) and commutes with θ  dims 79/27/27, aut 1.0e-15, [θ,σ] 5.4e-14
  [PASS] G3 θ' := θσ is an involution; fixed set F' closes, has dim 63 and trace-form signature (27,36,0) — consistent with su*(8) ONLY among the declared foils (label: fingerprint, not identification)  θ'²−1 6.8e-14, closure 1.2e-15, dim 63, sig (27, 36, 0), matches ['su*(8) [Table 2]']
  [PASS] G4 on C(H) = g_0, θ' = θ: the θ'-fixed part of C(H) is the SAME 36-dim subspace as the θ-compact part (max principal angle ≈ 0), trace form negative definite on it (USp(8) = Hull–Julia K_4)  dims 36/36, max principal angle 2.6e-08, sig (0, 36, 0)
  [PASS] G5 θ-adapted JM triple found (E Eᵀ − Eᵀ E = H at machine residual): θH = −H; the clock K = E−F is θ-FIXED (∈ su(8), Tr K² < 0) and θ'-ODD (∉ su*(8)); E+F is θ-odd, θ'-FIXED (∈ su*(8), Tr > 0, hyperbolic); [H,K] ≠ 0, [H,E+F] ≠ 0 ⇒ under EITHER involution the fixed-set element of the triple is outside C(H)  Cayley res 1.0e-12; θK−K 0.0e+00; θP+P 0.0e+00; θ'H+H 1.7e-15; θ'K+K 1.3e-15; θ'P−P 1.1e-15; TrK² -72.000; TrP² 72.000; ‖[H,K]‖ 16.971; ‖[H,E+F]‖ 16.971
  [PASS] G6 VERDICT INVARIANCE: the compact-candidate continuum in C(H) is identical under θ and θ' ⇒ the s1159 outcome on the 56/KK carrier ((c) FREE; loss condition MET; missing object = the angle law α) is invariant under SU(8) → SU*(8)  identical subspace: True
  [PASS] V1 vacuity: no check() predicate is a literal, a literal conjunct, or a literal-vs-literal comparison (AST scan of this file)  hits []
RESULT: 8/8 gates pass
wrote s1160_results.json
