── building Jordan structure constants (27x27)   OCTONION REAL FORM = SPLIT O_s ──
── validating the Jordan layer ──
   [PASS] jordan_product_matches_direct_construction
   [PASS] N_of_diagonal_is_product
   [PASS] N_of_Jvac_is_one
   [PASS] sharp_of_diagonal_is_cofactor
   [PASS] sharp_Jvac_is_inverse
   [PASS] sharp_sharp_equals_N_times_x
   [PASS] N_is_cubic_homogeneous

── FTS layer: the boundary restriction theorem ──
   [PASS] I4_boundary_restriction_is_-4*beta*N(X)
   [PASS] I4_is_quartic

── the normal expansion the returns claimed ──
   [PASS] expansion_I4(1,t*beta,X,t*Y)_matches_returns

── Hessian of I4 at the golden boundary point ──
   [PASS] I4_at_z0_is_-4
   ||dI4(z0)|| = 8.944272   (alpha-component = -4.000000)
   [PASS] dI4_at_z0_is_NONZERO_golden_point_not_stationary
   [PASS] dI4_alpha_component_is_-4N(Jvac)
   full Hessian  rank=56  signature=(29,27,0)
   [PASS] full_Hessian_rank_56
   [PASS] full_Hessian_signature_29_27
   normal 28-block  rank=28  signature=(14,14)
   [PASS] normal_Hessian_rank_28
   [PASS] normal_Hessian_signature_14_14
   boundary 28-block signature=(15,13)
   [PASS] boundary_Hessian_signature_15_13
   [PASS] blocks_do_not_mix
   [PASS] block_signatures_sum_to_full

── symplectic diagnostic  A = Omega^-1 Hess ──
   [PASS] Omega_antisymmetric
   [PASS] Omega_nondegenerate
   eigenvalues of A: +2 x0  -2 x0  +4 x26  -4 x26
   +/-sqrt(32+16sqrt7) = +/-8.621602 x2   +/-i*sqrt(16sqrt7-32) = +/-3.214346i x2
   [FAIL] charpoly_factor_(l^2-4)^24
   [FAIL] charpoly_factor_(l^2-16)^2
   [PASS] charpoly_factor_l^4-64l^2-768
   [PASS] real_hyperbolic_mode_count_54

── singlet/diagonal 4-block of the normal form ──
   char poly (monic): [   1.  -10. -128.  -96.  256.]
   det = 256.000000   roots = [-6.49584206 -2.11896876  1.05942334 17.55538748]
   [PASS] singlet_block_two_pos_two_neg

======================================================================
s973 HOUSE FTS BUILD:  25/27 gates
FAILED: ['charpoly_factor_(l^2-4)^24', 'charpoly_factor_(l^2-16)^2']
======================================================================
