s1153 — A1561 house verification (disjoint path)
  [PASS] C0 dim e6 = 78, common Fix on the 27 = 0  (78, 0)
  [PASS] C1 T is diagonal in the s494 coordinates with sign pattern (+3 | (+4,−4)×3) = Γ; Γ = s494 G_raw exactly  sig(T)=(15, 12, 0)
  [PASS] E1a Stab_e6(1, J_vac): dim 28, closed under bracket  dim=28, closure 1.5e-15
  [PASS] E1b intrinsic Killing signature of the pair stabilizer = (16,12,0) ⇒ so(4,4) (split), NOT so(8) compact (0,28,0) — lane D01 CONFIRMED, house 'spin(8)' was the complex type  sig=(16, 12, 0)
  [PASS] E2a h_Γ = TΓ is positive definite (27,0,0)  sig=(27, 0, 0)
  [PASS] E2b Stab_e6(h_Γ): dim 36, Killing signature (0,36,0) (compact ⇒ usp(8)), Fix 0, closed  dim=36, sig=(0, 36, 0), Fix=0
  [PASS] E3a Z_e6(Γ): dim 38, Fix 0, closed, perfect ([g,g] = g)  dim=38, Fix=0, dim[g,g]=38
  [PASS] E3b Killing signature of Z_e6(Γ) = (14,24,0) = (14,21)⊕(0,3): consistent with su*(6)⊕su(2) — lane D08 CONFIRMED; s1152 E4c conflated centralizer (38) with the Cartan fixed algebra (36)  sig=(14, 24, 0)
  [PASS] E3c Z_e6(Γ) splits into commuting ideals of dimensions {35, 3} (Casimir of the restricted 27-trace form has exactly two eigenvalues, multiplicities 35 and 3)  blocks={0.666667: 3, 2.0: 35}
  [PASS] E4a N(diag(ρ,1,1/ρ)) = 1 and spec(T⁻¹H_ρ) = ρ^k, k∈{−2,−1,0,1,2}, multiplicities (1,8,9,8,1) at ρ = 2 — the pattern is generic reciprocal anatomy; only ρ = φ is golden (lane P1 CONFIRMED)  mult={np.int64(-2): 1, np.int64(-1): 8, np.int64(0): 9, np.int64(1): 8, np.int64(2): 1}
  [PASS] E4b T⁻¹H_ρ is DIAGONAL in the Peirce coordinates and the eigen-supports are f1 / P12 / f2⊕P31 / P23 / f3 for k = −2,−1,0,+1,+2 (lane's table, with P13 ≡ P31)  {np.int64(-2): ['f1'], np.int64(-1): ['P12'], np.int64(0): ['f2', 'P31'], np.int64(1): ['P23'], np.int64(2): ['f3']}
  [PASS] E5 G_raw(s494)·Γ = I_27 exactly (s494's G_phys IS the identity matrix in Peirce coordinates) and Stab_e6(I_27) = 12 (not 36): the corrected positive form is TΓ with the 36-dim usp(8) stabilizer (lane P2 CONFIRMED)  dim Stab(I_27)=12
s1153: 12/12 checks passed; verdict PASS_S1153_A1561_LANE_CLAIMS_CONFIRMED_DISJOINT_PATH
