  [PASS] A1a unital: Ξ(e₁)+Ξ(e₂)+Ξ(e₃) = I₂ identically  
  [PASS] A1b reversal-covariant: Ξ(e₃) = ZΞ(e₁)Z, Ξ(e₂) = ZΞ(e₂)Z identically  
  [PASS] A1c freedom chain 12 → 6 (reversal) → 4 (unital) → 3 (odd image on Q-line)  (12, 6, 4, 3)
  [PASS] A2a eig Ξ(e₁) = a ± √(c²+μ²/4); eig Ξ(e₂) = 1−2a ± 2c (positivity ⇔ a ≥ √(c²+μ²/4), 1−2a ≥ 2|c|)  ([a - sqrt(4*c**2 + mu**2)/2, a + sqrt(4*c**2 + mu**2)/2], [-2*a - 2*c + 1, -2*a + 2*c + 1])
  [PASS] A2b |μ| ≤ 1 — ANALYTIC-WITH-CONTROLS: symbolic certificate (radicand gap = c² ≥ 0; a ≤ ½ from e₂) + endpoint μ=1 ⇒ a=½, c=0 PSD + μ=1.01 infeasible  
  [PASS] A3a ‖Ξ(D_φ)‖_HS / ‖D_φ‖_HS = |μ| exactly (‖μQ‖_HS = |μ|√2, ‖e₁−e₃‖_HS = √2)  
  [PASS] A3b (W_{λ,τ}∘Ξ_μ)(D_φ) = λμ τ H_sgn exactly ⇒ the tested amplitude is λμ, not λ  
  [PASS] A4 countermodels |λμ| ∈ {0.125, 0.5, 1, √2} realized by UCP pairs (|λ|≤√2, |μ|≤1)  
  [PASS] B1a order-3 permutations of 5 = 20  20
  [PASS] B1b commuting with S₅ = 12; fixing P_abs ∧ commuting = 4; order-3 ∧ both = 0  (12, 4, 0)
  [PASS] B1c exact unitary descents through C_* = 2 (identity + one reflection)  [(0, 1, 2, 3, 4), (0, 1, 4, 3, 2)]
  [PASS] B1d min ‖C_*P − UC_*‖ over order-3 P = √3/2 (basis-free residual floor)  0.866025403784
  [PASS] C1 M₅ lift system for a generic Ξ: 75 unknowns, constraint rank 62, affine dimension 13  rank=62, sv gap 1.17e+00/7.31e-16
s1150: 13/13 checks passed; verdict PASS_S1150_ALL
