s1152 — face-2 registered-datum stabilizer census
  [PASS] C0 unit: L_1 = I on the house product  ‖L_1−I‖=0.0e+00
  [PASS] C1 house product ⇒ s478 cubic N (convention lock), 6 random points  max|ΔN|=5.3e-15
  [PASS] C2 N(J_vac)=1 and N(1)=1: J_vac and 1 lie on the SAME exact-E6 level set  N(J_vac)=1.000000000000
  [PASS] E1a dim Der(J) = 52  dim=52, sv gap 1.70e+00/5.15e-15
  [PASS] E1b dim str_0(J) = 78 (= e6(6))  dim=78
  [PASS] E1c every X ∈ str_0 is N-preserving: max|∇N(v)·Xv| over 12 samples ≈ 0  2.4e-14
  [PASS] E1d common fixed-vector nullity of e6 on the 27 = 0 (face 2 DEFINITIONAL at exact E6; s1148 B3 re-derived)  smallest sv 1.21e+00
  [PASS] D0 −Hess ln N at 1 = Tr(u∘v) EXACTLY (the trace form IS the Koecher metric at the unit)  ‖Δ‖=0.0e+00
  [PASS] D1 sig(T)=(15,12,0), sig(H_gold)=(15,12,0) [A1263/s478 reproduced], sig(G_phys)=(27,0,0) [s494 G3]  (15, 12, 0) (15, 12, 0) (27, 0, 0)
  [PASS] E3a s494 G_raw is NOT proportional to the trace form: T = G_raw·diag(1,1,1 | 2×24) (factor 2 dropped on the octonion blocks)  diag ratio set=[np.float64(1.0), np.float64(2.0)]
  --- census ---
   T_trace        stab dim  52  Fix dim  1  unit: UNIQUE real t=1.732051 · x0 (N(t x0)=1.000000000)   [POINTED (defined at 1) — positive control]
   H_golden       stab dim  52  Fix dim  1  unit: UNIQUE real t=2.000000 · x0 (N(t x0)=1.000000000)   [POINTED (evaluated AT J_vac; A1263/s478)]
   G_raw_s494     stab dim  28  Fix dim  3  unit: solution set {N=1} ∩ Fix has dimension 2 (a 3-dim Fix) — NOT selected   [POINTED coords (s494 :27-31)]
   G_phys_s494    stab dim  12  Fix dim  3  unit: solution set {N=1} ∩ Fix has dimension 2 (a 3-dim Fix) — NOT selected   [POINTED coords (s494 :42)]
   Theta_phys     stab dim  38  Fix dim  0  unit: EMPTY (no fixed vector)   [POINTED coords (s494 :35-38)]
   vec_1          stab dim  52  Fix dim  1  unit: UNIQUE real t=1.732051 · x0 (N(t x0)=1.000000000)   [POINTED (is the unit)]
   vec_Jvac       stab dim  52  Fix dim  1  unit: UNIQUE real t=2.000000 · x0 (N(t x0)=1.000000000)   [POINTED (is J_vac)]
   pair_1_Jvac    stab dim  28  Fix dim  3  unit: solution set {N=1} ∩ Fix has dimension 2 (a 3-dim Fix) — NOT selected   [POINTED pair — the frame datum]
  [PASS] E2a T: stab dim 52 = f4, Fix nullity 1, Fix = span(1)  (52,1)
  [PASS] E2b H_golden: stab dim 52, Fix nullity 1, Fix = span(J_vac) ⇒ the golden Hessian selects ONLY the point it was evaluated at (circular)  (52,1)
  [PASS] E2c unit equation on Fix(T) and Fix(H_golden): UNIQUE real solution each  
  [PASS] E3b G_raw(s494): stabilizer strictly smaller than f4 and Fix nullity ≥ 3 ⇒ NOT a unit selector  (28,3) expected ~(28,3)
  [PASS] E4a G_phys(s494): Fix nullity ≥ 3 ⇒ NOT a unit selector  (12,3) expected ~(≤36,3)
  [PASS] E4b Theta_phys commutant selects NO unit (first-run finding: dim 38, Fix nullity 0 — guess ~3 FALSIFIED; EMPTY a fortiori)  (38,0)
  [PASS] E4c Theta_phys e6-commutant dim ≠ 36: s494's 'compact real structure' is NOT the Cartan involution of e6(6) (usp(8) would be 36); 38 is dimension-consistent with sl(6,R)⊕sl(2,R) — a dimension hint, NOT an identification  dim 38
  [PASS] E4d G_phys(s494) e6-stabilizer is only 12-dim (guess ~≤36 met, but far smaller): the S206 kinetic metric is a coordinate object, not an E6-natural one  dim 12
  [PASS] E5 pair (1,J_vac) stabilizer = 28 = spin(8): the Peirce frame is F4 ∩ F4'  (28,3)
  [PASS] E6a P(J_vac^{1/2}) 1 = J_vac and P(J_vac^{-1/2}) J_vac = 1  
  [PASS] E6b g = P(J_vac^{-1/2}) is N-preserving (N-multiplier N(J_vac^{-1/2})² = 1) ⇒ g ∈ E6(6)  N(J_vac^-0.5)²=1.000000000000
  [PASS] E6c INTERTWINER: H_golden = gᵀ T g EXACTLY (E6-congruent via an exhibited g; NOT equal in the registered frame)  ‖H−gᵀTg‖=5.1e-15, ‖H−T‖=4.460
  [PASS] E6d pair invariant spec(T⁻¹H_golden) is golden-valued (φ^k) and ≠ {1}: the 'golden' content is the RELATIVE datum (1, J_vac), not E6 data  exponents k: [-2, -1, 0, 1, 2] mult [1, 8, 9, 8, 1]
s1152: 23/23 checks passed; verdict PASS_S1152_FACE2_NO_REGISTERED_INTRINSIC_SELECTOR_GOLDEN_HESSIAN_CIRCULAR_S494_G2_REPAIRED
