E7(7) embedding-tensor layer  (house v2, S72)  -- V7/V8/V10
====================================================================
V7a LINEAR (Theta_SO8 in 912):  ||T*Th - 1/2 Th|| / ||Th|| = 1.196e-16   -> PASS (in 912)
V7b QC  (SO(8) X_M close):       max closure residual = 2.270e-16   -> PASS (QC=0)
V8  CLOSED ALGEBRA:              dim = 28  trace-form sig = (0+,28-)  -> so(8) [28-dim, COMPACT, D4 rank4]
V7c NEG ctrl (generic Theta):    linear-defect = 5.809e-01 (>>0, not in 912);  closure = 9.733e-01 (>>0)  -> PASS (correctly fails)
V7d in-912-but-QC-fails:         linear-defect = 2.192e-16 (in 912);  closure = 9.844e-01 (>>0)
    => QC is a GENUINE constraint beyond 912-membership  -> PASS
V10 COSET rho_70 = trace-form POSITIVE eigenspace:  dim = 70  (su(8) compact = 63)  -> PASS (70 = E7/SU(8) coset)
    70 = 54 + 16 split STAGED: needs the suite's E6/F4 Jordan frame
    (which 54 = 26+27+1 subset 70) -> P_54/P_16 pending D751 convention pin.
====================================================================
CERTIFIED V7/V8 + V10 coset machinery.
V7 SO(8) regression PASS: Theta_SO8 in 912 (linear), X_M close to so(8) (QC=0),
generic fails both, generic-in-912 fails QC. STAGED for D751: the EXACT de Wit-
Nicolai Theta normalization cross-check, the E6/F4-54 frame, and the gate ruling.
