Asymptotic su(2)-Isotropy of the Effective Quadratic Form and the Identification AH = 2

Papers Q7-Q9 of the Cosmochrony spectral geometry programme establish that the effective operator L₄₅₅ on R_ Heis₃ (R) has a principal symbol ₂ (L₄₅₅) |₇_₄₅₅ = AH (kX²+kY²) + AZ kZ² with AH, AZ > 0 and AZ = 2 = Cₒₔ (₂) (Casimir eigenvalue on Sym² (V_), Q8). The identification AH = 2 would complete the effective metric to g^ = diag (-A_, 2, 2, 2) and establish the isotropic Lorentzian geometry of the Cosmochrony framework. The present paper proves AH 2 from two structural inputs: (i) the asymptotic character-independence of the O-series spectral observables (c (n) _* (n) uniformly in c as q, established structurally from BI parity and confirmed numerically by the O25 campaign; and (ii) the uniqueness of the su (2) -invariant quadratic form on Sym² (V_) (Q7 Lemma 4. 3). The core argument is that character-independence forces the effective form on H₄₅₅ to be scalar under the su (2) action, and the unique such form is the Casimir with value 2. The result is established conditionally on the O-series universality (structurally supported, numerically confirmed for q 151) and the bridge non-obstruction hypothesis of Q7-Q9.