COUNTING INTEGRAL POINTS ON SOME HOMOGENEOUS VARIETIES WITH LARGE REDUCTIVE STABILIZERS

The paper proves that, under Conditions 1.1 and 1.2, the limit |Γ·v0 ∩ B_R|/μ_{G/H}(B_R) exists and equals a positive constant c, but it explicitly states that c is not given in closed form and may reflect focusing via intermediate subgroups (Theorem 1.3 and the remarks following it) . By contrast, the model’s solution incorrectly invokes Haar equidistribution of translates of μ_H (ignoring the focusing phenomena that the paper handles via Eskin–Mozes–Shah compactness and classification) and further asserts an explicit Siegel-type constant c=vol_H((Γ∩H)\H)^{-1}, which contradicts the paper’s own caveat that c is not explicitly identified . The model also leans on a two-sided wavefront/well-roundedness and a right-H-invariance statement on G/Γ that are not valid as stated, whereas the paper reduces counting to an averaged equidistribution statement and uses variety-theoretic methods (CLT10) to control the height balls and boundary, avoiding those pitfalls .