Exact degree of regularity of the quadratic equation in Corollary 4.1

Determine the exact degree of regularity of the nonlinear equation L_n = ∑_{i=1}^{n−1} 2^{2i}X_i^{2i} − X_n^{2n} − 2^{2n}X_{n+1}X_{n+2} = 0 for even n, for which the paper establishes only the bounds n−1 ≤ degree(L_n) ≤ n.

Background

Corollary 4.1 constructs a nonlinear equation whose degree of regularity is bounded between n−1 and n when n is even. The paper proves that the equation is (n−1)-regular and, under the stated parity condition, is not (n+1)-regular, but does not determine whether it is n-regular. Consequently, its exact degree of regularity remains unresolved.