A DISPROOF OF Lα POLYNOMIALS RUDIN CONJECTURE, 2 ≤ α < 4.

The paper proves that for α = 4 − ε (ε small), sup_x ∫_0^1 |∑_{n=1}^N e(n^2 t + n x)|^α dt ≥ C_α N^2 (Theorem 1.3), and from this deduces that the quadratic Rudin L^α-polynomial conjecture fails (Theorem 1.2). The model’s solution reproduces the same reduction-to-contradiction argument by testing the conjectured inequality on coefficients a_n = e(nx), relying on the same lower bound at α = 4 − ε. One mismatch is that the model overstates the scope of the lower bound (it claims it for every α ∈ (2,4)), whereas the paper only proves the sup_x bound at α = 4 − ε and gives a separate two-variable lower bound for general α > 2. Nevertheless, when specialized to α = 4 − ε, the model’s argument aligns with the paper and is correct. See the statement of Theorem 1.3 and the contradiction argument in the paper’s Section 2, which match the model’s steps precisely .