Bilinear realization from i/o data with NN

The paper derives the same lifted regression Y = U W with u_j defined recursively (its Eq. (4) and Def. 3), notes the underdetermined nature for a single run, and resolves uniqueness by stacking d = 2^k−1 experiments to make rank(Û)=2^k−1 (its Eq. (5)); it then constructs the bilinear Hankel Hb = OR and uses the SVD with the S_A/S_N partitions to identify Ar, Nr, Br, Cr via the standard formulas (Eqs. (6)–(10)) . The candidate solution mirrors these steps, adds an explicit induction proof for the lifted identity and a brief consistency/minimality argument for the SVD factorization. No substantive logical conflict was found; the approaches are essentially the same, with the model providing more proof details.