Preservation of dissipativity in dimensionality reduction

The paper proves existence and uniqueness of the dissipativity-preserving projector and derives the exact formula, including the necessary orthogonality of the restriction to ker D_x H, from half-space (dissipativity) preservation plus smoothness, using extension arguments and a near-equilibrium analysis; by contrast, the model’s solution, while reproducing the correct formula, leaves a spurious degree of freedom on ker D_x H and does not justify the key half-space-to-functional step, thereby conflicting with the paper’s uniqueness result (see Theorem 5 and Lemma 3 in the paper).