Some interesting birational morphisms of smooth affine quadric 3-folds

The paper proves positivity and log-concavity for Lefschetz numbers, and log-concavity for the degree sequences on cohomology, using regularization of positive currents via the automorphism group of an odd quadric and an inequality dj(g1∘g2) ≤ dj(g1)dj(g2). The candidate solution gives a clean, purely algebraic correspondence/Künneth-based proof of positivity and L(g^{n+n'}) ≤ L(g^n)L(g^{n'}) that matches the paper’s statements. One caveat: the model’s Step 3 invokes functoriality of the pullback on cohomology for meromorphic maps, which can fail without stability; however, the claimed log-concavity for ||(g^n)^*|| still follows directly from the established inequality for dj(g^n) and the fact H^{2j}(X) is one-dimensional for odd quadrics. With that minor correction, both are correct, using different methods.