An equidistribution theorem for birational maps of Pk

The paper proves equidistribution for birational maps under I_+^∞ ∩ I_-^∞ = ∅ with a trapping neighborhood V, via a carefully normalized dynamical super-potential V_S, an invariant current R_∞ supported on I_-^∞, and a key estimate d^{-n} U_{T_+^p}∘Λ^n → 0 (Proposition 5.12). This bypasses the (generally unknown) local continuity of U_{T_+^p} on arbitrary U ⊂⊂ P^k \ I_+^∞ (explicitly noted by the author) and uses refined local estimates near I_-^∞ to conclude V_{S_n} → 0 and hence S_n → T_+^p (Proposition 6.4 and Theorem 1.2) . The model’s proof sketches a superficially similar super-potential argument but incorrectly assumes Hölder control for U_{T_+^p} on the required domain and applies Hölder bounds on D̃^0(V) to currents f_*^n R that are not cohomologous to zero. It also omits the essential normalization constant (the paper’s c_S via R_∞) needed to make the functorial identity precise, and it treats cohomological growth without addressing the technical restrictions (admissibility and localization) needed for the f^*, f_* calculus. These issues are precisely the obstacles the paper overcomes with Proposition 5.12 and the construction of R_∞, which the model solution does not address. Therefore, the paper’s argument is correct and complete for its stated assumptions; the model’s proof is flawed in key technical steps.