The smooth birational model conjecture for rational maps and entropy

Let $Y$ be a smooth projective variety and $f:Y\dashrightarrow Y$ be a rational dominating map. A smooth birational model is a smooth projective variety $\hat Y$ together with a birational map $\iota:Y\dashrightarrow\hat Y$ such that the lifting $\hat f:\hat Y\dashrightarrow\hat Y$ is defined. Smooth birational model conjecture. There exists a smooth projective variety $\hat Y$ and a birational map $\iota:Y\dashrightarrow\hat Y$ such that the lifting $\hat f:\hat Y\dashrightarrow\hat Y$ satisfies the entropy equality stated in the source. This conjecture seeks a smooth birational model on which the entropy of the rational map is related by the cited equality to the corresponding volume-growth quantity; the supplied excerpt does not include that equality or evidence resolving the conjecture.