The large-[$*$] $U$-map isomorphism conjecture for prequantization bundles

Let $U$ denote the $U$ map on the chain complex computing embedded contact homology (ECH) of prequantization bundles, with the chain complex as in Proposition. Here $*$ denotes the relevant filtration or grading parameter.

Large-parameter $U$-map conjecture. For $*$ sufficiently large, the $U$ map is an isomorphism on the chain level of the ECH of prequantization bundles, for the chain complex of Proposition.

The statement concerns stabilization of the chain-level ECH computation for prequantization bundles. The supplied text does not indicate whether this conjecture has been proved or disproved.