Erratum

• Cluster algebras and semi-invariant rings I. Triple flags, Proc. Lond. Math. Soc. (3) 115 (2017), no. 1.

There is a gap in the proof in Lemma 6.6 where we deduce HomJ(M', T)=0 from T is g'-semi-stable. The argument is incomplete . To complete the argument we need T to be negative reachable, then apply Theorem 2.22 of [1]. Since each Ti,j in Section 2.6 is indeed negative reachable, this would not affect the main results.

1. Tropical F-polynomials and general presentations, J. Lond. Math. Soc. (2) 107 (2023), no. 6, 2079--2120.