Uniqueness conjecture for energy ground states on the \b1-metric graph

Let $p\in(2,6)$ and let $\nu>0$ be a mass. An energy ground state is a positive solution of the NLS variational problem on the $\mathcal{T}$-metric graph that minimizes the energy among functions of mass $\nu$. Uniqueness conjecture. For every $p\in(2,6)$, there exists a unique energy ground state for each mass $\nu>0$. The paper proves uniqueness of action ground states and recalls that uniqueness of energy ground states is known up to a countable set of masses; numerical simulations support uniqueness for every mass, which remains open.