Equivariant multiplicity inequality for wobbly components

Let $\theta:\mathcal{M}\to\mathbb{A}$ be an integrable system, with virtual and genuine equivariant multiplicities $\mu_F(t)$ and $m_F(t)$ for fixed components $F$. Wobbly-component inequality conjecture. For every wobbly $F\in\operatorname{Fix}^{\mathrm{WG}}$, one has

$$\mu_F(1)<m_F,$$

and, more generally,

$$\mu_F(t)<m_F(t)\qquad\text{for all }t>1.$$

The inequality at $t=1$ is established in the surrounding discussion for wobbly components; the conjecture proposes its refinement for all $t>1$.