Wojtkowski's falling particle conjecture

Let $n\ge 2$ point particles of masses $m_1\ge m_2\ge\dots\ge m_n>0$ move on the vertical half line $q\ge 0$, with positions $0\le q_1\le q_2\le\dots\le q_n$, under constant gravitational acceleration $a=-1$. They collide elastically with one another and with the hard floor $q=0$, and the total energy

$$H=\sum_{i=1}^n \left(m_iq_i+\frac{1}{2}m_iv_i^2\right)$$

is fixed at $H=1$. Let $\left(\mathbf{M},\{\psi^t\},\mu\right)$ be the resulting Hamiltonian flow with collisions, equipped with Liouville measure $\mu$. Wojtkowski's conjecture. If $m_1\ge m_2\ge\dots\ge m_n>0$ and $m_1\ne m_n$, then all but one characteristic (Lyapunov) exponents of the flow $\left(\mathbf{M},\{\psi^t\},\mu\right)$ are nonzero. Furthermore, the system is ergodic. The conjecture concerns the hyperbolicity and ergodicity of the falling-particle system. This paper is titled as a proof of the conjecture, but the supplied context does not include the paper's proof or a resolution statement, so its database status is left open pending verification.