3 problems

Let $\tau$ be a chain type, and let $P^\tau\in\mathbb{Z}[z,w]$ be the polynomial associated with $\tau$ in the paper's recursive construction. Nonnegative-coefficients conjecture.…

Maximal-loss conjecture. In each projection step, one loses the maximal number of quadrics, namely the codimension of the projected variety. Equivalently, successive general-point…

Real-point conjecture. For $p \in P_{3,6} \setminus \Sigma_{3,6}$ there exist $v_1,\ldots,v_9 \in \mathbb{R}^3$ yielding a separating extreme ray for $p$. Analogously, for…