9 problems

Let $\mathcal{M}(n)(\beta)$ be a truncated moment matrix with rank $r$ and variety cardinality $v$, in the cases under consideration. A representing measure for…

Quadratic-rank conjecture. The linear system suffices for tensor decompositions of rank up to $O(n^2)$, with a leading coefficient improved over existing results.

Determinantal radical conjecture. These relations generate the radical of the variety defined by the $|Y|\times |Y|$ minors of $\mathbf{A}$.

Very efficient format conjecture. 1. The format $(n,R_c(n))$ is very efficient if $c$ is such that $|E_1|\geq |Y|$. 2. The format $(n,r)$ is efficient if there exists $c$ with…

Gaitonde et al.'s moment-matrix necessity conjecture. Boundedness of certain moment matrices is necessary for learning throughout the entire high-temperature regime.

Uniqueness conjecture. The $(n+1)$-by-$n$ polynomial system

Let $H(m)$ be the universal constant appearing in Lemma referred to in the source as lem:detpoly, and let the Hilbert matrix of order $m$ be the $m\times m$ matrix with entries…

Finite-type representing measure conjecture. The following are equivalent:

Finite-degree completeness conjecture. The resulting generating set is complete for the real radical unless there is a minimum degree $d'>d$ at which prolongation determines new ge…