Open-problem statements, with their sources attached.

For $N = 6$ and $D = 5$, does there exist no solution to the monochromatic quantum graph equation system over $\mathbb{R}$?

For $N = 6$ and all $D \geq 3$, does there exist no solution to the monochromatic quantum graph equation system over $\mathbb{R}$?

For $N = 8$ and $D = 3$, does there exist no solution to the monochromatic quantum graph equation system over $\mathbb{R}$?

For $N = 10$ and $D = 3$, does there exist no solution to the monochromatic quantum graph equation system over $\mathbb{R}$?

For all even $N \geq 6$ and $D \geq 3$, does there exist no solution to the monochromatic quantum graph equation system over $\mathbb{R}$?

For $N = 6$ and $D = 3$, does there exist no solution to the monochromatic quantum graph equation system over $\mathbb{Z}$?

For $N = 6$ and $D = 5$, does there exist no solution to the monochromatic quantum graph equation system over $\mathbb{Z}$?

For $N = 6$ and all $D \geq 3$, does there exist no solution to the monochromatic quantum graph equation system over $\mathbb{Z}$?

For $N = 8$ and $D = 3$, does there exist no solution to the monochromatic quantum graph equation system over $\mathbb{Z}$?

For $N = 10$ and $D = 3$, does there exist no solution to the monochromatic quantum graph equation system over $\mathbb{Z}$?

For all even $N \geq 6$ and $D \geq 3$, does there exist no solution to the monochromatic quantum graph equation system over $\mathbb{Z}$?

For $N = 6$ and $D = 3$, does there exist no solution to the monochromatic quantum graph equation system over $\mathbb{Z}$ with weights in $\{-1, 0, 1\}$?

For $N = 6$ and $D = 5$, does there exist no solution to the monochromatic quantum graph equation system over $\mathbb{Z}$ with weights in $\{-1, 0, 1\}$?

For $N = 6$ and all $D \geq 3$, does there exist no solution to the monochromatic quantum graph equation system over $\mathbb{Z}$ with weights in $\{-1, 0, 1\}$?

For $N = 8$ and $D = 3$, does there exist no solution to the monochromatic quantum graph equation system over $\mathbb{Z}$ with weights in $\{-1, 0, 1\}$?

For $N = 10$ and $D = 3$, does there exist no solution to the monochromatic quantum graph equation system over $\mathbb{Z}$ with weights in $\{-1, 0, 1\}$?

For all even $N \geq 6$ and $D \geq 3$, does there exist no solution to the monochromatic quantum graph equation system over $\mathbb{Z}$ with weights in $\{-1, 0, 1\}$?

1. implies 2): if the coefficients of $f$ satisfy the $\omega$-integrality condition for some superlinear $\omega$, then there exists $N$ such that for all $n$, the $n$-th coefficient of $f$ is in $\mathbb{Z}[1/N]$.

1. implies 1): if the coefficients of $f$ are in $\mathbb{Z}[1/N]$ for some $N$, then $f$ is algebraic over $\mathbb{Q}[z]$. Also the version of conjecture of Litt's problem 1 on his website.

Conjecture by Goldfeld and Katz–Sarnak: if elliptic curves over ℚ are ordered by their heights, then 50% of the curves have rank 0 and 50% have rank 1. See p. 28 of https://people.maths.bris.ac.uk/~matyd/BSD2011/bsd2011-Bhargava.pdf.