7 problems

Let $\mathcal{A}\subseteq\mathbb{N}$ be finite, let $v$ be the primitive vector from the associated orbit, and let $L$ be a linear functional. Define … and let…

Hensley's conjecture. There are only finitely many exceptional natural numbers.

Niederreiter's conjecture. There are only finitely many exceptional natural numbers.

Haag–Kertzer–Rickards–Stange conjecture. The sporadic set $S({\mathcal P})$ is finite.

Graham–Lagarias–Mallows–Wilks–Yan density conjectures. The congruence obstruction is essentially the only obstruction, so the set of curvatures in a primitive integral Apollonian c…

Let … and consider its orbit of the indicated vector. Explicit $\Psi_1$ numerator conjecture. Every non-square integer $n>10569$ appears as a numerator in the orbit…

Define … The table of congruence and reciprocity obstructions specifies the stated restrictions on numerators and denominators in these orbits. Local-global conjecture for $\Psi_1$…