8 problems

Let $A$ be the partial combinatory algebra underlying the assembly category, and let $\mathrm{p}\mathbbm{Grpd}(\operatorname{Asm}(A))$ be the category of partitioned groupoid assem…

Let $A$ be the partial combinatory algebra underlying the assembly category, and let $\mathrm{p}\mathbbm{Grpd}(\operatorname{Asm}(A))$ denote the category of partitioned groupoid a…

Let $\mathcal{L}\subset\mathbb{RP}^2$ be an essential pseudoline arrangement, and let $M$ be its matroid. Let $Q$ be the Hirzebruch quadratic form of $M$, and let the semistable co…

Integer-scaling criterion. If $\{\frac{\lambda_1}{\alpha_1},\ldots,\frac{\lambda_n}{\alpha_n}\}$ is $C_{\mathbb{Q},3}$-realizable, then it is $C_{\mathbb{Q},3}$-realizable if and o…

Counterpart conjecture. Some of these local operators have counterparts in the toposes

Realizable fiber representation conjecture. Every locally realizable COM is a fiber of a realizable OM.

Realizability conjecture. For an arbitrary sign pattern ${\bar \sigma}$, the only type of pairs $(pos,\neg)$ which can be non-realizable has either $pos$ or $\neg$ vanishing. Equival…

Non-realizability conjecture. There is no arrangement in $\mathbb{C}^3$ with the same incidence as $\mathcal{A}$.