6 problems

Memorization conjecture. The later deterioration is caused by the networks memorizing the answers for all the $\sigma$ values except $5$, thereby degrading performance at…

Minimum-proof conjecture. The theoretical minimum in this case is $22$, attained first at proof number $6$ and often at the end.

Let $K$ be a field. The graph $\mathcal G_{2,K,2}$ is the subgraph associated with the relevant two-generated nilpotent semigroups of coclass $2$. Five-path conjecture. The graph…

Let $r\in\mathbb N_0$ and let $K$ be an arbitrary field. Let $\mathcal T$ be a maximal coclass tree in $\mathcal G_{r,K}$ with maximal infinite path $A_1\to A_2\to\cdots$. Write…

Let $r\in\mathbb N_0$ and let $K$ be an arbitrary field. For an algebra $A$ in $\mathcal G_{r,K}$, write $\mathcal T(A)$ for the rooted subgraph consisting of all paths starting at…

Let $r\in\mathbb N_0$ and let $K$ be an arbitrary field. The graph $\mathcal G_{r,K}$ has rooted-tree components, and a maximal infinite path is an infinite path starting at the ro…