5 problems

Let $a\in\mathbb{N}-\{0,1\}$ be an integer that is not a multiple of $10$. Let $\operatorname{APS}(a)$ denote the asymptotic phase shift of the tetration base $a$, represented as a…

Let $\smalloverbrace{\mathbb{A}}$ denote the set of polymorphic tetration bases, let $V(\smalloverbrace{a}^{*})$ be the limiting congruence speed of $\smalloverbrace{a}^{*}$, and l…

Congruence speed stabilization conjecture. If $a \not\equiv \{0,3,7\} \pmod {10}$ and $b \geq \operatorname{len}(a)+2$, then $V(a,b)=V(a)$. This gives a sufficient tetration height…

Backward-iteration conjecture.

For each base $b>1$, let ${\rm tet}_b$ denote the holomorphic tetrational constructed in the cited works, covering the base range $(1,\infty)$. Analyticity conjecture for holomorph…