9 problems

Let derivations be derivations in a natural-deduction system, and let two derivations be equivalent when they have the same assumptions and conclusion and belong to the reflexive,…

Per-layer RLCT reduction conjecture. The same RLCT reduction holds for each normalized weight matrix $W_l$ in a deep network under the wrLLC isolation protocol: freezing all parame…

Let $R$ be the original algorithm set, and introduce auxiliary algorithms into the benchmarking set. Auxiliary-algorithm conjecture. The more auxiliary algorithms are introduced, t…

Computational completeness conjecture. dTT, including its treatment of $\mathsf{SST}$, is fully computational in the sense of $\mathsf{Nat}$ canonicity, normalization, and decidabl…

Let $\Pi$ be a derivation in the natural-deduction system $\mathsf{NK}$, and consider the reduction steps described in the paper's rewriting system. A derivation is called “standar…

Let $f:(X,x)\to(S,s)$ be a flat morphism with $(S,s)$ normal, suppose that the non-normal locus $\operatorname{NNor}(f)$ is finite over $S$, and assume $\dim(X_0,x)\geq 1$. Equinor…

Let $X$ be an excellent scheme that is $S_2$ and has pure dimension $\geq 3$, let $x\in X$ be a closed point, and let $\pi:\bar X\to X$ be the normalization, with $\bar x$ denoting…

Let $D \subseteq S$ be a divisor in a complex manifold $S$ that is locally at a point $p$ given by $h=0$, and let $\pi:\widetilde D \rightarrow D$ be its normalization. Suppose tha…

Let $f:X\to Y$ be a projective morphism of complex spaces with $Y$ normal, and let ${\mathcal V}$ be a class of projective varieties. Assume there is a Zariski dense open subset…