7 problems

Naturalness conjecture for Benford's law. Benford's law is an act of nature and can be used to indicate the randomness of our world.

Let $k$ and $\epsilon$ be fixed and let $n$ be odd. Let $\mathcal{A}_n$ denote the class of admissible, antisymmetric functions on $n$ bits, and let $\mathsf{MAJ}_m$ denote the maj…

Let $k$ and $\epsilon$ be fixed and let $n$ be odd. Write $\mathcal{A}_n$ for the class of admissible functions on $n$ bits, and let $\mathcal{P}_k(f;\epsilon)$ denote the success…

Finite-alphabet and fixed-length conjecture. The assumptions that the auxiliary variable $V$ is finite-valued and that the codes are fixed-length are not restrictive.

Computable-subfield characterization. Then $K$ is random.

Let $k_2$ be the loop associated with a sequence $\zeta=(\zeta_n)$ satisfying $\zeta\in l^2$, and suppose the phases of the $\zeta_k$ are uniform and independent random variables.…

Let the decimal digits of $\pi$, $e$, $\sqrt{2}$, and other analytically defined irrational numbers be viewed through their digit-counting statistics and normalized partial sums. L…