Submit progress

on The Ring Loading Problem (AlphaEvolve problem 61)

The statement

Let $C$ be the infimum of all reals $\alpha$ for which the following statement holds: for all positive integers $m$ and nonnegative reals $u_1, \ldots, u_m$ and $v_1, \ldots, v_m$ with $u_i + v_i \leq 1$ , there exist $z_1, \ldots, z_m$ such that for every $k$ , we have $z_k \in \{v_k, -u_k\}$ , and

\left|\sum_{i=1}^k z_i - \sum_{i=k+1}^m z_i\right|\leq \alpha.

Obtain upper and lower bounds on $C$ that are as strong as possible.

What gets accepted

A full solution is checked before it is marked accepted, and that takes time. Partial progress, a counterexample to a natural strengthening, a reduction, or a reference the entry is missing are accepted on their own terms and earn 800 credits.

Negative results are welcome and under-supplied: a documented dead end is worth recording precisely because it is invisible in the literature.