arXiv:2602. 16807v2 Announce Type: replace Abstract: A collection of hyperplanes $\mathcal{H}$ slices all edges of the $n$-dimensional hypercube $Q_n$ with vertex set $\{-1,1\}^n$ if, for every edge $e$ in the hypercube, there exists a hyperplane in $\mathcal{H}$ intersecting $e$ in its interior.
arXiv:2607. 23004v1 Announce Type: cross Abstract: Let $t(N)$ be the largest $t$ for which there exist distinct sets $A_1,\dots,A_t \subseteq \{1,\dots,N\}$ such that $A_i \cap A_j$ is a nonempty arithmetic progression for all $i \neq j$ (Erdos Problem #272).
arXiv:2606. 29477v1 Announce Type: cross Abstract: The specification number $\sigma_n(f)$ of a Boolean threshold function $f$ on $n$ variables is the least number of points whose $f$-values determine $f$ uniquely among all threshold functions.
arXiv:2607. 10194v1 Announce Type: cross Abstract: We present IsalHG, a method for representing the structure of any finite, connected hypergraph of bounded hyperedge arity as a string over a compact instruction alphabet $\Sigma_{\mathrm{HG}}$.
arXiv:2607. 21651v1 Announce Type: new Abstract: We prove that the maximum of $n$ real numbers is exactly representable by a ReLU network with two hidden layers for every $n\le 10$.
arXiv:2608. 08154v1 Announce Type: cross Abstract: The Zarankiewicz number Z(m,n,s,t) is the maximum number of edges in a bipartite graph with parts of orders m and n containing no copy of Ks,t.
arXiv:2606. 03419v1 Announce Type: cross Abstract: The 2026 disproof of Erd\H{o}s's unit-distance conjecture and Sawin's subsequent explicit quantitative refinement show that the maximum number $u(n)$ of unit distances among $n$ planar points can exceed $n^{1+\varepsilon}$ for a fixed positive $\varepsilon$.
arXiv:2607. 29555v1 Announce Type: new Abstract: Lacoste-Julien and Jaggi conjectured in 2015 that the pyramidal width of a polytope cannot increase when a vertex is added, provided that every old point remains a vertex.
We study certain extremal problems in combinatorial geometry that ask about configurations of points in an $n \times n$ grid that satisfy strict, global geometric constraints. Classical exact solvers suffer from combinatorial explosion for these types of problems, and standard reinforcement learning and transformer-based models struggle with the sparse reward "validity cliff" and quadratic token-consumption limits.
arXiv:2606. 26399v1 Announce Type: new Abstract: We study certain extremal problems in combinatorial geometry that ask about configurations of points in an $n \times n$ grid that satisfy strict, global geometric constraints.
arXiv:2608. 11716v1 Announce Type: new Abstract: Chain of Thought (CoT) lifts the expressive ceiling of bounded-depth Transformers, with characterizations tying the number of CoT steps to circuit complexity classes.
arXiv:2607. 23500v1 Announce Type: cross Abstract: Razborov's flag algebra method is a powerful tool for proving asymptotic inequalities in extremal graph theory, often reducing the task to finding a finite certificate by semidefinite programming.
Chain of Thought (CoT) lifts the expressive ceiling of bounded-depth Transformers, with characterizations tying the number of CoT steps to circuit complexity classes. What remains largely missing are concrete instantiations with explicit, depth-bounded constructions, and the traversal procedures such characterizations presuppose.