The paper presents an exact 93‑move solution to a nonlocal crystal‑exchange puzzle on an 11×11 board, where a command swaps the player with the nearest crystal in a chosen row or column. The authors prove that no shorter solution exists by performing a cost‑bounded breadth‑first search that explores over 1.8 billion states, using a compressed core abstraction and several pruning conditions. The study includes a detailed description of the reductions, pruning rules, storage scheme, and provides source code, execution logs, and a reproduction driver.
arXiv:2610. 33259v1 Announce Type: new Abstract: Classical optimization and learning-guided search offer complementary approaches to open problems in discrete mathematics, but their outputs are difficult to compare when search spaces, validity checks, and stopping rules differ.
The paper introduces a hybrid framework for solving Satisfiability Modulo the Theory of Nonlinear Real Arithmetic (SMT‑NRA). It presents a new two‑dimensional cell‑jump move, called 2D‑cell‑jump, that generalizes the existing cell‑jump operation by allowing search over any chosen plane. Building on this, the authors develop an extended local search framework, 2D‑LS, and combine it with MCSAT and OpenCAD to form a hybrid solver that improves search efficiency through information exchange, as shown by experimental results.
arXiv:2609.39559v1 Announce Type: new Abstract: In this work we study the problem of MAPFC, a post-optimization step for Multi-Agent Path Finding (MAPF) plans where we are given a feasible plan produ...
arXiv:2511. 13391v4 Announce Type: replace-cross Abstract: Since Isaac Newton first studied the Kissing Number Problem in 1694, determining the maximal number of non-overlapping spheres around a central sphere has remained a defining challenge in discrete geometry.
Goal-Branching LaCAM introduces temporary goals as search branches to improve the LaCAM solver for dense multi-agent pathfinding. By assigning blocking agents temporary goals and exploring them as additional branches, the method preserves completeness while dramatically increasing success rates on dense maze and room maps. Experiments show up to 89% solved instances versus 44% for LaCAM*, with first solutions found 10–14× faster and median times nearly 200× faster at high densities, though solution cost rises modestly.
arXiv:2602. 10233v2 Announce Type: replace-cross Abstract: LLM-guided evolutionary computation, most notably AlphaEvolve, has been remarkably successful in discovering novel mathematical constructions by solving challenging optimization problems.
arXiv:2609. 29881v1 Announce Type: cross Abstract: Choosing Shellsort gaps is a well-known open problem.
The paper reports on a large‑scale verified search experiment using a 30B language model on a laptop, evaluating three operator packages—schematic notebooks, named obstacles, and behavioural repulsion—in a factorial design across nine construction problems. Results show that the full composition of operators closes the seed‑to‑record gap more effectively than any single component, increases construction‑hash diversity, and that memory plus repulsion consistently avoids collapse. A frontier proposer achieves similar gains in far fewer samples, but the search ultimately stalls near a plateau where the reference family is adopted and optimized only when provided as code.
The paper introduces Sanko, a parallel depth‑first proof‑number solver that addresses the challenges of solving Go under positional superko (PSK) by restoring transposition tables, static life‑and‑death recognition, and safe move pruning through a proof‑transfer theorem. Sanko achieves significant speedups, proving 5x5 Go in 16 minutes with six threads and establishing PSK values for twenty‑three additional boards, including eleven previously unsolved. The authors also release the solver source and detailed run data to enable reproducibility of their results.
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.
The paper presents a block‑wise differentiable Sinkhorn attention mechanism designed for long‑context balanced entropic optimal transport on TPU hardware. By stopping a $T$‑step Sinkhorn solve and unrolling a short refinement tail, the authors derive an exact surrogate gradient that achieves efficient block‑wise cost and memory usage. Experimental results on synthetic masked problems and a Pfam protein‑family screen demonstrate high numerical accuracy and sustained throughput on TPU v6e‑8, with notable improvements in reconstruction and sparse cross‑entropy metrics.
arXiv:2605. 30664v2 Announce Type: replace Abstract: Subgoal-based policy tree search, which uses a policy to guide search, is effective for complex single-agent deterministic problems but often relies on explicit subgoal generation that can incur substantial overhead and hinders scalability.