AI 中文总结
EULER作为多智能体系统，以桥梁为搜索单元，经压力测试筛选后，在120个组合数学猜想上获10个证明等结果，验证了其在数学发现中的有效性。
AI 中文摘要
数学研究社群使用不同的研究对象、不变量与工具，因此在不同社群间迁移问题的成本高昂，且常被忽略。我们提出EULER，这是一个以这类迁移（即“桥梁”）为搜索单元的多智能体系统。围绕一个固定猜想，EULER会并行运行直接路径、相邻领域路径与远程领域路径；仅当桥梁提供源表示无法执行的操作，且其目标侧证据经验证蕴含关系返回至原始命题时，该桥梁才会保留预算。在启动高成本搜索前，六项有序压力测试会剔除无效桥梁。我们在120个近期猜想上评估EULER，这些猜想在搜索前已被冻结且排除了污染，来自近期在组合数学顶级期刊《组合理论杂志A辑》发表过论文的作者的公开论文。EULER得出10个证明、3个反驳结果，以及45个有范围的部分结果。两项机制在消融实验中表现稳定：桥梁专用压力测试将错误结论从9个削减至3个，桥梁材料结合目标原生操作产生了+4.2个已解决任务的正向交互作用，这一效果是任一因素单独无法实现的；领域距离无法可靠预测成功，可执行操作增益与有效返回才可以。
英文摘要
Mathematical communities work with different objects, invariants, and tools, so transferring a problem across them is expensive and often skipped. We present EULER, a multi-agent system that takes such a transfer--a bridge--as its unit of search. Around a fixed conjecture, EULER runs direct, adjacent-domain, and distant-domain routes in competition; a bridge keeps its budget only if it supplies an operation the source representation cannot execute and its target-side evidence returns to the original statement along a checked implication. Six ordered stress tests reject invalid bridges before expensive search begins. We evaluate EULER on 120 recent conjectures. The conjectures were frozen before search and screened for contamination, and are drawn from public papers by authors who had recently published in the Journal of Combinatorial Theory, Series A, a leading journal in combinatorics. EULER produced 10 proofs and 3 refutations, plus 45 scoped partial results. Two mechanisms held up under ablation: bridge-specific stress tests cut incorrect conclusions from 9 to 3, and bridge material combined with a target-native operation yielded a positive interaction of +4.2 resolved tasks that neither factor produced alone. Domain distance did not reliably predict success; executable operation gain and valid return did.
Comments55 pages, 10 figures, 29 tables; includes a 13-page companion candidate-proof manuscript as Appendix P
