AI 中文总结
该研究刻画了有界对称实核的无穷小有限可强制性，证明了核为阶梯核时其图密度梯度张成有限维空间，结合已有结果肯定回答了Lovász和Szegedy的相关问题，采用谱方法与书图压缩论证完成证明。
AI 中文摘要
我们刻画了有界对称实核的无穷小有限可强制性。我们证明，当且仅当核为阶梯核时，其图密度梯度张成有限维空间。结合阶梯核已知的有限强制结果，这对Lovász和Szegedy提出的“每个无穷小有限可强制核是否均为有限可强制核”的问题给出了肯定回答。该证明将谱方法与基于书图的压缩论证相结合。
英文摘要
We characterize infinitesimal finite forcibility for bounded symmetric real kernels. We prove that the graph-density gradients at a kernel span a finite-dimensional space if and only if the kernel is a step kernel. Combined with known finite-forcing results for step kernels, this gives a positive answer to a question of Lovász and Szegedy on whether every infinitesimally finitely forcible kernel is finitely forcible. The proof combines spectral methods with a compression argument based on book graphs.
Comments9 pages
