发表机构
Scripps College; Department of Natural Sciences, Scripps and Pitzer Colleges, Claremont Colleges Consortium（斯克里普斯学院; 克莱蒙特学院联盟斯克里普斯和皮策学院自然科学系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究确定了可推广牛顿外壳定理的径向相互作用势，扩展了Gurzadyan的宇宙学定理，将理论扩展至多极源并在任意空间维度建立分类，发现了新势族且分类形成嵌套层级。
AI 中文摘要
我们确定了所有可推广牛顿外壳定理的径向相互作用势，对于这些势，均匀分布的球壳在强度重整化和径向重标度下与点源不可区分，我们将这些相互作用称为保形壳相互作用，扩展了仅考虑强度重整化的Gurzadyan宇宙学定理。我们进一步将理论从单极源扩展到多极源，并在任意空间维度中建立相应分类，发现了超出球属性子类的势族，且多极保形相互作用的分类形成嵌套层级，每个低阶类是更高阶类的子集。
英文摘要
We identify all radial interaction potentials that generalize Newton's exterior shell theorem, for which a uniformly distributed spherical shell is indistinguishable from a point-source up to strength renormalization and radial rescaling. We call these shape-preserving shell interactions, extending Gurzadyan's cosmological theorem which considers strength renormalization alone. We further expand the theory from monopolar to multipolar sources and establish the corresponding classification in arbitrary spatial dimensions. We find potential families beyond the spherical property subclass and show that the classifications for multipolar shape-preserving interactions form a nested hierarchy, with each lower-rank class being a subset of the next higher-rank class.
