The orthoscheme complex of a graded poset is a metrization of its order complex such that the simplex of each maximal chain is isometric to the Euclidean simplex of vertices \(0, e_1,e_1+e_2,\ldots , e_1+e_2+ \cdots + e_n\). This notion was introduced by Brady and McCammond in geometric group theory, and has applications in discrete optimization and submodularity theory. We address the question of which poset can yield the orthoscheme complex with CAT(0) property. The orthoscheme complex of a modular lattice has been shown to be CAT(0), and it is conjectured that this is the case for a modular semilattice. In this paper, we prove this conjecture affirmatively. This result implies that a larger class of weakly modular graphs yields CAT(0) complexes.

渐变姿势的原形复杂度是其阶数复杂度的度量，因此每个最大链的单纯形与顶点的欧几里得单纯形等距\（0，e_1，e_1 + e_2，\ ldots，e_1 + e_2 + \ cdots + e_n \）。这个概念是布雷迪和麦卡蒙德（Brady and McCammond）在几何群论中提出的，并在离散优化和子模量理论中得到了应用。我们解决了哪个坐姿可以产生具有CAT（0）属性的正统复合体的问题。模块化格架的正统复合体已显示为CAT（0），并且可以推测，模块化半格架就是这种情况。在本文中，我们肯定地证明了这一猜想。此结果表明，一大类弱模块化图会产生C​​AT（0）复数。