AI 中文总结
该研究证明阿蒂亚的闵可夫斯基空间线性无关猜想对所有n≥3不成立，通过n=3的显式反例及零平移构造得到所有n>3的反例，明确n=2时该猜想成立。
AI 中文摘要
阿蒂亚提出的闵可夫斯基空间版本的点构型构造，为n条世界线的容许标记构型赋予n个n-1次二元形式，其根为有序延迟天体方向，他猜想这些形式总是线性无关。我们对所有n≥3证明该猜想不成立：对于n=3，一个显式平面单参数族在指定区间内产生一个恰有一个单零点的实系数行列式，在该参数处，所有6个有序天体根互不相同，系数矩阵秩恰好为2；通过零平移构造，将前三个形式乘以公共因子，得到所有n>3的反例。因此，在完全两两不交的类时仿射直线类中，n=2时普遍成立线性无关，n≥3时均不成立；对每个反例，归一化阿蒂亚-萨特克利夫行列式均有定义且为零。
英文摘要
Atiyah's Minkowski-space version of the configuration-of-points construction assigns to an admissible marked configuration of $n$ worldlines a collection of $n$ binary forms of degree $n-1$, whose roots are the ordered retarded celestial directions. He conjectured that these forms are always linearly independent. We disprove this conjecture for every $n\ge3$. For $n=3$, an explicit planar one-parameter family yields a real coefficient determinant with exactly one simple zero in a specified interval. At this parameter, all six ordered celestial roots are distinct and the coefficient matrix has rank exactly two. A null-translation construction then multiplies the first three forms by a common factor and produces counterexamples for every $n>3$. Consequently, within the class of complete pairwise disjoint timelike affine lines, universal independence holds at $n=2$ and fails for every $n\ge3$; for each of the counterexamples, the normalized Atiyah--Sutcliffe determinant is defined and vanishes.
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