LayerNorm-based GNNs routinely erase the topology signals (degree, centrality, $k$-core) that node-selection policies should depend on, but the literature has not located where in the residual block the erasure happens. We answer that question: a positive per-node scalar inserted before LayerNorm is divided out up to a stabilizer term, while the same scalar inserted after LayerNorm reaches the score head as representation magnitude. The surviving slot is the post-LayerNorm position. We instantiate it with PostDeg, a parameter-free post-LayerNorm inverse-degree scale, and pre-register four falsifiers (graphwise scalars, extra LayerNorm, expressive same-slot capacity, backbone-agnostic source) that would reject the rule. PostDeg gains $+3.5\%/+2.5\%/+5.6\%$ over the LN backbone on influence maximization, network dismantling, and maximum independent set, with $10/10$ paired-seed wins per task; none of the four falsifiers fires. The takeaway is that placement, not parameterization, carries the gain -- a small invariance check that generalizes to any positive topology scalar in any normalized residual stack.

翻译：基于LayerNorm的图神经网络通常会抹去节点选择策略应依赖的拓扑信号（度、中心性、$k$-核），但现有文献尚未定位该信号在残差块中被擦除的具体位置。我们给出了答案：在LayerNorm之前插入的每个节点正标量会被除以一个稳定项而抵消，而插入在LayerNorm之后的相同标量则会以表征幅度的形式到达评分头部。幸存下来的位置是LayerNorm之后的位置。我们通过PostDeg——一种无参数的后LayerNorm逆度缩放——实例化了该位置，并预先注册了四个拒斥性检验指标（图级标量、额外LayerNorm、相同槽位的表达能力、骨架无关来源），这些指标本应推翻该规则。在影响力最大化、网络瓦解和最大独立集任务上，PostDeg相较LN基线获得$+3.5\%/+2.5\%/+5.6\%$的提升，且每项任务在10/10配对随机种子实验中均胜出；四个拒斥性检验指标无一触发。结论是：性能提升源于位置而非参数化——这是一个可推广至任意归一化残差堆栈中任意正拓扑标量的小型不变性检验。