Large language models hallucinate in predictable ways: attention routing fails by over-concentrating on a narrow set of positions, or by spreading so diffusely that relevance is diluted, and the shape of the failure carries diagnostic signal. A widely used family of spectral methods analyzes the symmetric component of the degree-normalized attention operator, which governs transport capacity; we prove that every transpose-invariant spectral diagnostic of this operator is structurally orientation-blind (it cannot distinguish an operator from its transpose, and therefore cannot detect information-flow direction), with a quantitative converse establishing the asymmetry coefficient $G$ as the unique control parameter for direction. Pairing this with a closed-form bipartite-Cheeger landscape for canonical causal architectures, we show that uniform causal attention satisfies an $n$-independent floor $φ\ge 1/5$ with worst cut at $t^\ast/n \approx 0.32$, while window attention pierces the floor as $O(w/n)$; failure modes are shape-different, not just value-different. The resulting two-axis diagnostic ($φ$ for capacity, $G$ for direction) yields a falsifiable polarity prediction: bottleneck- and diffuse-dominated benchmarks should exhibit opposite polarity. Under length-controlled evaluation, transport features retain interpretable signal (LC-AUROC from 0.62 to 0.84) on tested models up to 8B parameters, with polarity reversing as predicted between HaluEval and MedHallu.

翻译：大语言模型以可预测的方式产生幻觉：注意力路由因过度集中于狭窄位置而失败，或因扩散过于分散导致相关性稀释，而失败形态携带有诊断信号。一类广泛使用的谱方法分析控制传输能力的度归一化注意力算子的对称分量；我们证明该算子的每个转置不变的谱诊断在结构上都是方向盲的（它无法区分算子与其转置，因此无法检测信息流方向），并给出一个定量逆定理，确立非对称系数$G$作为方向的唯一控制参数。结合典型因果架构的闭式二分Cheeger景观，我们证明均匀因果注意力满足与$n$无关的下界$\phi\ge 1/5$，最差切分位置在$t^\ast/n \approx 0.32$，而窗口注意力以$O(w/n)$的速率突破下界；失败模式具有形状差异而不仅仅是数值差异。由此产生的双轴诊断（$\phi$衡量容量，$G$衡量方向）产生一个可证伪的极性预测：瓶颈主导型与扩散主导型基准应呈现相反的极性。在长度可控评估下，传输特征在测试的8B参数以下模型中保留可解释信号（LC-AUROC从0.62到0.84），其极性在HaluEval与MedHallu之间如预测般反转。