Probing frozen vision transformers typically uses permutation-invariant aggregation (GAP or $\texttt{[CLS]}$), treating patch tokens as an unstructured set. Content-dependent probes such as self-attention are useful accuracy controls, but they do not expose a fixed token schedule or fixed position weights for auditing. We introduce SSMProbe, a probe of frozen vision transformers that learns a Sinkhorn patch route and reads it with a diagonal S4 decoder. The decoder's causal linear time-invariant (LTI) recurrence yields fixed position coefficients, exposing how patch arrangement interacts with sequential weighting. Held-out spatial predictability measures route organization beyond a location-bias null. On CUB and Cars, MAE, BEiT, DINOv2, and supervised ViT yield spatially organized routes with distinct readout profiles: DINOv2 is $\texttt{[CLS]}$-dominant, while MAE benefits from learned routing over fixed scans. On MAE/ImageNet, Sinkhorn reaches 70.33% accuracy, 5.55 percentage points above the strongest fixed scan.

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