Dual Collinearity in Sparse Time Probes of Chronos

Linear probes of time-series foundation model (TSFM) representations are increasingly used to assess whether models encode "metric time" under sparse observation. We show that under order-preserving sparse sampling with a Beta keep law, a common probe target (the OLS-residualized observation time $m^{\perp}$) remains a smooth function of token index $k$, making it a control-task-easy target that measures positional feature capacity rather than physical-time inference. In an audit of Chronos-T5-base encoder states (8 UCR series, Beta$(0.35,4)$ keep, linear ridge probe), we find: (i) matched-keep white-noise inputs yield median $r(H,m^{\perp})=0.759$, below the index-spline ceiling ($0.900$) but well above zero; (ii) real-data median $r=0.821$, with median paired excess $\Delta r=+0.090$ (IQR $0.091$) that sits well below the geometry ceiling; (iii) both $r(H,i)$ and $r(H,m^{\perp})$ show the same mid-stack peak then decline at layer 12. We conclude that $m^{\perp}$ under this keep law is not a valid test of metric-time inference, and that Chronos encoder states linearly expose a large fraction of the index-geometry ceiling. The result is a scoped evaluation warning for this probe class, together with a characterization of nonlinear positional accessibility in T5-RPE encoders.