What Do Time-Series Foundation Models Share? An Input-Kernel Accounting of Representational Agreement

Do time-series foundation models organize input histories in a shared way? We compare the matrices of pairwise history similarities produced by ten variants from seven families on 17 datasets. Released pretrained weights (PT) agree more than independent architecture-matched initializations (INIT). On the full inventory, more of the additional agreement lies in the input kernels for mean pooling than for last-position pooling. The last-position residual stays positive across depth, reference expansion and family deletion. The mean-linear endpoint interval crosses zero; mean-RBF and intermediate mean-linear depths stay positive. On later Wikipedia records the mean-linear residual is larger than the last-linear residual. The last-linear remainder is a difference in residual direction: PT and INIT have similar residual norms, and permuting each released parameter tensor removes the additional agreement. Small MLP and CNN predictors that improve within-dataset forecasting also develop additional last-position agreement outside the same input span. The balance between the input span and the residual depends on the readout and the population.