Can grid cells produce hexadirectional signals?
Hexadirectional modulation is widely treated as a proxy for population-level grid-cell activity in humans. Here we show that this interpretation is generally not supported by the statistics of grid-cell firing. Conventional analyses test symmetric sixfold modulation of the mean response, whereas grid-cell firing predicts a dominant sixfold modulation of cell-level variance, rather than population-level mean. Using analytical deduction, simulations and a large-scale rodent dataset, we show that the previously reported mean hexadirectional effect is not a principal consequence of grid-cell activity. Among current hypotheses, a signal compatible with empirical rodent MEC cell population characteristics can emerge only with a second-order nonlinearity, and only under restricted conditions. Even then, the expected population-level mean modulation is small, approximately 2%. These findings suggest that the existing human literature targets a weak, indirect signature rather than a diagnostic readout of grid-cell population coding. Moreover, many reported hexadirectional effects may arise from testing a single sixfold component without establishing the full spectral response is robust against an appropriate null distribution. We provide a more comprehensive framework for testing hexadirectional symmetry in future studies.