Median spike times on inward and outward runs across all 73 grid cells with sufficient runs. On inward runs, grid cells showed prospective time shifts (n = 73), median 132 ms (IQR 167); WSRT,Z= 6.3, p = 2.8 × 10−10; outward runs had significantly shorter time horizons (median difference between time shifts of inward and outward runs in each map), 130 ms (IQR 214); WSRT,Z= 5.7, p = 1.4 × 10−8; and were neither prospective nor retrospective (median 25 ms [IQR 156]; WSRT,Z= −1.6, p = 0.10). Place cells showed similar results: inward runs tended to have larger prospective shifts than outward runs. Median difference between time shifts of inward and outward runs in each map, 260 ms (IQR 281), n = 29 place cells with sufficient runs; WSRT,Z= 3.7, p = 2.3 × 10−5. For place cells, both inward and outward runs showed significant prospective time shifts (inward runs, median 300 ms [IQR 310]; WSRT,Z= 4.6, p = 4.8 × 10−6; outward runs, median 70 ms [IQR 184]; WSRT,Z= 3.0, p = 2.6 × 10−3). See alsoFigures S2–S5.