the field was ramped at 0.02 T s$^{-1}$ while the magnetization and temperature of the sample were continuously recorded. For the slow CC protocol measurements shown in Fig. 3, the samples were first heated to 900 mK for 10 s, then cooled at a rate of approximately 0.01 K s$^{-1}$, followed by a waiting period of 1000 s.

Data availability {#data-availability .unnumbered}
=================

Information on the data underpinning the results presented here, including how to access them, can be found in the Cardiff University data catalogue at http://doi.org/10.17035/d.2019.0069144874.\
The datasets obtained and/or analyzed in this study are also available from the corresponding author on reasonable request.

[99]{} Harris, M. J., Bramwell, S. T., McMorrow, D. F., Zeiske T. & Godfrey, K. W. Geometrical frustration in the ferromagnetic pyrochlore Ho$_2$Ti$_2$O$_7$. [*Phys. Rev. Lett.*]{} [**79**]{}, 2554 – 2557 (1997). Bramwell, S. T. & Harris, M. J. Frustration in Ising-type spin models on the pyrochlore lattice. [*J. Phys.: Condens. Matter*]{} [**10**]{}, L215 - L220 (1998). Ramirez, A. P., Hayashi, A., Cava, R. J., Siddharthan, R. B. & Shastry, S. Zero-point entropy in Ôspin iceÕ. [*Nature*]{} [**399**]{}, 333 – 335 (1999). Bramwell, S. T. & Gingras, M. J. P. Spin ice state in frustrated 