[@Harris1997; @BramwellHarris98; @Ramirez; @BramwellGingras], rare earth ions with total angular momentum $J = 15/2$ (Dy$^{3+}$) and $J = 8$ (Ho$^{3+}$) are densely packed on a cubic pyrochlore lattice of corner-linked tetrahedra. The ions experience a very strong $\langle111\rangle$ crystal field, resulting in two effective spin states ($M_{\rm J} = \pm J$) that define a local Ising-like anisotropy. At the millikelvin temperatures discussed here ($0.08~{\rm K}<T<0.2$ K), a lattice array of such large and closely-spaced spins would normally be ordered by the dipole-dipole interaction [@LuttingerTisza], but the pyrochlore geometry of spin ice frustrates the dipole interaction and suppresses long-range order. Instead, the system is controlled by an ice-rule, that maps to the Pauling model of water ice [@Harris1997; @BramwellHarris98; @Ramirez; @BramwellGingras]. In the effective ground state, the spins describe a flux with closed-loop topology and critical correlations, that may be described by a local gauge symmetry rather than by a traditional broken symmetry [@CMS]. This strongly correlated spin ice state is stabilised by a remarkable self-screening of the dipole interaction [@Isakov; @Gingras]. Excitations out of the spin ice state fractionalise to form effective magnetic monopoles [@CMS; @Ryzhkin], but the excited states are no longer self-screened and this manifests as an effective 