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on Does the two-dimensional Hubbard model superconduct?

The statement

Consider the repulsive Hubbard model on the two-dimensional square lattice,

H = -t\sum_{\langle i,j\rangle,\sigma} c^\dagger_{i\sigma}c_{j\sigma} + U\sum_i n_{i\uparrow}n_{i\downarrow},

with $U > 0$ . Determine whether the ground state exhibits $d$ -wave superconducting order away from half filling, and map the phase diagram in the $(U/t, \text{doping}, T)$ space.

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Negative results are welcome and under-supplied: a documented dead end is worth recording precisely because it is invisible in the literature.