We consider a very wide class of models for sparse random Boolean 2CSPs; equivalently, degree-2 optimization problems over~${pm 1}^n$. For each model $mathcal{M}$, we identify the high-probability value~$s^*_{mathcal{M}}$ of the natural SDP relaxation (equivalently, the quantum value). That is, for all $varepsilon > 0$ we show that the SDP optimum of a random $n$-variable instance is (when normalized by~$n$) in the range $(s^*_{mathcal{M}}-varepsilon, s^*_{mathcal{M}}+varepsilon)$ with high probability. Our class of models includes non-regular CSPs, and ones where the SDP relaxation value is strictly smaller than the spectral relaxation value.
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