NP-hardness of p-adic linear regression

$p$-adic linear regression is the problem of finding coefficients $\beta$ that minimise ${\sum }_i\mathrm{\mid }{y}_i-x_i^{\mathrm{\top }}\beta {\mathrm{\mid }}_p$. We prove that computing an optimal solution is NP-hard via a polynomial-time reduction from Max Cut using a regularisation gadget.