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It is shown that the neutron matter interacting through Argonne V18 pair-potential plus modern variants of Urbana or Illinois three-body forces is unstable. For the energy of N neutrons E(N), which interact through these forces, we prove mathematically that $$E(N) = - cN^3 + \mathcal{O}(N^{8/3} )$$ , where c > 0 is a constant. This means that: i) the energy per particle and neutron density...