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A local counterexample to the triangle inequality ineq_l1

The inequality s_111(p) - 0.475 Delta_1(p) <= 0.289, which E. Bäumer, V. Gitton, T. Kriváchy, N. Gisin and R. Renner (arXiv:2405.08939, eq. ineq_l1) state should hold for every distribution that is local in the triangle network, fails: a local model with four outcomes per party has Delta_1 = 0 and s_111 = 11/36.

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A local distribution violating ineq_l1

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A fully symmetric triangle-local distribution with p(A = B = C) above 1/4A fully symmetric triangle-local distribution with p(A = B= C) above 1/4A local counterexample to the triangle inequality ineq_l1A local counterexample to thetriangle inequality ineq_l1
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