Claims

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2014_12_20_tao: Tao's blog post of 20 December 2014 shows that the Bombieri-Lang conjecture for surfaces over the rationals implies that no dense subset of the plane has all pairwise distances rational; the hypothesis is unproven.

2014_12_31_shaffaf: Shaffaf's refereed paper proves that the Bombieri-Lang conjecture implies that no dense subset of the plane has all pairwise distances rational; the hypothesis is unproven, so the page derives nothing for the standing.

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