OpenAI reports the higher-dimensional Erdős distinct-distance bound
- Mathematics
For every fixed dimension d≥3, a constant c_d>0 makes every n-point set of distinct points in ℝᵈ determine at least c_d n^(2/d) distinct distances.
OpenAI reports the higher-dimensional Erdős distinct-distance bound
- Mathematics
For every fixed dimension d≥3, a constant c_d>0 makes every n-point set of distinct points in ℝᵈ determine at least c_d n^(2/d) distinct distances.
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Understand the problem ↓Understanding the problem
Read the background
For every fixed dimension d≥3, a constant c_d>0 makes every n-point set of distinct points in ℝᵈ determine at least c_d n^(2/d) distinct distances.
Why it matters
If correct, resolves the higher-dimensional Erdős distinct-distances conjecture at the optimal exponent.
What counts as progress
Must n points in every fixed higher dimension determine on the order of n^(2/d) distinct distances?
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OpenAI reports the higher-dimensional Erdős distinct-distance bound