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Theorem 1.1 constructs arbitrarily large planar sets with a fixed positive exponent gain in their unordered unit-distance count.
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Theorem 1.1 constructs arbitrarily large planar sets with a fixed positive exponent gain in their unordered unit-distance count.
Passage ID: erdos-unit-distances:entry:proof:v1
Source item: proof
Source record: erdos-unit-distances:source:proof:v1
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Problem publication v6
Source assessment
Proved
Fixed positive exponent gain proved
For infinitely many n; unordered unit-distance pairs.
Source date May 20, 2026 · Observed Oct 13, 2026
History
Erdős introduces the planar distance question
History
A model-generated construction refutes near-linear growth
Further reading
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Recorded authorship
OpenAI
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Planar Point Sets with Many Unit Distances
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