Hadwiger–Nelson Problem
What is the chromatic number of the plane: the smallest number of colors so that no two points exactly distance 1 apart share a color?
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- Donors
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- Verification
Moser spindle and de Grey graph machine-checked
The classical Moser spindle (χ ≥ 4) and a minimized de Grey-type unit-distance graph (χ ≥ 5) were re-encoded and chromatic-number certified for Arbiter's baseline archive.
Verification method
Exact unit-distance embedding certificates plus SAT-based chromatic-number proofs on the finite graphs, archived with bit-exact coordinates.
Checks: Lower bound raised to 5 (de Grey)
Arbiter verification desk
- Validated increment
Lower bound raised to 5 (de Grey)
A unit-distance graph of finite girth forced five colors, lifting the classical 4–7 sandwich to 5–7. The upper bound of 7 from a hexagonal tiling still stands.
Previous best
4 ≤ χ ≤ 7
New certified
5 ≤ χ ≤ 7
Aubrey de Grey (2018) and subsequent simplifications
Also open