Limits RegistryPUBLIC RECORD
Limits RegistryAubrey de Grey, a biogerontologist working as a mathematics hobbyist, found an explicit 1,581-vertex unit-distance graph in April 2018 that cannot be properly colored with only 4 colors, raising the long-standing lower bound on the Hadwiger-Nelson problem from 4 to 5 for the first time since the bound was established in the 1950s. The exact chromatic number of the plane remains an open problem, bounded between 5 and 7.
The question, scope, and sources behind this Registry record.
Aubrey de Grey, a biogerontologist working as a mathematics hobbyist, found an explicit 1,581-vertex unit-distance graph in April 2018 that cannot be properly colored with only 4 colors, raising the long-standing lower bound on the Hadwiger-Nelson problem from 4 to 5 for the first time since the bound was established in the 1950s. The exact chromatic number of the plane remains an open problem, bounded between 5 and 7.
The minimum number of colors needed to color every point in the Euclidean plane so that no two points at exactly unit distance apart share the same color is at least 5 (the exact value remains unknown, with an upper bound of 7).
Change a parameter to stress-test whether a proposed result is still inside the published specification. This is an audit aid, not a proof checker.
This record has no editable parameters. Read the formal question and assumptions before challenging it.
Current frontiers derived from accepted Claims.
An observed or demonstrated result; no opposing bound is implied.
The frontier is not sacred
Most progress starts with a disagreement that survives contact with evidence. If you can push the known lower bound up or pull the upper bound down, show us the work.
≥ when you have shown that at least this value is achievable.≤ when you have shown that anything above this value is impossible.No vibes. State the value, define the scope, and link the paper, proof, code, or reproduction that lets another person check it. Editors review every challenge before the public record changes.
Challenge this recordAssertions tied to evidence, attribution, and review.
The frontier as it changed over time.
Only accepted Claims matching the current specification contribute to the displayed bounds. Strict inequalities remain open; contradictory Claims require editorial review.
1 accepted Claim, with 1 linked evidence records.
Permanent ID limitsregistry.com/limits/LR-HADWIGER-NELSON-LOWER-BOUND
No active verified bounties are linked to this Limit.
View verified bounty tracker ↗No accepted machine-checked reproductions are recorded for this Limit.
Limits Registry. LR-HADWIGER-NELSON-LOWER-BOUND. Hadwiger-Nelson problem — chromatic number of the plane, lower bound raised to 5. 2026.