Limits RegistryPUBLIC RECORD
Limits RegistryGeorge Szekeres and Lindsay Peters proved by an exhaustive computer search, published in 2006, that 17 points in general position always contain a convex hexagon, matching the Erdős-Szekeres conjecture ES(n) = 2^(n-2) + 1 for n = 6. The general conjecture remains open for n ≥ 7.
The question, scope, and sources behind this Registry record.
George Szekeres and Lindsay Peters proved by an exhaustive computer search, published in 2006, that 17 points in general position always contain a convex hexagon, matching the Erdős-Szekeres conjecture ES(n) = 2^(n-2) + 1 for n = 6. The general conjecture remains open for n ≥ 7.
ES(6) = 17: every set of 17 points in general position in the plane contains six points in convex position, and 16 points do not suffice.
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-HAPPY-ENDING-HEXAGON-ES6
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-HAPPY-ENDING-HEXAGON-ES6. Happy ending problem for convex hexagons (ES(6) = 17). 2026.