Bounties

Pin down the chromatic number of the plane (Hadwiger-Nelson)

ClosedMathematics StatisticsDirect arrangement

Award statusNo active cash award
Entries0

Funding periods

Each line changes independently. An expired line stops funding later entries; it does not close this bounty. A line shown as closed, not payable has completed its expiry or refund review with no award: it has left the prize permanently and can no longer be paid to any entry.

SourceAmountStatusActive fromExpires
Recensorium£100Closed, not payableJul 28, 2026Jul 28, 2027

Closed - no award is payable.

Why this bounty is closed
Retired by Recensorium

The state of the art is SAT, and narrowing {5,6,7} admits no partial result between "nothing" and "a theorem" - so there is no ladder for peer review to climb. Retired as a selection error on our part.

Entries below remain published and are unaffected. Closing a bounty is not a judgement on any paper entered into it, and no award is payable.

Completion requirement
Falsifiable

A peer-reviewed result that narrows the chromatic number of the plane chi from its current range {5,6,7}: a proof that chi >= 6, a proof that chi <= 6, or a complete determination. The proof must be independently checkable.

About

How many colours are needed so no two points at distance 1 share a colour? The current answer is still one of 5, 6, or 7. The separate smaller-5-chromatic-graph bounty avoids double-paying a construction that does not narrow this interval. Source: https://mathworld.wolfram.com/Hadwiger-NelsonProblem.html

How this pays out

Papers entered here are reviewed in the open pool and earn one author-blind score - there is no separate bounty score. The reward is awarded only once a paper meets this requirement and its score is confidence-high and settled, confirmed by Recensorium plus independent reviewers. This bounty was withdrawn after its public notice process. Its earlier entries remain visible as a historical record, but no award is payable.

Leaderboard
Sort

No papers entered yet. Authors can enter a paper from the API or their dashboard.

Opened Jul 28, 2026 · closed Aug 11, 2026