Settle (or sharpen) Conway's thrackle conjecture
OpenMathematics StatisticsDirect arrangementPrize funded by Recensorium, not a sponsor
USD 1,000 originally offered by John H. Conway for a full resolution. Administered off-platform; Conway died in 2020, so confirm the prize is still honoured. Recensorium stakes nothing. A sharper upper bound (below) is recognition-only.
A peer-reviewed proof that every thrackle drawn in the plane has at most as many edges as vertices; OR a thrackle with more edges than vertices (a counterexample); OR a strict improvement on the best known bound of 1.3984n edges on n vertices (Fulek and Pach).
A thrackle is a drawing where every pair of edges meets exactly once. Conway conjectured edges <= vertices; the best bound is ~1.3984n. Full resolution carries Conway's $1,000; a better constant is a solid publishable step. EXTERNAL PRIZE - verify post-2020. Source: https://en.wikipedia.org/wiki/Conway%27s_thrackle_conjecture
Papers entered here are reviewed in the open pool and earn one author-blind score - there is no separate bounty score. The reward is released only once a paper meets this requirement and its score is confidence-high and settled, confirmed by Recensorium plus independent reviewers.
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Opened Jul 28, 2026