OpenMathematics StatisticsDirect arrangement
No prize from Recensorium - recognition and leaderboard standing only. Erdos attached a standing prize to the exact conjecture, administered off-platform by the Combinatorics Foundation and settled after journal publication; its current amount and status are listed at erdosproblems.com. Recensorium stakes nothing and is not party to it.
A peer-reviewed proof that every set of 2^(n-2) + 1 points in general position in the plane contains n in convex position - the exact Erdos-Szekeres conjecture; OR a determination of f(n) for a specific n where the exact value is open; OR a strict improvement to the best published upper bound on f(n) for such an n. The submission must state which n it addresses and what the best published bound for that n is, with a citation. f(n) is settled for n at most 6, f(6) = 17, and a submission there scores nothing. EVIDENCE FOR A COMPUTATIONAL RESULT. A determination of f(n) by search must state how configurations were enumerated up to the relevant equivalence, how many were examined, and why the enumeration is complete. A search that reports no counterexample without establishing its own completeness is not a determination and does not score. [certificate: none]
The happy ending problem asks for f(n), the smallest number of points in general position in the plane that forces n of them into convex position. Erdos and Szekeres conjectured f(n) = 2^(n-2) + 1. It is verified for n up to 6: f(6) = 17, settled by Szekeres and Peters in 2006 by an exhaustive computer search. Beyond that the exact value is unknown for every n. The best published general upper bound is Suk's 2^(n + o(n)) from 2016, which reaches the conjectured order of magnitude without pinning down any individual value. Both halves are live. The conjecture in general is a proof problem. A single value of f(n) is a computational one, and the 2006 result shows that a case can be settled outright that way. References: Suk, On the Erdos-Szekeres convex polygon problem (arXiv:1604.08657); Szekeres and Peters, Computer solution to the 17-point Erdos-Szekeres problem (2006).
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.
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Opened Jul 28, 2026