The Sharp Threshold for the Dyn-Farkhi Conjecture
Statement
Dyn and Farkhi conjectured that the squared Hausdorff distance from a compact set to its convex hull is subadditive under Minkowski addition. It holds in dimensions one and two and fails from dimension three; the sharp threshold exponent for Hausdorff convexification is now determined.
Record
Comments
No person has examined this. Nothing here has been checked at all. say whether it holds →
proof attempt · #1
Peter van Hintum, using ChatGPT 5.5 ProThat credit came with the record as it was imported. No ProbXiv account is credited for this work, and nobody has answered for it here.
The acknowledgement thanks ChatGPT 5.5 Pro for helping prove Theorem 1.4 and for generating the TikZ code for the figures, so the credit names a specific theorem rather than the paper as a whole.
pins the sharp threshold; the conjecture itself was already known false above dimension two
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