{
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  "path": "/report/2026/063",
  "publishedAt": "2026-04-30T15:54:08.000Z",
  "site": "https://eccc.weizmann.ac.il",
  "textContent": "We study two conjectures posed in the analysis of Boolean functions $f : \\\\{-1, 1\\\\}^n ? \\\\{?1, 1\\\\}$, in both of which, the Majority function plays a central role: the \"Majority is Least Stable\" (Benjamini et al., 1999) and the \"Non-Interactive Correlation Distillation for Erasures\" (Yang, 2004; O'Donnell and Wright, 2012). While both conjectures have been refuted in their originally stated form, we obtain a nearly tight characterization of the noise parameter regime in which each of the conjectures hold, for all $n \\ge 5$. Whereas, for $n = 3$, both conjectures hold in all noise parameter regimes. We state refined versions of both conjectures that we believe captures the spirit of the original conjectures.",
  "title": "TR26-063 |  When Majority Fails: Tight Bounds for Correlation Distillation Conjectures | \n\n\tPritish Kamath, \n\n\tRavi Kumar, \n\n\tPasin Manurangsi"
}