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  "problem_id": "vibemathed:nazarov-truncation-conjecture",
  "title": "Nazarov's Conjecture on Truncations for Fractional Laplacians",
  "canonical_statement": "Nazarov conjectured that for $s \\in (1, 3/2)$ the quadratic form of the spectral fractional Dirichlet Laplacian strictly increases under $u \\mapsto |u|$ when $u$ changes sign. Proved and substantially generalized, with the same conclusion for the restricted form.",
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