Fourth-moment conjectures for Rademacher sums

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Corrects Fourth-moment conjectures for Rademacher sums →

Supersedes Fourth-moment conjectures for Rademacher sums →

Fourth-moment conjectures for Rademacher sums evidence for this event

Four results, and the first is partly a refutation. Jakimiuk conjectured $c_p = \mu_p - 1$ is optimal for every $p \ge 3$; the paper proves that for $p \ge 4$ and gives a counterexample for every $2 < p < 4$, so the conjecture is false as posed and the corrected range is $p \ge 4$. The witness is the two-coordinate vector $S_2 = (\varepsilon_1+\varepsilon_2)/\sqrt2$. The Baranski-Murawski-Nayar-Oleszkiewicz flat-point conjecture is proved outright, in the stronger form that $x \mapsto \|x+S_n\|_p/\|x+S_n\|_4$ is strictly decreasing on $[1,\infty)$ for every real $p \ge 5$; that range is the one they conjectured, so nothing is left over. Jakimiuk's second conjecture, dimension-free quadratic stability at $p = 3$, is proved with an explicit constant, though the optimal constant there is only bracketed and stays open. The paper also records the exact fixed-$q$ moment and Laplace-transform envelopes, from which coefficient-sensitive tail bounds follow. parent of this event

Fourth-moment conjectures for Rademacher sums parent of this event

Jakimiuk, Stability of Khintchine inequalities with optimal constants (Bernoulli 32, 2026) evidence for this event

Baranski, Murawski, Nayar, Oleszkiewicz - On the optimal Lp-L4 Khintchine inequality evidence for this event

This event attributed to Jian Qian

VibeMathed record: Fourth-moment conjectures for Rademacher sums evidence for this event

This event attributed to ChatGPT 5.6 Sol

This site's numerical check of Theorems 1.1 and 1.3 and of Proposition 4.3 evidence for this event

This event attributed to Peigan Gao