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Letrouit's square-root stability conjecture for Brenier maps from a uniform convex source

Theorem 1.1: for $K$ compact convex with interior in $\mathbb R^d$ , $d\ge2$ , and $Y$ compact, $\|T_\mu-T_\nu\|_{L^2(\rho)}\le C(K,Y)W_2(\mu,\nu)^{1/3}$ for all probability measures $\mu,\nu$ on $Y$ , atomic or not; the exponent $1/3$ cannot be raised even for $K=Y=[-1,1]^d$ and three-atom targets, so Letrouit's square-root conjecture is false and $1/3$ is the sharp uniform exponent. Not shown: sharp exponents in $W_1$ (a sharp $W_1^{1/4}$ bound is attributed to Merigot) or for nonuniform source densities.

Exact FrontierDelta

Prior state unknown→disproved

Scope and record

Occurred: Sep 25, 2026

Delta type: SOURCE CLAIM

Assumptions: VibeMathed verification: lean-checked. Publication: announcement. AI contribution: ai-discovered. VibeMathed editorial classifications, scores, notes, relations, and dataset structure are CC BY 4.0. Source statements and linked content retain their own rights.

Canonical aliases: Letrouit's square-root stability conjecture for Brenier maps from a uniform convex source · Letrouit's Brenier stability conjecture

Confidence: Not scored

Registry verification: lean checked · announcement · candidate

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VibeMathed
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Unreleased internal OpenAI model
model · ai model contributor · OpenAI

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VibeMathed record: Letrouit's square-root stability conjecture for Brenier maps from a uniform convex source

specialist registry · passed

No independent mathematician has checked this yet. Checked here: introduction and Theorem 1.1 read against Letrouit's Conjecture 3 as the manuscript cites it. Lean: the challenge lean/ComparatorChallenges/Brenier.json (solution_module OAI.Analysis.Brenier.Stability, present at the pinned commit) is not in the formalization catalogue lean/formalization.yaml. The statements one_third_stability and one_third_exponent_is_sharp were read here: a uniform constant for $W_2^{1/3}$ stability of unique quadratic optimal maps from the uniform measure on any compact convex body with interior, $d\ge2$ , and, for every exponent above $1/3$ and every constant, two three-atom targets on the cube violating the bound. The second disproves the conjecture; both state the headline. Not rebuilt here.

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Letrouit's square-root stability conjecture for Brenier maps from a uniform convex source

witness · pending

Primary source named by the VibeMathed record. Presence in this import is not an independent mathematical verification.

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Letrouit, Unstable optimal transport maps (arXiv 2510.13265), Conjecture 3

specialist registry · pending

problem-record link supplied by the VibeMathed registry.

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Lean formalization (Brenier stability and sharpness)

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Lean formalization (Brenier stability and sharpness)

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This event attributed to Unreleased internal OpenAI model

Letrouit's square-root stability conjecture for Brenier maps from a uniform convex source evidence for this event

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Letrouit, Unstable optimal transport maps (arXiv 2510.13265), Conjecture 3 evidence for this event

Lean formalization (Brenier stability and sharpness) evidence for this event

VibeMathed record: Letrouit's square-root stability conjecture for Brenier maps from a uniform convex source evidence for this event

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