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An L3 bound for the trilinear Hilbert transform

OpenAI groups related papers into a “family”. OpenAI’s catalogue describes this one:

Proves that the principal-value trilinear Hilbert transform with shifts \(x-t\), \(x-2t\), \(x-3t\) is bounded from \(L^3(\mathbb R)^3\) to \(L^1(\mathbb R)\). This resolves the L3 exponent case of the standard conjecture for slopes 1, 2, 3.

The release has no Lean statement for this family, so there is no formal statement to compare with the result described above.

What the papers state

The paper states

Theorem 1.1

In An L3 bound for the trilinear Hilbert transform, 5 October 2026

Possible match to OpenAI’s description, selected from shared wording. No review confirming the selection is recorded.

There is a finite constant C such that

\norm{T(f_1,f_2,f_3)}_{L^1(\R)} \le C\prod_{j=1}^3\norm{f_j}_{L^3(\R)} \qquad(f_1,f_2,f_3\in\mathcal S(\R)).

Consequently T has a unique bounded trilinear extension from L^3(\R)\times L^3(\R)\times L^3(\R) to L^1(\R).

The release does not say which paper theorem its catalogue describes. The statement above shares the most wording with the description; the atlas has not reviewed that choice. Identifying it is listed under Questions awaiting review.

Reported proof verification
The release has no Lean statement for this family. The papers are available to read and assess.
Papers and explanations
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Papers

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An L3 bound for the trilinear Hilbert transform

5 October 2026, current edition.

Read it herePDF

We prove that the trilinear Hilbert transform with fixed slopes 1, 2, 3 maps \(L^3(\mathbb R)\times L^3(\mathbb R)\times L^3(\mathbb R)\) to \(L^1(\mathbb R)\), resolving this case of the trilinear Hilbert transform conjecture.

Lean statements

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Independent comparisons and proof-verification reports

Does the Lean express the advertised result?

The release contains no Lean statement for this family, so there is no formal statement to compare with OpenAI’s description.

What these papers cite in the release, and what cites them

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Papers elsewhere in the release that this family’s papers cite

This family’s papers cite no paper elsewhere in the release.

References outside the release

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Explain a result, compare statements or propose a correction

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What people have said

Commentary on this family by others, dated and credited. It is commentary, not a finding.

  • An unsigned public tier list, the OpenAI Math Tier List, classes it as a proof and rates its significance, if it holds up, as “Career-defining publication”. The page says that nothing on it is verified.

    Author not stated. Source

Questions awaiting review

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Identify the theorem the catalogue describes

  • Family 086 No single paper statement clearly matches OpenAI’s description by wording, and no review identifying the intended theorem is recorded. Open the form

State the result in Lean

  • Family 086 The release has no Lean statement for this family. Open the form