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Paper Referee

A counterexample to the nearby Lagrangian conjecture

OpenAI preprintReviewed version: September 23, 2026

Findings and severity labels come from OSVerify’s internal review and do not necessarily establish that the paper’s main theorem is false.

Major issues 0

No major issues were released in this report.

Minor issues 1

Minor · Issue 01Link

The Porcelli–Smith citation has the wrong theorem number

Where the issue occurs

Section 1.1, paragraph on further necessary conditions for nearby Lagrangians · p. 2

Porcelli and Smith’s Floer-homotopy approach places this normal invariant in the image of the stable Hopf action B(G/O) → G/O [25, Theorem 6].

In the cited version arXiv:2509.21587v2, this factorization is Theorem 1.17 on page 8.

Issue & evidence

The Porcelli–Smith citation has an incorrect theorem number: in the bibliography’s specified arXiv version 2509.21587v2, the stated normal-invariant factorization is Theorem 1.17 on page 8, not Theorem 6.

Proposed repair by OSVerify

Replace [25, Theorem 6] with [25, Theorem 1.17]. This corrects the locator for the stated background result without changing its hypotheses or conclusion.

Related context
  • Background References, entry [25]

    Specifies version 2 of Porcelli–Smith (arXiv:2509.21587v2), the version against which the theorem number is checked.