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Paper Referee

Renewal and changes of law for critical honeycomb walks

OpenAI preprintReviewed version: September 26, 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 signed-cylinder citation points to the wrong propositions

Where the issue occurs

Section 11.1, opening paragraph identifying the signed-cylinder inputs · p. 71

The finite inputs come from the signed cylinder representation [22, Section 2, Propositions 9.1–9.2 and Theorems 1.1–1.2].

Only the proposition locators are wrong here: the corresponding results in the cited paper are Propositions 10.1 and 10.7.

Issue & evidence

The signed-cylinder citation in the opening paragraph of Section 11.1 has incorrect proposition numbers. In the supplied cited PDF, the boundary-arch result is Proposition 10.1 (page 76), and the interior-visit comparison is Proposition 10.7 (statement on page 89, proof through page 90). These results support the corresponding inputs in Equation (66) and the following interior-visit comparison under matching conventions.

Proposed repair by OSVerify

In that citation, replace “Propositions 9.1–9.2” with “Propositions 10.1 and 10.7”. Retain Section 2 and Theorems 1.1–1.2 in that citation. This corrects the locators without changing the stated finite inputs or their downstream uses.

Related context
  • Downstream use Section 11.1, Equation (66) and the following interior-visit comparison

    States the finite boundary and interior-visit inputs supported by the corrected citations. These statements are not identified as errors.