Exact 2026 overlap: Zhang–Zhang, versions 1 and 2

Date checked: 17 September 2026.

Correction to the earlier audit

The earlier audit was incomplete. The file sources/sublinear-v1.html had been retrieved, but its explicit planar superlinear claim was not incorporated into the manuscript or the publication assessment. That omission is corrected here. Merely downloading a source is not a completed source comparison.

Chengxiang Zhang and Xu Zhang, Uniqueness of bound states for sublinear elliptic equations, arXiv:2606.17840, directly addresses the Q66 target in Section 6 despite its title.

• Version 1: submitted 16 June 2026, 12:10:07 UTC.
• Version 2: submitted 27 June 2026, 08:52:28 UTC; latest version shown on the arXiv record when checked.
• Version 1's abstract explicitly announces the superlinear planar extension.
• Version 2's abstract omits that announcement, but Section 6 remains present and still asserts that Tang's Theorems 1 and 2 hold for , .
• After replacing MathML by its TeX alttext and normalizing inter-element spacing, the complete Section 6 text in v1 and v2 is identical. Local extracts are saved as sublinear-v1-section6.txt and sublinear-v2-section6.txt.

Thus the abstract edit is not evidence that the planar claim was withdrawn. No withdrawal notice or identified mathematical correction was found in the version record or the scoped searches.

Mathematical read scope

Section 6 was read in full and compared against Tang's phase-transition proof, especially Lemma 5.6 and the order of Steps 1–5 in Section 5.7. Its central observation is that Tang's auxiliary equals in dimension two; the latter is positive under the hypotheses established before the final step. At a possible negative-side minimum of , a paired-level integral has nonnegative integrand and a positive integral, providing the needed positivity. The strict decrease of supplies the other planar replacement.

This is a statement of the read scope and proposed mechanism, not an independent verification of every dependency in the full Zhang–Zhang/Tang argument. No claim of peer review or journal acceptance is inferred from an arXiv posting.

Consequence for Q66

There are now two precise pre-existing statements of the whole-plane target: CGY11 Theorem 1.1 and Zhang–Zhang 2026 Section 6. The latter explicitly frames its argument as a completion of Tang's planar case and also claims the stronger Theorems 1 and 2.

The local comparison reconstruction cannot be presented as the first announced proof of the planar conjecture. A contribution would have to be assessed as a distinct proof or correction, with both sources credited. Any claim that a substantive gap leaves the target open now needs to address the exact latest 2026 argument as well as the 2011 paper.

Published in the GitHub archive as P55 at the author's request. This archival identifier does not certify a new theorem, correctness, or priority. The exact overlap changes the priority assessment; it does not itself prove or disprove the manuscript's mathematics.

Scoped searches in this continuation

Queries included the CGY authors with “2011 mistake”, “bound states gap uniqueness”, and Tang/CGY/two-dimensional uniqueness; and 2606.17840 correction OR error OR gap OR withdrawn. Search-result absence is not proof that no correction exists. The authoritative version claim above comes from the arXiv record and full v1/v2 HTML, not from secondary summaries.