Official journal edition: counterexample comparison

21 October 2026. Coordinator source comparison of the user-supplied official PDF, separate from native model assessments. The explicit counterexample was supplied by Astra (as identified by the user); the all-integer shortest-vector argument and matrix calculations were checked locally. This does not claim discovery priority.

The same counterexample refutes the published Theorems 1.2 and 1.3 on p. 192. Their critical Diophantine threshold, time window, matrices and quantifiers agree with the checked arXiv v6 statements. The removal step on p. 203 also has the demonstrated failure. This is a false-statement finding, stronger than an unresolved proof gap. It does not refute every corollary or certify an amended theorem.

Frozen edition and scope

Lei Yang, Effective version of Ratner's equidistribution theorem for SL(3,R), Annals of Mathematics 202 (2025), 189–264; DOI 10.4007/annals.2025.202.1.3. The user supplied ratner.pdf from the project root. The unmodified campaign snapshot is paper-journal.pdf, 76 physical pages, SHA-256 fe44b57f5aa5f50884b4a126da589fe38029f1a3035f9c57bd1e325c031d9e4f. Physical page 1 is printed page 189.

The coordinator compared extracted text and visually inspected the rendered pages below. This is a targeted comparison, not a claim that every line of the journal and preprint is identical.

Journal location	Checked content	Consequence
p. 191	Both vector and exterior-square tests defining the thick part; matrices u, a, a0	The dual-lattice and fixed-vector calculations apply to the journal conventions.
p. 192, Theorems 1.2–1.3	Threshold exp(-abs(ell)/3), window 0.99t to 1.01t, universal starting-point quantifiers and full Haar target	The explicit counterexample applies to both published formulations.
p. 201, Proposition 4.1	Printed endpoint hypothesis uses nonmembership	The separate reversed-condition issue also occurs in print; correcting it would not remove the main counterexample.
pp. 202–203	Parameter definitions, Definition 6.1 and (6.7)	The permitted translate removes every point of the initial orbit segment for all sufficiently large t.
p. 194	Curve proof uses intervals of size exp(-t/2) and claims an exponentially small approximation	The checked rescaled quadratic remainder remains a proof-level scaling objection, not a counterexample to the curve corollary.

The complete journal PDF is included in the reading materials; rendered pages and extracted text were checked.

Why the contradiction transfers

For

$$g=\begin{pmatrix}2&2/3&0\\0&1&0\\0&0&1/2\end{pmatrix},\qquad \Lambda=g\mathbb Z^3,$$

the four exact shortest lengths, for L at least 10, are

$$\lambda_1(a_0(L)\Lambda)=\tfrac12e^{-L/6},\qquad \lambda_1((a_0(L)\Lambda)^*)=\tfrac32e^{-L/3},$$

$$\lambda_1(a_0(-L)\Lambda)=2e^{-L/3},\qquad \lambda_1((a_0(-L)\Lambda)^*)=e^{-L/6}.$$

Both signs therefore pass the published thick-part tests with at least a factor 3/2 margin. The original counterexample check proves these minima over all integer vectors; finite-box computations are only sanity checks. The exact results verify inversion, the exterior-square/dual identification and the required action identities.

Every orbit lattice a(t)u(r)Lambda contains the same vector 2e1. The locus of lattices containing this prescribed vector is closed and proper. A fixed nonzero nonnegative smooth compactly supported function in its complement has orbit integral zero and strictly positive Haar integral. Its discrepancy cannot tend to zero. This contradicts Theorem 1.3 while its exceptional alternative is absent. Applying Theorem 1.2 to x_t=a(t)gGamma gives the same contradiction; its quantifiers permit this starting point to depend on t.

For Definition 6.1, take ell=0 and ell'=-2 delta1 t. Every initial orbit lattice then contains a vector of length 2 exp(-2 delta1 t/3), eventually smaller than beta^(1/4). Thus F is empty, contradicting the small discarded-proportion assertion in (6.7).

Independent panel and limitations

The frozen native panel still receives arXiv v6 source only: one complete-source Sol assessment and eight targeted Sol/Opus/Gemini assessments over four obligations. Its initial prompts contain neither the supplied Astra analysis nor these coordinator findings. No native prompt or hash-locked source was changed to add the journal PDF. The comparison above establishes edition applicability for the specified passages independently of what the models report.

The earlier source manifest, reading guide, exact-check output and counterexample note record journal unavailability at preparation time. They remain unchanged as historical receipts; this dated supplement supersedes that availability limitation only. The original received-date cutoff remains 26 September 2022. No later theorem is needed for the elementary counterexample. No complete repair, statement about every application, exhaustive erratum search or publication priority is established here. This publication presents the targeted journal comparison.

Source record

Additional supporting archive items are identified in the original report. View the manuscript hashes and repository snapshot.