# Current priority statement — version 1.0.1

26 September 2026. This statement supersedes the historical access/status
wording in the version 1.0.0 manuscript and dated audit reports.

**Historical priority remains unresolved. No first-resolution claim is made,
and the preprint does not assert that the question remained open at publication.**
The paper proves an explicit negative answer to Kurose's printed Question 3(e).
That mathematical assertion is separate from the historical question of who
first observed or published the answer. An earlier answer or implicit resolution
in unread sources cannot be excluded.

The documented searches found no earlier explicit answer within their scope:
the initial audit, a bounded citation/index follow-up, and complete reading of
three supplied papers. The citation inventory contains 175 raw records including
duplicates; title screening is not full-text review. Nine follow-up PDFs totaling
193 pages were keyword-screened with relevant passages read. The three supplied
papers were separately read in full. This is not an exhaustive literature audit.

## Established ingredients and attribution

- Radial integrability for Levi–Civita connections is a classical consequence
  of the first variation of energy (Gauss lemma).
- Kurose's 1994 curvature/projective criterion is established background.
  The manuscript independently derives its necessary curvature obstruction.
- The exact non-self-dual deformation is the standard statistical
  (-1)-conformal change in Matsuzoe (1999), p.178, equation (2.1),
  [DOI 10.32917/hmj/1206125160](https://doi.org/10.32917/hmj/1206125160).
  The revision credits this earlier, directly inspected source.

Combining known facts gives the counterexample. The preprint offers an explicit
application to the printed question and a concise, checkable presentation;
novelty of the ingredients or historical priority of the assembled answer is
not claimed.

## Principal remaining source gaps

1. Kurose (1999), *1-conformally flat statistical manifolds and their realization
   in affine space*, Fukuoka University Science Reports 29(2). Sources disagree
   between pp.209–219 and pp.201–219; the original remains unread and no DOI was
   located.
2. Binder–Simon (2000), *Progress in affine differential geometry—problem list
   and continued bibliography*, Geometry and Topology of Submanifolds X, pp.1–17,
   [DOI 10.1142/9789812792051_0001](https://doi.org/10.1142/9789812792051_0001).
3. The full content or notes of Kurose's 2016 talk on Gauss-type lemmas and
   generalizations of Hessian structures. A program is not the complete talk.

Narrower uninspected citation leads, the 2008 tangent-bundle paper, and a private
letter cited by Matsuzoe also remain outside the audit. No claim about their
contents follows from inability to obtain them. No outreach was prepared or made.

## What changed since version 1.0.0

The live database annotations were successfully read on 23 September 2026.
Its partial-status label refers to machine-generated research progress; the
expanded report identifies no verified proof or counterexample. This is not
evidence establishing priority or continued open status. Matsuzoe 1999, Matsuzoe
2010, and Kurose 2024 (online 2023) were then read in full; none explicitly gives
the answer or cylinder example, and their results do not contradict the proof.
Version 1.0.1 incorporates these findings into the paper, site, and upload kit.
The mathematical construction and proof are unchanged.

Detailed evidence is preserved in the repository and source archive:

- [Initial audit](https://github.com/AlecKriebel/Math/blob/main/radial_statistical_counterexample/reviews/priority_audit.md).
- [Citation and index follow-up](https://github.com/AlecKriebel/Math/blob/main/radial_statistical_counterexample/reviews/priority_followup.md).
- [Complete reviews of the three supplied papers](https://github.com/AlecKriebel/Math/blob/main/radial_statistical_counterexample/reviews/priority_supplied_papers.md).
- [Successful database recheck](https://github.com/AlecKriebel/Math/blob/main/radial_statistical_counterexample/research/DATABASE_RECHECK.md).