Scope, prior work, and admission assessment

The exact question is Dramburg, arXiv:2609.03288v1, Question 6.2, PDF page 10. Definition 1.1 specifies the standard, locally finite and semiconnected hypotheses. The earlier MathOverflow question 479788 (September 29, 2024) explicitly allows an algebraically closed ground field of characteristic zero. Both primary statements were read on September 9, 2026. No answer is displayed on the retrieved MathOverflow page. Targeted searches located no later resolution of this exact split Koszul case; a negative search is not proof of historical novelty.

The theorem supplies an explicit counterexample over C, and a uniform extension over every field. Its center has a presentation by two quadrics, and the matrix algebra is Koszul. The finite-jet consequence uses one fixed algebra and is included in the same paper. This gives a concrete boundary for attempts to choose homogeneous primitive systems in graded representation theory.

Important prior work is not claimed as new:

• Petersson, Idempotent 2-by-2 matrices, Sections 5 and 6: line modules, inner conjugacy and the Picard obstruction to automorphisms. The author PDF's relevant sections were read directly.
• Kanwar--Leroy--Matczuk, Idempotents in ring extensions, J. Algebra 389 (2013): polynomial and formal conjugacy results, and a quaternion example based on Ojanguren--Sridharan. The primary introduction and page-9 example were retrieved through web indexing; direct local download timed out. The paper does not claim to be the first obstruction over an arbitrary ground field. The quaternion example does not itself supply a split example over an algebraically closed field.
• De Jong, Graded idempotents (2013): line-bundle construction in a Laurent-graded extension. That displayed degree-zero algebra is not finite-dimensional semisimple.
• The quadratic-Groebner-basis criterion for Koszulness, cited to Conca, is classical.

The proposed contribution is the explicit counterexample meeting all the grading assumptions with a split matrix degree-zero algebra over any field, plus the fixed-algebra arbitrary-jet family. No full computation of the Picard group, new general patching theorem, classification of arbitrary automorphism orbits, or result for normal centers or finite global dimension is claimed.

This is a concise research note answering a specific literature-posed question, rather than a broad classification theorem. Citation potential cannot be certified or predicted. It is admitted as one internally checked proposed manuscript; external proof review, exhaustive priority checking and significance assessment remain outstanding. The program's global count of certified significant open-problem solutions remains uncertified.