Human–ChatGPT collaboration reports harmonic norms over arbitrary complete non-Archimedean fields

Oren Ben-Bassat reports that every polystable representation of a finite quiver over any complete non-Archimedean field admits a split HKKP harmonic norm, without spherical-completeness or value-group restrictions.

Sources for this record

What was already known

The HKKP existence question and split attainment over general complete fields were unresolved in the stated setting. The trivial-valuation case was already covered and is retained for uniformity.

AI involvement AI-centered

The author’s initial arguments contained substantial gaps. Extensive ChatGPT-6.0 Sol conversations produced roughly equal human and AI contributions to the ideas and development, according to the author; Codex and Prism also helped revise arguments and text.

Ben-Bassat says his initial proofs had substantial gaps and that he and ChatGPT made roughly equal contributions to the article’s ideas and development; he selected the examples.

Importance Notable

Removes a substantial field-completeness restriction from a categorical geometric existence problem.

Limitations

The result concerns polystable representations of finite quivers and the paper’s split HKKP norm. The author describes roughly equal human and ChatGPT contributions to the ideas and development. A completed independent or formal proof check is not documented in the reviewed version.

Technical verification Reported

The manuscript gives a proof, but the reviewed version does not document a completed independent or formal check of the scoped existence theorem. Reported is the evidence default, not a failed check.

Human understanding Full

Ben-Bassat describes his role in developing the argument and explains the coercivity, minimization and split-attainment mechanism in the paper.

Correction and publication history

2026-10-18 · publication

Primary-source review under the four independent curation dimensions. This restores the original archived contribution identity without subscriber notification.

Read this published revision