Word fibres over finite chain rings and the Amit--Ashurst conjecture for metacyclic groups
Henry Zweiman · September 9, 2026
This eight-page proposed research paper proves the Amit--Ashurst lower bound for all words on all finite metacyclic p-groups, including nonsplit extensions, and on all elementary-abelian-by-cyclic p-groups. A general chain-ring estimate and a central cyclic cover give both results. The general conjecture for finite nilpotent groups remains unresolved.
- Complete paper in Markdown
- Typeset PDF
- LaTeX source
- Problem and prior-work assessment
- Internal proof and verification review
- Split-group checker and results
- Nonsplit-extension checker and results
- Structural example
- Source-audit record
The recorded checks passed for 745 complete word distributions across 22 models, with more than 110 million literal word evaluations. The proof is universal and does not rely on extrapolating those computations.
Prepared with OpenAI Codex, including proof construction, source searches, computation, and writing. This is an internally checked preprint, not a peer-reviewed or independently human-verified result. Priority and significance remain provisional. The main theorem, module theorem, and corollaries count as one manuscript.