The Margulis–Platonov conjecture over number fields

OpenAI

For an absolutely almost simple simply connected group G over a number field k, every noncentral abstract normal subgroup of G(k) is the inverse image of an open normal subgroup of the product of G(kᵥ) over anisotropic nonarchimedean places.

Sources for this record

What was already known

The isotropic and inner type A cases, among others, were known; anisotropic outer A, trialitarian D₄ and E₆ cases remained.

AI involvement AI-led

OpenAI is credited as author, and its release attributes the mathematical results in this collection to an internal frontier model. The interaction for this theorem is not disclosed.

An AI institution is the manuscript's credited author and the official release attributes repository results to its model; autonomy is not established.

Importance Major

Would settle the number-field Margulis–Platonov conjecture in full.

Limitations

A proof manuscript is available, but no named complete human check or machine verification of this exact number-field theorem is documented.

Technical verification Reported

A full proof manuscript exists, but neither a named completed human check nor a machine check of this exact theorem was documented in the reviewed sources.

Human understanding Few

Default for missing evidence: the manuscript outlines its strategy, but no named human explanation of this specific model argument was located.

Correction and publication history

2026-10-18 · publication

The number-field theorem is distinct from the separately reported function-field result.

Read this published revision