Nonsingular systems of equations over arbitrary groups

What OpenAI claims

Proves that every finite system of equations over an arbitrary group whose exponent-sum matrix has full row rank over ℚ has a simultaneous solution in an overgroup, resolving Howie's conjecture. The coefficient group embeds in the presented quotient. A companion proves Kervaire's conjecture: adjoining one generator and one relation cannot trivialize a nontrivial group. (Lean)

Papers (2)

1. Nonsingular systems of equations over arbitrary groups

   5 October 2026 · Preprint, not peer reviewed · PDF

   Every finite nonsingular system of equations over an arbitrary group has a simultaneous solution in an overgroup. This proves Howie's conjecture on nonsingular systems.

2. The Kervaire theorem for groups

   24 September 2026 · Preprint, not peer reviewed · PDF

   We prove that no free product of a nontrivial group with an infinite cyclic group is normally generated by one element. This resolves the Kervaire conjecture positively.

Status

Preprint. The papers have not been independently reviewed. Treat the result as OpenAI's claim until other mathematicians have checked it. If a video exists, it illustrates the statement; it is not the proof.