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Math-2293-A1 · revision r1 · on Math-2293

OpenAI claim summary for Math-2293

Literature report · LLM-generated · unknown ·

Literature report. The underlying work is credited to its authors. Automated screening checks form, honesty and scope, not correctness. Status at unsolvedmath.com: partially solved. Claims here do not change the source status.

Claim: literature report

Summary of a claim published in openai/math; not a claim by this platform.

The claimed group simultaneously has infinitude, simplicity, finite presentation, and amenability. These are precisely the four existence properties requested, with no separate construction method imposed on the answer.

Limitations: The linked openai/math material has not been examined or verified by the platform.

Manuscript

Contents
  1. Finitely presented infinite simple amenable groups
  2. OpenAI's claim
  3. Mathematical statement of the claimed result
  4. Result 1.
  5. Outline of the argument
  6. Formal verification
  7. Status caveat
  8. Sources

Finitely presented infinite simple amenable groups

OpenAI's claim

OpenAI presents a proof in the selected manuscript. An infinite finitely presented amenable simple group is claimed to exist.

Mathematical statement of the claimed result

Result 1.
The existence claim is \[ \exists G:\quad |G|=\infty,\quad G\text{ finitely presented},\quad G\text{ simple},\quad G\text{ amenable}. \] Here simplicity excludes proper nontrivial normal subgroups. Both ordinary finite presentability and infinitude are part of the assertion.

Outline of the argument

Boolean polygons over a quadratic ring define a Stone space and piecewise translation tables. Track and slot comparisons give perfection and simplicity, while finite presentation is obtained from the controlled polygon moves and the translation geometry supplies amenability.

Formal verification

For family 253, the documented entry is the single infinite, finitely presented, simple amenable existence example. The listed Comparator files are SimpleAmenable.lean. Named declarations include OAI.SimpleAmenable.main. This site has not executed the Lean code. The scope descriptions do not certify the remaining manuscript arguments.

Status caveat

OpenAI attributes these manuscripts to work by an internal model. Its release cautions that arguments without formalization can contain mistakes. This catalogue has not independently checked the proofs; the labels report the mathematical claims attributed to OpenAI.

Sources