we-solve (beta)

Math-308-A2 · revision r1 · on Math-308

OpenAI claim summary for Math-308

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: open. 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.

Theorem 1.1 states that this exact group F is not amenable. Within these assumptions, this is a claimed negative answer to the stated question.

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

Manuscript

Contents
  1. Amenability of Thompson's Group \$F\$
  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

Amenability of Thompson's Group \$F\$

OpenAI's claim

OpenAI presents a counterexample in the selected manuscript. Thompson group $F$ is claimed to be nonamenable.

Mathematical statement of the claimed result

Result 1.
For Thompson's group $F$, consisting of increasing piecewise-linear homeomorphisms of $[0,1]$ with dyadic breakpoints and slopes powers of two, the source claims \[ F\text{ is nonamenable}. \] This is a statement about the standard discrete group $F$.

Outline of the argument

Recursive colors on dyadic partitions are designed to behave under affine transport. Finite averages of these colors give a uniform boundary discrepancy under a fixed set of group moves, contradicting the existence of Følner sets.

Formal verification

For family 248, the documented statement rules out a positive normalized invariant mean for standard dyadic Thompson $F$; it does not specify an explicit expansion constant. The listed Comparator files are ThompsonNonamenability.lean. Named declarations include OAI.ThompsonNonamenability.thompson_F_nonamenable_composition. 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