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Math-417-A2 · revision r1 · on Math-417

OpenAI claim summary for Math-417

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.

The result supplies the conclusion in this problem with its displayed hypotheses and quantifiers. The broader statements and applications in the manuscript are kept separate from the particular question above. The supporting result is manuscript 1 (family 005; 2026-09-24).

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

Manuscript

Contents
  1. Irrationality of Catalan’s Constant
  2. OpenAI's claim
  3. Mathematical statement of the claimed result
  4. Manuscript 1.
  5. Outline of the argument
  6. Formal verification
  7. Status caveat
  8. Sources

Irrationality of Catalan’s Constant

OpenAI's claim

OpenAI presents the following claims relevant to this question, with manuscript numbers following paper order in Sources. In manuscript 1 (family 005; 2026-09-24), the asserted result is that Catalan's constant is irrational.

Mathematical statement of the claimed result

Manuscript 1.
The claimed irrationality assertion is \[ G=\sum_{n=0}^{\infty}\frac{(-1)^n}{(2n+1)^2}\notin\mathbb Q. \] This is Catalan's constant, defined by its absolutely convergent series.

Outline of the argument

For manuscript 1 (family 005; 2026-09-24), polynomial moment rows are arranged so that contact conditions eliminate the unwanted zeta value. A nonzero determinant is bounded at the real place and at finite primes, with a separate two-adic calculation; denominator clearing makes these bounds contradictory under rationality.

Formal verification

For manuscript 1 (family 005; 2026-09-24), OpenAI lists Lean statements for this assertion: Catalan's constant is irrational.

The central assertion is within the documented formal scope; the additional applications retain their own scope limits.

The linked family Comparator checks are Catalan.lean.

Their named declarations include OAI.InternalCatalan.catalan_irrational.

This site has not executed the Lean code. Described statement coverage is not an independent proof check.

Status caveat

The manuscripts were produced by an internal OpenAI model. OpenAI cautions that results without formalization can contain mistakes. This site has not independently checked the proofs; the label records the scope of OpenAI's claim.

Sources