# Constant approximation and Flint–Hills reference

Family 017: The irrationality exponent of <i>π</i> is 2. First application triage, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Numerical researchers can record the sharp asymptotic irrationality exponent and series convergence consequence.

## Applicability and commercial boundary

Sufficiently-large denominator thresholds depend on epsilon and may be ineffective. The claim gives no immediate finite floating-point sine error certificate.

## Initial business decision

Research infrastructure or conditional engineering until a computable implementation, effective bounds and a recurring buyer need are demonstrated. No commercial novelty or profitability is established.

## Next verification action

Extract effective constants before claiming improved numerical precision management.

## Evidence scope

The catalog statement was individually reviewed. Manuscript proof and selected formal scope comparison remain queued. No independent Lean verification was run. Source revision `fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb`. See [source metadata](source.json).

[The irrationality exponent of pi is 2](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-irrationality-exponent-of-pi-is-2-September-24-2026/paper.pdf).