# Exact constant provenance teaching module

Family 005: Irrationality of Catalan’s constant. First application triage, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Researchers and educators can record Catalan’s irrationality and the source proof’s exact statement.

## Applicability and commercial boundary

Irrationality gives no improved numerical evaluation, usable approximation error or practical random-number property.

## 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

Inspect effective approximation bounds if a numerical use is proposed.

## 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).

[Catalan's constant is irrational](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Catalans-constant-is-irrational-September-24-2026/paper.pdf).