# Egyptian fraction construction research library

Family 025: Short Egyptian fractions. First application triage, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Symbolic arithmetic and education tools could explore shorter exact unit-fraction expansions and prescribed denominator appearances.

## Applicability and commercial boundary

Term count O(log log b) does not control denominator bit length or construction runtime. The scope’s constants and doubly exponential bounds can be impractical.

## 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 the algorithm and denominator growth before proposing a compact rational representation.

## Evidence scope

The catalog statement was individually reviewed. Main-paper abstracts and available selected formal scope notes were also inspected. No independent Lean verification was run. Source revision `fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb`. See [source metadata](source.json).

[Short Egyptian fractions](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Short-Egyptian-fractions-September-25-2026/Short-Egyptian-fractions-September-25-2026.pdf).