# Arithmetic packet equidistribution research benchmark

Family 015: Torus-packet equidistribution in prime, quartic, and sextic degrees. First application triage, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Researchers can compare volume-weighted torus packets to the correct Haar limit in prime, primitive quartic and primitive sextic settings.

## Applicability and commercial boundary

Order type, local conditions, weighting and no-escape-of-mass statements do not give finite random sampling accuracy.

## 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 rates and finite packet-generation cost.

## 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).

[Equidistribution of Prime-Degree Torus Packets with Arbitrary Local Type](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Equidistribution-of-Prime-Degree-Torus-Packets-with-Arbitrary-Local-Type-September-24-2026/paper.pdf).