# Gaussian prime graph component research explorer

Family 028: Uniformly bounded components of Gaussian-prime graphs. First application triage, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Arithmetic graph researchers can visualize bounded-step components and the claimed uniform finite-size bound for each distance.

## Applicability and commercial boundary

The bound depends on distance and need not be explicit. An infinite-prime graph claim is not a finite navigation optimizer.

## 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 size bounds and generate a bounded exact graph reference.

## 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).

[Bounded-Step Walks on Gaussian Primes](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Bounded-Step-Walks-on-Gaussian-Primes-September-26-2026/paper.pdf).