# Unique gating strategy identifier based on the Prime Population System and Gödel Numbers

## TL;DR

This paper introduces a new method to uniquely identify and share cytometry gating strategies using prime numbers and Gödel encoding.

## Contribution

A novel approach combining the Prime Population System and Gödel Numbers to uniquely encode hierarchical gating strategies.

## Key findings

- The Prime Population System identifies gates on bivariate plots effectively.
- Gödel Numbers uniquely encode the sequence of hierarchical gating strategies.
- The method ensures unique identifiers due to the fundamental theorem of arithmetic.

## Abstract

Gating is a fundamental and essential process in cytometry data analysis since it defines cell types of interest. Currently, there is no universally accepted method for representing and sharing gating strategies among software, publications, and repositories. I propose using the Prime Population system combined with a modified version of Gödel Numbers to identify any gating strategy uniquely. The Prime Population System is first used to identify gates on bivariate plots; successively, Gödel Numbers are used to set the sequence of the hierarchical gating strategy. The process results are unique identifiers for any existing and future gating strategy. The unique identifiers hold since according to the fundamental theorem of arithmetic, every natural number other than one either is a prime or is a product of prime numbers, and every nonprime number can be factored into a product of prime in only one way. This method represents a further step towards the arithmetization of cytometry metadata.