# Gaussian distribution of LMOV numbers

## TL;DR

The paper discovers that LMOV numbers, which count BPS state degeneracies in topological theories, follow a Gaussian distribution across genus and are characterized by only three parameters, suggesting a possible compositeness of BPS states.

## Contribution

It introduces a novel Gaussian distribution pattern for LMOV numbers and proposes a new interpretation of BPS states as potentially composite objects.

## Key findings

- LMOV numbers are randomly distributed in genus.
- LMOV numbers are well parameterized by three parameters.
- This pattern suggests BPS states may be composites.

## Abstract

Recent advances in knot polynomial calculus allowed us to obtain a huge variety of LMOV integers counting degeneracy of the BPS spectrum of topological theories on the resolved conifold and appearing in the genus expansion of the plethystic logarithm of the Ooguri-Vafa partition functions. Already the very first look at this data reveals that the LMOV numbers are randomly distributed in genus (!) and are very well parameterized by just three parameters depending on the representation, an integer and the knot. We present an accurate formulation and evidence in support of this new puzzling observation about the old puzzling quantities. It probably implies that the BPS states, counted by the LMOV numbers can actually be composites made from some still more elementary objects.