# Emergent unitarity from the amplituhedron

## TL;DR

This paper proves perturbative unitarity in $
=4$ SYM using the geometric structure of the amplituhedron, applicable to all amplitudes regardless of multiplicity, loop order, or MHV degree.

## Contribution

It provides a geometric proof of unitarity in $
=4$ SYM based on the amplituhedron, extending to all multiplicities, loops, and MHV degrees.

## Key findings

- Perturbative unitarity is derived from the amplituhedron geometry.
- The proof applies universally to all amplitude configurations in $
=4$ SYM.
- The approach links geometric structures to fundamental quantum field theory principles.

## Abstract

We present a proof of perturbative unitarity for $\mathcal{N}=4$ SYM, following from the geometry of the amplituhedron. This proof is valid for amplitudes of arbitrary multiplicity $n$, loop order $L$ and MHV degree $k$.