# Noether Converse: all identically conserved geometric tensors are metric variations of an action in (at least) D = 2

## TL;DR

This paper proves that in two-dimensional spacetime, all geometric tensors that are identically conserved originate from metric variations of an action, confirming a long-standing conjecture.

## Contribution

It establishes the century-old Noether converse conjecture for D=2 and suggests it likely holds in higher dimensions.

## Key findings

- Confirmed the conjecture for D=2
- All conserved geometric tensors derive from an action
- Supports the conjecture's validity in higher dimensions

## Abstract

The title's century-old conjecture is established fpr D=2 and is likely for all D.