Yang-Mills Existence and Mass Gap

### What is the conjecture
Yang–Mills Existence and Mass Gap. Prove that for any compact simple [gauge group](https://en.wikipedia.org/wiki/Gauge_group_(mathematics)) G, a [non-trivial](https://en.wikipedia.org/wiki/Non-trivial) quantum [Yang–Mills theory](https://en.wikipedia.org/wiki/Yang%E2%80%93Mills_theory) exists on R 4 {\displaystyle \mathbb {R} ^{4}} and has a [mass gap](https://en.wikipedia.org/wiki/Mass_gap) Δ > 0. Existence includes establishing axiomatic properties at least as strong as those cited in [Streater & Wightman (1964)](https://en.wikipedia.org/wiki/Yang%E2%80%93Mills_existence_and_mass_gap#CITEREFStreaterWightman1964), [Osterwalder & Schrader (1973)](https://en.wikipedia.org/wiki/Yang%E2%80%93Mills_existence_and_mass_gap#CITEREFOsterwalderSchrader1973) and [Osterwalder & Schrader (1975)](https://en.wikipedia.org/wiki/Yang%E2%80%93Mills_existence_and_mass_gap#CITEREFOsterwalderSchrader1975).

One of the Millennium Problems posed by the Clay Mathematics Institute.

See here for the PDF by the Clay Mathematics Institute:
https://www.claymath.org/wp-content/uploads/2022/06/yangmills.pdf

### Prerequisites needed
A lot of Quantum Field Theory I suppose. If we ever get to state, where we could formalize it in, then we probably would need the Prerequisites from PhysLean.

### [AMS categories](https://github.com/google-deepmind/formal-conjectures/labels?q=ams-)

* ams-81

### Choose either option
- [ ] I plan on adding this conjecture to the repository
- [x] This issue is up for grabs: I would like to see this conjecture added by somebody else

The issue names no target file, test, or entry point. Start by reading the Clay Mathematics Institute PDF and reviewing the stated PhysLean prerequisites; completion would require adding a formal Lean statement of the Yang–Mills conjecture, but the issue does not define an achievable implementation scope.

Written by the indexing model from the issue text.