GMC(2) - Gaussian Moments Conjecture specialized to dimension 2

### What is the conjecture
A proof for the Gaussian Moments Conjecture (Conjecture 1.1 from Derksen et al. arXiv:1506.05192, 2015), specialized to dimension 2, was recently announced (https://x.com/swe_acc/status/2079881074826420446). That original paper (arXiv:1506.05192) only proved the homogeneous two-variable case. A recent counterexample (not part of this formalization attempt) rules out every dimension greater than or equal to 3 (Long, arXiv:2607.18186).

### Prerequisites needed
None.

### [AMS categories](https://github.com/google-deepmind/formal-conjectures/labels?q=ams-)
* ams-14
* ams-33
* ams-60

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

Start by reading Conjecture 1.1 in Derksen et al., arXiv:1506.05192, together with the issue's dimension-2 specialization and the repository's existing formalized conjectures. No file or test is named; done means adding the specialized Gaussian Moments Conjecture as an accepted formal statement in the repository.

Written by the indexing model from the issue text.