add picket-fence hamiltonian tutorial

[iamkagwe]

A new tutorial notebook examples/picket_fence.ipynb ( see #145 ) that demonstrates how to build a standard “picket-fence” pairing (Richardson–Gaudin) Hamiltonian using the HamRG class.

[PaulWAyers]

@RichRick1 any thoughts on this? I'm happy to look at it next week too.

[RichRick1]

I would be interesting to compare results with ones available in literature and include FCI calculations too

[iamkagwe]

@PaulWAyers @RichRick1 I submitted the initial picket-fence tutorial two months ago, referring to previous discussion and other tutorials. Without feedback or assigned issues, I noticed several duplicate PRs were opened after mine, turning this into competition rather than collaborative work.

#187 demonstrates valuable rigor (literature benchmarking + FCI validation) that should be the standard moving forward. Since you're happy with the merge of #187, I think this should be closed, and the other tutorials should be edited to match.

[RichRick1]

@iamkagwe we apologize for delaying reviewing your pull request. Unfortunately, we do need a way to access potential contributors, that's why some duplication in pull requests may occur. We agree that the current overlap in pull requests isn't ideal for a collaborative environment. We’re adjusting our evaluation and onboarding procedures now to ensure that contributors have clear feedback and that efforts aren't duplicated. We appreciate you bringing this to our attention.