11.4.3 Can you answer these questions?

11.4.3.1 Mathematica code for PXP Hamiltonian

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=310452

I am looking for a construction of the PXP Hamiltonian in Mathematica and finding its eigenvalues. I know that the Hilbert space is constrained, and a sample code in Python is given inhttps://quspin.... 
[matrix] [linear-algebra] [eigenvalues]
 

asked by Math_hepth https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=105806 Score of 1

11.4.3.2 FoldList while changing List

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=310482

While trying to write a prime sieve using  FoldList I got as far as 
... 
[list-manipulation] [functions]
 

asked by user57467 https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=57467 Score of 1

11.4.3.3 $Pre disables downvalue involving Condition?

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=310589

I notice this when exploring this question, I think it's better to start a new question for it. Consider this toy example: 
... 
[pattern-matching] [core-language] [conditional] [downvalues]
 

asked by xzczd https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=1871 Score of 3