I have failed to follow this discussion very closely. That said, to what
extent could frameworks like those that underlie  spring rank
<https://github.com/cdebacco/SpringRank>   or gauge-theoretic  price as
curvature <https://arxiv.org/pdf/0908.3043.pdf>   give reasonable
characterizations of reciprocity over circuits? To what extent does 
Levine's
<https://www.sciencedirect.com/science/article/abs/pii/002251938090288X>  
(painfully straightforward) solving for eigenstates?
* Apologies for any paywalls, I am often stymied to find better access.



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