I presume the proof the OP is referring to can be found in this monograph by Hava Siegelmann?
In his article 'The Myth of Hypercomputation', the eminent computer scientist Martin Davis explains (p8-9) that there is nothing 'super Turing' about this formulation.
EDIT: It's looking like the claim about rational weights being super-Turing is made in this ...
Digital and Analog
The question about analog computing is important.
Digital circuitry gained popularity as a replacement for analog circuitry during the four decades between 1975 to 2015 due to three compelling qualities.
Greater noise immunity
Greater drift immunity (accuracy)
No leakage of stored values
This quickly led to digital signaling standards, ...
You mean real numbered weights (specifically, irrational). This would require a machine that has unlimited precision over irrational values. I've seen machine parts that have many qualities. I've never seen one that has unlimited qualities. QM may give us some magical transistors that can hold an unlimited number of different values - or by deferring ...