Fun with active feedback!

Preparing a paper about active feedback, sharing these counter-intuitive results might give some insight in the operation of amplifiers.

Shown in the illustration, IOP1 and IOP3 (Tina-TI simulation, IOP='ideal opamp') have their inputs swapped, but not the active feedback operational amplifiers IOP2 and IOP4. The feedback network consisting of R2 and R3 are identical.

Both circuits behave as inverters, what was not immediately expected with the IOP1/IOP2 configuration, whereas it was obvious with the IOP3/IOP4 configuration.
To avoid lengthly derivations of formulas, consider the outputs of IOP2 and IOP4 as "Vz", being -(R2/R3)* Vout.
For the IOP1/IOP2 configuration, Vout = Ao * ( Vin - Vz ), which boils down to Au = -R3/R2!
For the IOP3/IOP4 configuration, Vout = Ao * ( Vz - Vin ), which boils down to Au = -R3/R2!

Concluding that not the forward configured amplifier (IOP1, IOP3) determines the overall performance, but the active (in this case) controller (IOP2, IOP4).
Notice that amplifiers in general behave less then perfect at extremes (high frequency, start up / shut down sequences, to name just those two), and the poltergeist Murphy (In Ravels Gaspard de la Nuit named Scarbo) can pop up everywhere, mostly quite unwanted...

Other more developed similar circuits (a passive feedback in IOP1/IOP3 or non-inverting feedback controlling IOP2/IOP4) show none to less favourable solutions, as a simple resistive divider and a buffer has proven already.

And I promised N. Pass a headstart, so here it is.
R1 is left out (obvious, no real zener here), μ is approx (R3/R2)^2.
 

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VF3 looks legit and consistent with reality but VF1 looks like a sim artifact. It looks physically impossible, and I am pretty sure that if you breadboard it, it will behave as a schmitt trigger.
In an AC analysis, such a circuit can appear to work, but not in transient mode, unless there are simulation quirks, or invisible opamp properties
 
Revisited.
Many thanks for all the constructive contributions!
Replaced the timed generator output to a simple sine, the opamps only the humble 741's.
The positive input (upper one) is stuck to the negatieve rail - this won't work in real life.
So after elaborate calculations at my desk, where things proove right, the silicium halts me to a no on this one.
If wanted, I'll post my hand-written notes (captures) also about the flawed pos-input variation.
Just happy to notice the active controlled inverter acts as expected, as this counts for the above mentioned link in #1.
 

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