Where do you get such funny ideas reading things that I have not stated?

Because you stated:

It doesn't happen because the work required for each new withdrawal **similarly** increases.

And the word "similarly" was later clarified to refer to current, so your revised quote now reads:

"It doesn't happen because the work required for each new withdrawal increases similarly to current."

So if the work increases than so does the current.

According to you the work required to move the magnet depends on its speed and so does the current.

Or: If the work required to quickly withdraw the magnet is different than the work required to slowly push in the magnet, then currents must be different, too... and the absurd machine woulld accumulate current without a theoretical limit at the expense of the work performed by the agency turning the Whitworth mechanism. - yet "it does not happen".

**Let's remember what we are discussing here:**You claim that the current left in the superconducting loop after the movement of the magnet

depends on dΦ/dt and I claim that it depends on ΔΦ.

That's what the whole discussion boils down to.

As a side note, it worth to remember, that the ratio of to flux to current (a.k.a. inductance) stays constant in that SC loop.

Work performed is not proportional to the current. It is proportional to the square of the current.

Yes. It is merely more precise to state that work is proportional to the square of the current.

When the current does not change its direction (as in the absurd machine scenario) work increases with the square of the current and also the work increases with the current itself. The derivatives of x an x

^{2} have the same sign for x>0.

I was trying to keep it simple but that lack of precision does not invalidate my line of thinking.

Actually the one thing that I overlooked is that the coil looking like a perfect inductor will identically integrate the rate of change in flux with respect to time,

...and the integral of dΦ/dt with respect to time evaluates to Φ.

Retracting the magnet in the opposite direction to its initial position relative to the ring reverses out whatever current was induced by bringing the magnet closer to the ring.

Yes, and for clarity for other readers, the word "reverses" in that statement should not mean reversing the direction (sign) of current.

If you don't believe Maxwell then it is up to you to show that you have found a violation.

You seem highly resistant to the notion of BEMF from the inductance of the loop exactly matching the induced EMF.

I believe Maxwell. I just don't want to misapply his equations.

I am not resistant to the notion of EMF - BEMF = 0 across a superconducting loop.

I just do not go the "EMF route" and analyze voltage across zero-resistance because it leads to division by zero.

Then you should consider how E = 0.5*LI^{2} is derived. The big hint should be that I is the time integral of V/L.

Derivation by Kirchhoff's voltage law is just one of the derivations. Using it means using voltage.

For the energy stored by a coil I prefer to use the derivation that does not involve voltage and uses L=Φ/I to prove that W=½ΦI.

The "spring's" energy is defined by the magnet and the path it travels relative to the ring.

Yes, "path" - not the speed along this path.

... a power source driving a winding coupled to the ring can transfer a variable amount of energy into the ring's field.

...but the energy transferred to the SC loop by such winding does not depend on the risetime or falltime of the current in that winding (as in e.g. sawtooth waveform).

For example the energy and current in the secondary superconducting winding (W2) of an aircore transformer shown below does not increase from cycle to cycle and its maximum value is always be proportional to I

_{MAX} even if the current in the primary (W1) exhibits different di/dt generating different dΦ/dt.

Over the integer number of cycles the work done by the current source is zero ...+ resistive losses.

Furthermore the

line integral of the flux penetrating the contour of the SC secondary winding (W2) will be

**constant**, regardless of the dΦ/dt generated by the primary winding (W1).