Free energy does not exist and neither does electrical reactance. Both are fictions whose theorized existence has weathered our doubts for over a century of workable mathematics. This does not prove the existence of imaginary numbers, nor does it prove that they succeed at representing any variety of electrical reactance, free energy or otherwise. Instead, it demonstrates that we can “get by” without having to prove how to take the square root of a negative number. No one has a clue how to do that, and nobody expects to find out any time soon...

Without this proof, we have no proof for the existence of free energy, and we have no proof for the existence of electrical reactance (since the two are closely related). All we know is that our mathematical modeling succeeds with their simulations based on over a century of “street-wise” expertise.

Alternate, introduction ...
Relativity is to the physicist what reactance, both electrical and magnetic, are to the electrical engineer in that both deliver a perspective which is subject to circumstance for accurately assessing the measurements of energy.

“Energy IN must equal energy OUT” has no meaning by itself. Likewise, a kilowatt has no relevance unless coupled with a per-hour reference or else the electric utility company could never bill us for using their energy.

Duration is one aspect of time, a generic aspect, which holds true for both magnetic and electrical reactances. Frequency is another aspect: an aspect which is (at the very least) specific to electrical reactance and not germane to reactance in general.

Yet, ...
Electrical reactance, alone, also possesses the properties of: capacitance (acting as a causative agent for its own unique form of reactance), while inductance spawns its own unique variety of reactance, and both possess a phase relation between them which can maximize at a half-cycle of oscillation and -thus- qualify the overunity circuit as a passive generator of electricity possessing no significant prime mover acting, instead, as a mere stimulant for inducing overunity.

BTW, ...
An equivalent term for overunity is over-reactance allowed by the negative impedance of Foster's reactance theorem.

So, to overly simplify a measurement of energy – to mere duration, alone, as its frame of reference – is an over-simplification of how thorough is the impact that a relativistic perspective has upon our measurements of energy. The broad topic of reactance is a fertile field for investigating the flexibility which this field of imaginary numbers has upon our measurements of real power (enumerated by real numbers) since our measurements of real power are completely dependent upon an imaginary frame of reference existing within the domain of reactance.

In other words, our physical measurements of energy are always at the mercy of requiring that these measurements be predicated upon the non-real, imaginary world of the square root of negative one. This imaginary world is a manmade fiction. It can never be proven. Yet, over a century of engineering expertise is testimonial to the efficacy of imaginary numbers filling the gap in our physical assessment of energy.

A thorough measurement, and an accurate one at that, must be predicated upon all of the factors of reactance or else suffer from the consequence of our jumping to false conclusions about energy IN versus energy OUT espoused by physics. Duration, alone, is not enough to measure energy in terms of. We have to include all of the other factors of reactance as well as its generic factor of duration. Kilowatt-hours merely scratches the surface of credibility!

My six years of experience with simulations of overunity circuitry has led me to this conclusion: that energy does not appear out of nowhere in an overunity circuit, nor does it disappear into nowhere. Instead, the circuit's point of view has become altered over a duration of time which can span any number of seconds ranging from as little as nano seconds to as much as ten million seconds. And this is merely an example of the window of duration which may be affected by this alteration of the circuit's perception of how much energy did you give it versus how much energy does it spit out. For, this window of duration is limitless is in its potential scope for an adequate reactance to occur to alter the circuit's perception of its internal energy and give us sufficient energy to run an electric car at 100kW despite the nanowatt input from a meager solar panel or whip antenna.

I've seen simulations in which I cannot make a determination as to how quickly does the circuit explode with overunity no matter how small I make the simulation's time-step.

Likewise, I may be at a loss (and all of us as well) at having the patience to wait long enough to see whether or not a prospective overunity circuit is capable of generating overunity if its duration of operation were long enough.

But, it's not necessary to wait so long unless our development of an overunity circuit is in its initial stages of development. With increased efficiency, an overunity circuit can have its required wait-time shortened to mere nano seconds if its designer is willing to “do whatever it takes” to shorten that wait-time.

This is accomplished by recognizing that there are other factors, besides duration, that can be modified to affect a shorter duration of the circuit's recognizable overunity. These additional factors are all of the factors of both electrical and magnetic reactance.