This article was originally written by Hive account@beneficencetv as a Google Doc and he has given me permission to post it on the Hive blockchain.

---

As you know, my Synthetic AC model is a good start for bridging the gap between the abstract concepts of vortex based math, teslas impulse technology, and Thomas Bearden's asymmetric regauging principles with mainstream electrical engineering practices. However, part of the theory has always been an extension of what others have said for decades. A cold hard truth. That this type of energy cannot be accurately measured with our standard tools. In order to understand how to develop a work around for this issue I had to ask myself why. Why is it that this type of energy cannot be accurately measured with standard methods? Engineers will be demanding a mathematical framework to go along with my synthetic AC model if it is to be taken seriously. This is my attempt at providing that mathematical framework.

Before we continue, we have to take a look at how mainstream engineering operates.

Mainstream electrical engineering treats everything as a closed system governed by the laws of Equilibrium Thermodynamics. But this completely ignores the fact that a separate set of laws called Non-Equilibrium Thermodynamics governs open systems interacting with environmental gradients.

Example

[Equilibrium thermodynamics in a Closed View] --> Stagnant Water in a Sealed Pot (there is Uniform temperature and zero net flow)

[Non-Equilibrium thermodynamics in an Open View] --> Can be thought of as a Persistent Whirlpool that is maintained continuously by a drainage gradient.

Before diving into the new power calculations we must fundamentally change how we look at an electrical circuit.

As I just mentioned, mainstream electrical engineering relies on this basic oversimplification: That all electrical systems are closed, symmetrical, and in equilibrium. Because of this, standard measurement tools are engineered with built-in mathematical blind spots for certain unconventional systems.

To understand the mathematics of an open, non-equilibrium system, you must first understand three foundational concepts:

1st Concept: "The Loop" Fallacy

Conventional electronics teaches us that current must flow in a complete, closed loop from a battery's terminal, through a load, and back to the opposite terminal. While this is true for moving electron charge carriers, energy itself does not travel inside the wire.

Energy travels through the space around the wire as an electromagnetic field envelope (called the Poynting vector). When you use specialized geometry—like the ABHA coil—coupled with rapid, time-asymmetric switching, you can physically partition these field vectors using something as simple as a high speed diode.

The forward energy and the backward collapse do not have to fight each other in the same wire; they can be geometrically guided along entirely separate pathways while still being coupled via a field bridge.

2nd Concept: Reversal Symmetry vs. Asymmetric Sequencing

This goes back to my synthetic AC model where we differentiate between True AC and synthetic AC.

• True AC (Reversal): Imagine a closed pipe filled with water. A piston pushes the water forward, then pulls it back along the exact same path. The water simply sloshes back and forth in place. Because the fluid is constantly reversing direction, it fights its own momentum, creating friction and heat. Every forward push is entirely undone by the backward pull.
• Synthetic AC (Sequencing of two or more bidirectional pulses): Imagine two separate people standing on opposite sides of a room, taking turns firing pingpong balls into a central zone. On a standard meter, it looks like an alternating wave. But in reality, it is a choreographed sequence of independent, time-asymmetric events. These two waves might look identical on an RMS meter. However, as we peak behind the curtain we realize the stark truth. They are not the same. True ac is not the same as a synthetically created alternating current. So why do we categorize them as being the same? My synthetic AC model aims to correct this inherent contradiction. But we need a new mathematical formula to determine the actual efficiency of the system if we are going to get anywhere with the engineers. A new methodology needs to be formed from this thesis. This is my attempt at a potential method for calculating the instantaneous power potential of non-linear systems that utilize synthetic AC.

3rd Concept: The RMS Blind Spot

A standard digital multimeter or an averaging oscilloscope does not look at reality in real time. It uses a mathematical smoothing tool called Root-Mean-Square (RMS).

RMS acts like a statistical blender: it takes sharp, high-energy spikes such as the reactive -168V output from our coil and smooths them out over time into a gentle, artificial average.

If you have a true sine wave and a highly non-linear, pulse-driven synthetic wave, their integrated averages might yield the exact same RMS voltage. However, how they release energy is different. How they interact with the environment is different. How they perform work under load is also radically different from one another. Thus, is the need for the new synthetic ac classification. Remember, the Synthetic AC model at its core is a taxonomy correction.

What the Upcoming Math Proves

The mathematics that follow will completely abandon the artificial averaging of RMS. Instead, we will look at Instantaneous Power Integration over Time, measured in absolute units of work: Joules.

By calculating the forward path and the backward recovery path as independent thermodynamic events in Joules, we can accurately track how a geometry-dependent open system successfully harvests energy from environmental gradients. From this we can extrapolate how much energy, if any, is being extracted from the surrounding vacuum.

Let's look at what lt. col. Thomas Bearden has to say before we go over the standard way to calculate efficiency:

Tom Bearden - How the MEG Really Works

---

STANDARD WAY TO CALCULATE EFFICIENCY:

Root-Mean-Square (RMS) is a non-linear, statistical calculation based on squaring the voltage or current values, integrating them over time, and then taking the square root:

Because of the square root and squaring operations, RMS voltages do not obey linear addition. For example, if you have two independent, orthogonal AC waveforms at 5v rms and 5v rms adding them together does not equal 10v rms. Their combined effective voltage is calculated via the vector sum (square root of the sum of squares):

The Correct Methodology to fix the COP Equation is to properly account for all partitioned energy events.

To properly account for all partitioned energy events and prove the COP is greater than 1 (COP > 1), we must completely abandon the concept of RMS and focus strictly on Instantaneous Power Integration over Time (Joules).

Remember:

Energy is work, measured in Joules (J). Power is the rate of energy transfer, measured in Watts (W). We must measure the input and output energy independently by calculating the exact area under their respective power curves.

Use this structured method to mathematically correct your COP calculations:

First we have to define the time domains. These domains are Time Asymmetric.

Unlike standard AC, where a cycle is split into two equal, symmetrical halves, a Synthetic AC cycle must be evaluated as a series of discrete, non-linear time segments (t₁, t₂, ...) within a total period (T).

Let:

• t₁ = The duration of the active forward excitation pulse (Driving Phase).
• t₂ = The duration of the asymmetric field collapse/radiant recovery event (Collapse Phase).
• T = The total cycle time (t₁ + t₂ = T).

2. Equation 1: True Instantaneous Input Energy (U_in)

Because the backward pulse dynamically alters the battery source's local scalar potential, you cannot use average input current. You must integrate the instantaneous product of input voltage (v_in) and input current (i_in):

Input Equations

True input energy equals the integral from zero to capital T, of input voltage times input current, with respect to time.

Track the True Input Energy (U_in).

You cannot use an average current or voltage meter on the battery source because the high-dV/dt backward pulse is altering the battery's potential dynamically.

• The Method: Capture high-speed, synchronized oscilloscope traces of the instantaneous input voltage (v_in(t)) and input current (i_in(t)) directly at the source terminals.
• The Equation: Multiply them to find instantaneous power, then integrate over the exact time cycle (T):

Output Equations

Track the Two Partitioned Output Energies Separately

Because our system partitions energy into two distinct spatial/temporal pathways (Forward to load, Backward to recovery terminal), we must compute their energies individually in Joules, then add the Joules together. Joules can be added linearly; RMS values cannot.

(W)Forward: Forward work equals the integral from zero to t-one, of load voltage times load current, with respect to time.
(W)Backward: Backward work equals the integral from t-one to capital T, of recovery voltage times recovery current, with respect to time.
(W)total: Total work equals forward work plus backward work.

• Forward Energy (W_forward):

• Backward / Recovery Energy (W_backward):

The final equation is the Correct Unified COP Equation

Once we have the total work performed by both partitioned loops in Joules, our corrected COP formula is as follows:

The Coefficient of Performance for Synthetic AC equals forward work plus backward work, divided by true input energy.

By calculating the system this way, we respect the laws of calculus and standard thermodynamics while perfectly accounting for both energy vectors. This mathematical approach is unassailable by mainstream engineers simply because it relies on the absolute conservation of energy across individual partitioned events.

This equation is unassailable because Joules are a scalar metric of absolute work.

By integrating the instantaneous product of Voltage(V) and Current(I) at high sampling frequencies, we account for the Theta or phase angle dynamically at every microscopic point in time. Mainstream engineers cannot argue with this because it treats each temporal window as an isolated, standard thermodynamic event. It proves that if the sum of the work done in the partitioned paths exceeds the integrated input, the system must be open and extracting energy from an environmental or vacuum gradient. When we think about the Rodin coil for a minute, its not just one thing. Its not just a capacitor. It's not just an inductor. Its not just a transformer. This is the exact scientific distinction that makes the Rodin coils geometry so unique. Taxonomy is how we demystify the coil. Because It’s not one thing. It's an all in one system. When we view it as a single, unified component that combines inductance, capacitance, voltage transformation, and resonance, we are describing what advanced electromagnetic theory calls a Distributed Element Network or sometimes referred to as a Resonant Electromagnetic Structure. A singularity. A perfect representation of free flowing energy in the form of a localized and stable desktop black hole. A reactionless drive, unaffected by the weight that it carries. Black holes are thought to exist on the microscopic scale but instead of using gravity to suck everything in, they use a different force to suck in stray electrons and free ions. Apparently the same force the coil uses to do the same during field cavitation. The universe is a fractal of itself. It displays self similarities whether we look at the quantum scale or the cosmic scale. Everything is connected, if you know where to look for the patterns. This is the heart of Divine Science. The idea that the universe was intentionally created, and not just the byproduct of random chaos and nothingness. There is purpose everywhere in nature.

---

For Experimental Purposes

Step 1: The Measurement Setup (Avoiding Ground Loops)

Because our system uses a high-speed diode to partition energy into different paths, a standard grounded oscilloscope probe can accidentally create a "ground bridge." This will short out the very separation we are trying to measure.

              [ Modified Joule Thief ]
                        │
                [High-Speed Diode]
                        │
            ┌───────────┴───────────┐
            ▼                       ▼
      Forward Path              Backward Path
   (To Resistor Load)        (To Battery Negative)
            │                       │
   [Current Probe A]       [Current Probe B]
   [Voltage Probe A]       [Voltage Probe B]

• For Voltage (v(t)): Use differential probes or your floating probe setup. Measure the voltage directly across the load for the forward path, and directly across the recovery terminal/battery negative for the backward path.
• For Current (i(t)): Use a high-bandwidth current probe (like a Tektronix, Lecroy, or a specialized high-frequency Rogowski coil/current viewing resistor). Do not use standard multimeters.

Step 2: Capturing the Data on Your High-Speed Scope

Set your scope to its maximum sampling rate (e.g., 1GS/s or higher) to capture the sharp, high-dV/dt transients.

1. Channel 1: Forward Voltage (v_forward(t))
2. Channel 2: Forward Current (i_forward(t))
3. Channel 3: Backward Voltage (v_backward(t))
4. Channel 4: Backward Current (i_backward(t))

Step 3: Performing the Math (The Joules Calculation)

Most modern high-speed digital oscilloscopes have a built-in Math Function that can handle this automatically. If yours does not, you can export the raw CSV data into Excel, MATLAB, or Python.

1. Calculate Instantaneous Power (P)

For every single data point on your screen, multiply the voltage by the current. This gives you a new waveform representing instantaneous power in Watts (W)

1. Integrate to Find Joules (W)

Use the scope’s built-in "Integral" (Intg) math function on your new Power waveforms over one full cycle (T). Integration simply calculates the exact geometric area under that power curve. This gives you the energy in Joules:

• W_forward = Integral of P_forward
• W_backward = Integral of P_backward

(Do the exact same thing for your input source to find U_in in Joules.)

---

Step 4: The Final Bulletproof COP Calculation

Now that you have all three values converted into raw energy (Joules), you simply add the two output components together and divide by the input:

Because you converted the non-linear, asymmetric waveforms into absolute units of energy (Joules) before adding them, this calculation is mathematically unassailable. No one can claim you are inflating your numbers with "fake" RMS additions.

If your open system is truly drawing ambient energy via your geometric cavitation field bridge, your final COP number will cleanly land above 1.0, proving your thesis empirically.