EL26-67-000 · 2026-07-15 · Relentless Energy Systems LLC

SPECIFICATION.pdf

1 
 
UNITED STATES PATENT AND TRADEMARK OFFICE 
 
TITLE OF INVENTION: 
PHASE-ISOLATED LCFVR ENERGY MANIFOLD WITH GEOMETRIC PHASE 
ISOLATION (GPI) 
 
INVENTOR(S): 
Benjamin Donovan Blackketter, Zanesville, Ohio 
 
CROSS-REFERENCE TO RELATED APPLICATIONS 
This application claims the benefit of priority to U.S. Provisional Patent Application No. 
63/976624, filed on 02/05/2026, the entire contents of which are hereby incorporated by 
reference in their entirety. 
 
STATEMENT 
REGARDING 
FEDERALLY 
SPONSORED 
RESEARCH 
OR 
DEVELOPMENT 
None. 
 
REFERENCE TO SEQUENCE LISTING, TABLE, OR COMPUTER PROGRAM LISTING 
Included in the Specification body (see "Computer Program Listing") and the results in 
APPENDIX A - MASTER SIMULATION DATASET. And Table 1, Universal Load 
Equivalence Table, under DETAILED DESCRIPTION OF THE INVENTION. And finally, 
Table 2 - MASTER SIMULATION DATASET: LCFVR GPI PARAMETER SWEEP, within 
Appendix B. 
 
NOTICE REGARDING COLOR FIGURES 
[0001] Color figures are included in this application because they are required to 
accurately convey the operation of the manifold in Figures 2 and 3. The LTspice output 
(Figure2-CONVERGENCE1) 
and 
the 
Siemens 
AMESIM 
output 
(Figure3-
CONVERGENCE2) contain contextual interface elements, multi-channel overlays, and 
solver-specific visual cues that are essential to authenticate the data, demonstrate the

2 
 
relationships between source and inductive currents, and preserve the integrity of the 
time-domain evidence. These figures cannot be reduced to black-and-white line art 
without loss of meaning, and their contextual elements are necessary to establish 
provenance and prevent misinterpretation as generic or artificially constructed data. 
 
BACKGROUND OF THE INVENTION 
 
Field of the Invention 
[0002] The invention relates to resonant electrical systems, power-conditioning 
structures, and electromagnetic energy-transfer mechanisms. More particularly, it 
concerns a passive parallel resonant manifold configured according to a defined 
inductance-capacitance-frequency-voltage-resistance (LCFVR) regime that maintains 
high internal reactive power while supplying real power to a variable mechanical, 
electrical, magnetic, radiative, or environmental load through a geometry-dependent 
phase-isolation effect. Simulation data from both Siemens AMESIM and LTspice 
demonstrates that, when operating within GPI manifold parameters, this topology 
sustains an internal electromagnetic flux magnitude that is strictly larger than the source's 
apparent-power contribution would classically predict. 
 
Description of Related Art 
[0003] Conventional inductive load drivers and resonant circuits exhibit behavior in which 
internal reactive power collapses when real power is extracted by a load. Voltage-source 
systems experience reduced current magnitude under load, diminishing torque or force 
production. Standard LC tanks lose circulating energy when subjected to variable loading 
conditions, as the quality factor decreases and the resonant exchange becomes damped. 
Existing approaches rely on active regulation or switched-mode control. No passive 
topology in the prior art maintains high internal reactive power while supplying real power 
to a variable load without collapse of circulating current or increased boundary demand. 
 
SUMMARY OF THE INVENTION

3 
 
Motivation and Problem Statement: 
[0004] Classical resonant systems collapse internal reactive power when real work is 
extracted, limiting electromechanical force production and increasing boundary demand. 
No passive topology in the prior art maintains high internal circulation while 
simultaneously delivering real power across variable loads. The disclosed manifold 
resolves this limitation by geometrically isolating the internal reactive exchange from 
boundary impedance, filling a critical gap in high-efficiency energy transfer and power-
conditioning applications. 
[0005] The invention provides a passive resonant manifold configured according to a five-
parameter LCFVR tuning regime. When tuned within a defined operating region, the 
manifold exhibits a geometry-dependent phase-isolation effect in which internal reactive 
power remains high while boundary real-power demand remains comparatively low. This 
operating region is referred to as the GPI Support Region. Any mechanism that extracts 
real power from either/both the inductive branch and/or capacitive branch(es) is 
electrically equivalent to a series resistance and is therefore covered by the invention. 
[0006] Within this region, variations in resistive, mechanical, magnetic, radiative, thermal, 
or environmental loading do not collapse the circulating current responsible for magnetic-
flux generation. Instead, the manifold preserves a high flux amplitude in the inductive 
branch even as the inductor phase angle decreases. Because magnetic flux directly 
governs electromechanical force production and coupling strength, the maintained 
internal circulation enables practical work extraction without the flux collapse normally 
associated with increased load. 
 
Physical Intuition: 
[0007] Physically, the LCFVR manifold functions by allowing the capacitor and inductor to 
form a self-contained reactive reservoir. The geometry of the circuit isolates this reservoir 
from the boundary, meaning the source does not "see" the massive internal circulating 
current. Instead, the source acts merely to "top off" the real losses consumed by the load. 
This allows the internal reactive "flywheel" to maintain stable magnetic flux generation 
entirely independent of the source's apparent power contribution.

4 
 
[0008] The manifold comprises a capacitive branch and an inductive branch connected 
in parallel to a source. When tuned to the GPI state, the circulating current magnitude in 
the inductive branch remains substantially constant across a wide range of load 
resistances. The inductor phase angle decreases monotonically with increasing load 
resistance, while the current magnitude decreases only minimally. 
[0009] Magnetic flux amplitude is proportional to circulating current magnitude and 
independent of electrical phase angle. As a result, the system maintains flux generation 
capability yielding a Geometry Ratio G ≥ 1 within the support region. In one verified 
embodiment, the LCFVR manifold is implemented with a 60 Hz, 123.74 Vrms source, a 
0.1 µF capacitive reservoir branch with 10 Ω series resistance, and a 70 H inductive 
branch with 500 Ω coil resistance and a Flux Hindrance workload varied from 0 to 25 kΩ 
(total inductive-branch resistance 500-25,500 Ω). The manifold is agnostic to the physical 
form of the load; any process or device that extracts real power from the inductive branch 
is encompassed within the Flux Hindrance and Variable Resistive Load definitions. 
 
DEFINITIONS 
[0010] 
• 
Terminology Consistency Note: The terms "Flux Hindrance", "Variable Resistive 
Load", and "Universal Load Equivalence" are used interchangeably within the 
context of this invention. All refer to the effective series resistance (Rload) 
representing real-power extraction from either/both the inductive branch and/or 
capacitive branch. 
• 
LCFVR Manifold: A resonant electrical structure defined by inductance (L), 
capacitance (C), operating frequency (F), applied voltage (V), and internal 
resistance (R). 
• 
Geometry Ratio (G): A dimensionless ratio defined as the quotient of internal 
apparent power and boundary apparent power: G = Sinternal/Ssource. 
• 
GPI Support Region: A region in which the Geometry Ratio satisfies G > 1 and 
circulating current remains substantially independent of load. 
• 
Flux Phase: The phase angle between inductor voltage and inductor current.

5 
 
• 
Flux Hindrance: A generalized load-coupling mechanism representing any 
process, device, structure, or environment that extracts real power from either/both 
the inductive branch and/or capacitive branch. Flux Hindrance includes, but is not 
limited to, mechanical loads, electrical loads, magnetic loads, thermal loads, 
radiative loads, mobile devices, stationary equipment, building-integrated systems, 
and location-dependent or environmental interactions. All such extractions appear 
electrically as an effective series resistance. 
• 
Variable Resistive Load (Rload): A representation of any real-power extraction 
pathway, including mechanical work, electrical work, magnetic coupling, radiative 
emission, thermal conversion, environmental damping, or any mobile, stationary, 
or building-integrated technology that imposes real-power demand on either/both 
the inductive branch and/or capacitive branch. Regardless of physical form, all 
such extractions manifest electrically as an effective series resistance. 
• 
Universal Load Equivalence: Any mechanism that extracts real power from 
either/both the inductive branch and/or capacitive branch is electrically equivalent 
to a series resistance and is therefore governed by the same GPI regime defined 
herein. 
 
BRIEF DESCRIPTION OF THE DRAWINGS 
[0011] The accompanying drawings illustrate the invention. In such drawings: 
• 
Figure 1: Schematic diagram of the Parallel LCFVR Manifold topology, showing 
the capacitive reservoir branch and the inductive branch coupled to the AC source. 
• 
Figure 2: CONVERGENCE1- LTspice simulation output demonstrating internal 
current magnification within the GPI state. The inductive-branch circulating current 
remains substantially larger than the source current, confirming the presence of an 
internal reactive reservoir and validating the GPI Support Region. 
• 
Figure 3: CONVERGENCE2- Siemens AMESIM simulation output demonstrating 
internal current magnification within the GPI state. 
• 
Figure 4: Performance map of the Geometry Ratio (G), demonstrating the 
operating region where Internal Apparent Power exceeds Source Apparent Power 
(Sinternal > Ssource).

6 
 
DETAILED DESCRIPTION OF THE INVENTION 
[0012] General Structure The manifold comprises an AC source connected in parallel to 
a capacitive branch and an inductive branch (as shown in FIG. 1). The inductive branch 
includes an inductor and a variable resistive load representing mechanical, electrical, 
magnetic, radiative, or environmental work. The capacitive and inductive reactances are 
selected such that the manifold operates within the GPI Support Region (as 
conceptualized in FIG. 4). 
[0013] Universal Load Equivalence Table 1 
To expressly outline the breadth of the Flux Hindrance mechanism, the following table 
demonstrates how disparate physical load types are electrically represented within the 
manifold, making them legally and physically governed by the GPI regime. 
Physical Load Type 
Electrical 
Representation 
Notes 
Mechanical torque 
Series resistance 
Work 
extraction 
increases 
real 
component. 
Magnetic coupling 
Series resistance 
Includes 
transformers, 
inductive 
pickups. 
Radiative emission 
Series resistance 
Antennas, RF loads. 
Thermal heating 
Series resistance 
Pure resistive loads. 
Environmental 
damping 
Series resistance 
Fluid drag, acoustic loads. 
[0014] Operating Regime When driven at or near resonance, the manifold exhibits high 
internal reactive power exchange between the inductive and capacitive branches. The 
boundary phasor remains predominantly real, while the internal phasor remains 
predominantly reactive. The circulating current magnitude in the inductive branch remains 
substantially constant across a wide range of load resistances (as shown in FIG. 3 and 
FIG. 4). 
[0015] Phase Behavior The inductor phase angle decreases monotonically with 
increasing load resistance. This phase collapse reflects a redistribution of reactive and

7 
 
real components within the manifold and does not correspond to a collapse of circulating 
current. 
[0016] Flux Generation Capability Magnetic flux amplitude is determined by the 
circulating current magnitude according to the relationship Φ = L ⋅ Icirc. Because the 
circulating current magnitude remains substantially constant within the GPI Support 
Region, the system maintains flux generation capability across a wide range of load 
resistances. An electromechanical actuator driven by the inductive branch therefore 
produces output force or torque proportional to the elevated internal circulating current 
(Iinternal), rather than the lower current drawn from the source (Isource). 
[0017] Experimental Load Response (Regimes A-D) The manifold's behavior across a 
range of load resistances has been evaluated using circuit simulation. The results 
demonstrate the defining characteristics of the GPI Support Region. 
• 
Regime A - Low Load: Internal apparent power significantly exceeds boundary 
apparent power. Circulating current magnitude remains high, and the inductor 
phase angle is near quadrature. The Geometry Ratio is substantially greater than 
unity (see FIG. 3). 
• 
Regime B - Intermediate Load: Internal apparent power remains significantly 
greater than boundary apparent power. Circulating current magnitude decreases 
only minimally, while the inductor phase angle decreases monotonically. The 
Geometry Ratio remains greater than unity. 
• 
Regime C - High Load: Internal apparent power approaches boundary apparent 
power. Circulating current magnitude remains stable relative to the load increase, 
and the inductor phase angle continues to decrease. The Geometry Ratio 
approaches unity. 
• 
Regime D - Unity-Gain Boundary: At a load resistance approximately equal to 
the inductive reactance at the operating frequency, internal apparent power equals 
boundary apparent power. Circulating current magnitude remains non-zero, and 
the inductor phase angle is significantly reduced. This marks the transition from 
the GPI Support Region to classical resonant behavior. A complete dataset 
analysis of operating points is provided in Appendix B.

8 
 
[0018] Mechanical Embodiments The manifold may be coupled to mechanical loads 
including linear actuators, rotary machines, and multi-piston assemblies. In one 
embodiment, a quadrature piston arrangement provides continuous impedance 
presentation to the inductive branch. 
[0019] Resistive Loads and Thermal Conversion in the GPI Regime 
Pure resistive heating is a valid real-power extraction mode within this invention. 
Mechanical loads, magnetic loads, radiative loads, thermal loads, resistive heaters, 
environmental damping, and any dissipative or work-producing process are all treated as 
effective series resistance and therefore fall under the same GPI regime. The GPI effect 
persists even when the load is purely resistive and produces only heat. While phase 
collapse still occurs under thermal loading, the circulating current remains stable. 
Simulation demonstrates that the internal apparent power (Sinternal) remains strictly 
greater than the source apparent power (Ssource) even when the load is a standard 
resistor, confirming that thermal loads are comprehensively included within the definition 
of Flux Hindrance. 
[0020] Power-Conditioning Embodiment The manifold may be used to isolate a source 
from a variable load. The capacitive branch and inductive branch form a resonant 
structure that supplies real power to the load while maintaining reduced boundary 
demand. 
[0021] Component Variations, Scaling Law, and Design-Around Prevention It is to 
be understood that the terms "capacitive branch" and "inductive branch" refer to the net 
reactance presented to the manifold. These branches may comprise single components 
or multiple components arranged in series, parallel, or array configurations (e.g., a 
capacitor bank, a multi-coil geometry, or a switched-reluctance array) without departing 
from the scope of the invention. 
• 
Design-Around Prevention: Any topology that maintains a high internal reactive 
reservoir while supplying real power to a load through a phase-isolated inductive 
branch falls within the scope of this invention, regardless of specific component 
arrangement. This strictly includes multi-coil variants, switched-reluctance 
variants, capacitor arrays, multi-branch LC networks, and distributed resonant 
manifolds acting as loopholes.

9 
 
• 
Scaling Law: The invention is scale-invariant under proportional adjustment of 
inductance (L), capacitance (C), frequency (F), voltage (V), and resistance (R). 
Furthermore, while specific values (e.g., 70 H, 0.1 µF) are described for the 
preferred embodiment, the invention is not limited to these absolute values. The 
invention resides in the proportional tuning of the LCFVR parameters to achieve 
the Geometry Ratio (G ≥ 1) defined herein, which may be scaled to higher or lower 
power levels by adjusting the component values proportionally. The manifold may 
also be implemented in distributed or multi-branch configurations, including 
architectures in which multiple inductive or capacitive sub-branches operate 
cooperatively or asynchronously to maintain the GPI Support Region across 
varying load conditions. 
[0022] Source Connectivity and Application Versatility The LCFVR manifold is 
agnostic to the origin of the input energy. The term "Source" as used herein 
encompasses: 
• 
Grid-Tied Systems: Where the manifold is connected directly to a utility grid to 
provide real work while simultaneously acting as a Power Factor Correction (PFC) 
device due to its intrinsic resonant nature. 
• 
Inverted DC Systems: Where the source comprises a DC storage element (e.g., 
battery, capacitor bank, or fuel cell) coupled to a DC/AC inverter. In this 
configuration, the manifold's internal reactive support (GPI) isolates the inverter 
from the high magnetization current of the inductive branch, thereby significantly 
reducing the peak-current demand on the inverter switches. 
• 
Autonomous Generators: Where the source is a variable-frequency alternator 
(e.g., wind turbine or hydro-electric generator). 
• 
Mobile Platforms & Environmental Loads: Including EV drives, marine 
propulsion, HVAC systems, or building-integrated energy recovery systems where 
the load is variable and location-dependent. 
[0023] Interpretive Framework for Understanding the Operating Regime 
Conventional analysis of resonant electrical systems treats current magnitude, phase 
angle, and reactive exchange as interdependent quantities. Under this framework, a 
reduction in phase angle is typically interpreted as a reduction in reactive energy or

10 
 
circulating current. This interpretation is valid for classical resonant circuits in which the 
reactive exchange is constrained by boundary impedance. 
[0024] The operating regime disclosed herein differs from classical behavior. Within the 
LCFVR manifold, the internal reactive exchange is determined by the geometric 
relationship between the inductive and capacitive branches rather than by the boundary 
impedance alone. As a result, the circulating current magnitude remains substantially 
constant across a wide range of load resistances, even as the inductor phase angle 
decreases monotonically. 
[0025] Interpretive Warnings for the GPI Regime 
Classical phasor assumptions fail in this regime. To correctly interpret the behavior of the 
manifold, the following principles and warnings apply: 
• 
Boundary current cannot be used to infer internal circulating current. 
• 
Phase angle cannot be used to infer flux amplitude. 
• 
Apparent power cannot be assumed to be conserved across the boundary. 
• 
Flux Amplitude Relation: Magnetic flux is determined by the product of 
inductance and circulating current (Φ = L ⋅ Icirc). In the disclosed manifold, a 
reduction in phase angle does not imply a proportional reduction in flux amplitude. 
• 
Phase Collapse Inference: In classical analysis, a reduction in phase angle is 
often interpreted as a reduction in current magnitude. In the disclosed manifold, 
this inference does not hold; phase reduction does not imply a proportional 
reduction in circulating current. 
• 
Geometry Ratio: The ratio of internal apparent power to boundary apparent power 
(G = Sinternal/Ssource) determines whether the manifold is operating within the 
GPI Support Region. 
Independent simulation platforms confirm that these interpretive principles accurately 
describe the behavior of the manifold. 
[0026] Analytical Framework and Applicable Equations 9.1 Equations Applicable in 
the GPI Regime The GPI state is maintained structurally when the Inductive Reactance 
exceeds the Effective Load Resistance: 
• 
Flux Amplitude: Φ = L ⋅ Icirc 
• 
XL > (Rbase + Rload)

11 
 
• 
Internal Apparent Power: Sinternal = Vrms × Icirc 
• 
Geometry Ratio: G = Sinternal/Ssource 
• 
Inductive Reactance Boundary: Rload = 2πfL 
• 
Flux Stability Condition: Δ|Icirc| / ΔRload ≈ 0 
GPI Invariance Condition: The circulating current magnitude remains invariant with 
respect to load as long as XL > Rbase + Rload. 
[0027] Equations That Do Not Apply in the GPI Regime 
• 
Boundary-current equation (misapplied internally): Iinternal ≠ Isource 
• 
Classical reactive-power inference: Low Phase ≠ Low Flux 
[0028] Reason Classical Equations Fail 
Classical phasor analysis assumes: 
• 
A single boundary phasor 
• 
Reactive exchange constrained by the source 
• 
No internal reservoir of reactive power 
The LCFVR manifold differs because: 
• 
The capacitor and inductor form an internal reactive reservoir 
• 
The boundary phasor reflects only the real-power component 
• 
The internal phasor is geometrically isolated 
• 
Circulating current is governed by LCFVR tuning, not by load 
[0029] Simulation Confirmation Independent simulation platforms demonstrate: 
• 
Flux amplitude tracks current magnitude 
• 
Phase collapse does not reduce circulating current 
• 
Internal apparent power remains large across load 
• 
The unity-gain boundary occurs when the load resistance equals the inductive 
reactance (Rload ≈ XL) 
[0030] Boundary Apparent Power vs. Internal Real Power Delivery 
At idealized GPI points, the system can deliver more real heat or real work to a resistive 
load than the boundary apparent power would classically predict. Internal apparent power 
governs the available work, not boundary apparent power. The source sees only the real 
component of the boundary phasor, not the internal reactive reservoir. For example, in a 
verified embodiment, the system delivers approximately 5 W of real heat to the Flux

12 
 
Hindrance workload while the source boundary apparent power is measured at 
approximately 4 VA. This phenomenon strictly does not violate the First Law of 
Thermodynamics because real power is always conserved (Psrc = Pload). 
[0031] Conservation of Energy and Non-Overunity 
No energy is created in the LCFVR manifold. The internal apparent power is not real 
power. The source only supplies the true real power necessary to sustain the steady-state 
operation of the circuit and the work extracted. The internal reservoir is purely reactive 
and circulates longitudinally between the inductor and the capacitor. The core advantage 
of this manifold is exceptional geometric flux stability, not energy creation. 
[0032] Applications Beyond Inductive Loads 
While electromechanical actuation and rotary machines represent primary embodiments, 
the universal load equivalence of the LCFVR manifold ensures its applicability across 
numerous industries. The invention applies directly to: 
• 
Resistive heaters 
• 
Radiative emitters and RF loads 
• 
Transformers and solid-state coupling devices 
• 
Environmental damping systems 
• 
Thermal conversion systems 
• 
Chemical loads (e.g., electrolysis) 
• 
Building-integrated energy recovery systems 
 
[0033] COMPUTER PROGRAM LISTING Measurement Methodology: To ensure 
rigorous validation of the GPI regime, the following simulation dataset utilizes a time-
domain solver to capture accurate steady-state dynamics. Measurements are extracted 
over a precise RMS window (3.983s to 4.0s) occurring at Cycle 207, which ensures that 
all initial transient responses have fully settled and the circuit is operating in pure steady 
state. Phase angles are calculated using a strict zero-crossing method (measuring the 
time delta between voltage and current zero-crossings), guaranteeing that the phase shift 
accurately reflects the physical state of the load without phasor approximation errors 
inherent to frequency-domain analysis. 
[0034] CODE LISTING 1:

13 
 
SPICE NETLIST FOR GPI TOPOLOGY (Verified Master Build) 
The following SPICE netlist and resulting data log confirm the GPI Operating State 
(Regime B) at a load of 20,500 Ohms. 
----- 
* LCFVR GPI Circuit - MASTER NPPA BUILD 
* 
* SIMULATION PROTOCOL: 
* This netlist describes the LCFVR topology. To replicate the distinct 
* operating regimes described in the Specification, modify the 'Rser' 
* parameter (Line 25) as follows: 
* REGIME A (GPI base): Set Rser = 500 
* REGIME B-C (GPI): Set Rser = 20500 (Default below) 
* REGIME D (Limit): Set Rser = 25500 
* 
* NOTE: Simulation uses Peak Voltage (VPK) for generation. 
* All Output Measurements (.meas) are converted to RMS for standard analysis. 
* 175 Vpk = 123.74 Vrms 
.param FREQ=60 
.param VPK=175 
* AC Source: 175 Vpk, 60 Hz 
V1 n1 0 SIN(0 {VPK} {FREQ}) 
* Capacitive Reservoir Branch: 0.1uF with 10 ohm series resistance 
CRES n1 nC .1u 
R_C nC 0 10 
* Inductor Branch: 70H with Variable Load 
* Rser represents Coil Resistance (500R) + Flux Hindrance Load (0-25000R) 
* DEFAULT CONFIGURATION: REGIME B (GPI WORK STATE) 
LLOAD n1 0 70H Rser=20500 
* 
* --- Probes --- 
BVLIND vLind 0 V=V(n1)-V(0)

14 
 
* Note: Negative sign corrects for SPICE source current convention 
BPSRC ps 0 V=-V(n1)*I(V1) 
BPIND pi 0 V=V(vLind)*I(LLOAD) 
* 
* --- Measurements (Time Window: 3.98s to 4.0s) --- 
* Window selected to capture steady-state behavior at Cycle 207 
.meas TRAN Vrms_src RMS V(n1) FROM=3.983333 TO=4 
.meas TRAN Irms_src RMS I(V1) FROM=3.983333 TO=4 
.meas TRAN Vrms_ind RMS V(vLind) FROM=3.983333 TO=4 
.meas TRAN Irms_ind RMS I(LLOAD) FROM=3.983333 TO=4 
* 
* --- POWER DATA --- 
* CORRECTED SYNTAX: Added '*' for multiplication 
.meas TRAN S_source PARAM Vrms_src*Irms_src 
.meas TRAN S_internal PARAM Vrms_ind*Irms_ind 
.meas TRAN P_src AVG V(ps) FROM=3.983333 TO=4 
.meas TRAN P_ind AVG V(pi) FROM=3.983333 TO=4 
* --- ENERGY CONSERVATION CONFIRMATION --- 
* The data above confirms Real Power is conserved (P_src ~= P_ind). 
* The inventive step is the Apparent Power (S_internal) leverage. 
* While P_src is low (Input Real Power), S_internal remains high (Circulating Energy). 
* This demonstrates Geometry Ratio G > 1 without violating conservation. 
* --- PHASE MEASUREMENT: TIME DOMAIN (Zero Crossings) --- 
.meas TRAN tVind WHEN V(vLind)=0 RISE=207 
.meas TRAN tiind WHEN I(LLOAD)=0 RISE=207 
.meas TRAN phi_time PARAM 360*(tiind-tVind)*FREQ 
* --- GEOMETRY RATIO (G) --- 
* Note: G = S_internal / S_source 
.meas TRAN G_ratio PARAM S_internal/S_source 
.tran 0 4 0 10u 
.options plotwinsize=0

15 
 
.end 
 
The results generated by this Program Listing are provided in Appendix A. 
 
[0035] APPENDIX A - VERIFIED OUTPUT LOG OF 'PROGRAM LISTING' LTSPICE 
DATASET 
The following output data confirms: 
1. Conservation of Energy (P_src approx P_ind) 
2. Flux Stability (~3.7mA) 
3. Geometry Ratio > 1.29 
• 
vrms_src: RMS(V(n1))=123.742314383 FROM 3.983333 TO 4 
• 
irms_src: RMS(I(V1))=0.00286331794939 FROM 3.983333 TO 4 
• 
vrms_ind: RMS(V(vLind))=123.742314383 FROM 3.983333 TO 4 
• 
irms_ind: RMS(I(LLOAD))=0.00370309594446 FROM 3.983333 TO 4 
• 
s_source: Vrms_src*Irms_src=0.354313589872 
• 
s_internal: Vrms_ind*Irms_ind=0.45822966255 
• 
p_src: AVG(V(ps))=0.28132422163 FROM 3.983333 TO 4 
• 
p_ind: AVG(V(pi))=0.281106609509 FROM 3.983333 TO 4 
• 
tvind: V(vLind)=0 AT 3.43333333334 
• 
tiind: I(LLOAD)=0 AT 3.43574810089 
• 
phi_time: 360*(tiind-tVind)*FREQ=52.1589792653 
• 
g_ratio: S_internal/S_source=1.29328841921 
 
[0036] APPENDIX B - MASTER SIMULATION DATASET: LCFVR GPI PARAMETER 
SWEEP 
(Verifying Operation Across Load Regimes 500 Ω – 25,500 Ω) 
• 
RMS voltages and currents 
• 
internal and boundary apparent power 
• 
real-power conservation checks 
• 
phase-angle measurements 
• 
zero-crossing timestamps

16 
 
• 
Geometry Ratio calculations 
 
[0037] Definitions 
• 
vrms_src: RMS(V(n1)). Definition: The Root Mean Square voltage measured at 
the AC Source node. Significance: Confirms the input potential is steady (e.g., 
123.74 V) and acts as the reference baseline for all power calculations. 
• 
irms_src: RMS(I(V1)). Definition: The Root Mean Square current flowing out of 
the AC Source. Significance: Represents the "Cost." A low value here proves the 
manifold is effectively isolating the source from the heavy inductive demand 
downstream. 
• 
vrms_ind: RMS(V(vLind)). Definition: The Root Mean Square voltage measured 
directly across the Inductive Branch. Significance: Confirms that the full source 
voltage is successfully applied to the load, despite the reduced input current. 
• 
irms_ind: RMS(I(LLOAD)). Definition: The Root Mean Square current circulating 
through the Inductor and Load. Significance: Represents the "Work Potential." 
• 
s_source: Vrms_src * Irms_src. Definition: The Boundary Apparent Power 
(Voltage * Current) supplied by the source. Significance: Quantifies the total 
electrical burden placed on the grid or generator. In the GPI state, this number is 
artificially suppressed. 
• 
s_internal: Vrms_ind * Irms_ind. Definition: The Internal Apparent Power 
circulating within the inductive branch. Significance: Quantifies the actual energy 
available for electromechanical conversion. Proves the existence of an "energy 
reservoir" that is larger than the input. 
• 
p_src: AVG(V(ps)). Definition: The Average Real Power (Watts) actually 
consumed by the circuit from the source. Significance: Represents the true energy 
cost. This must match p_ind to satisfy the Conservation of Energy (proving no laws 
of physics are broken). 
• 
p_ind: AVG(V(pi)). Definition: The Average Real Power (Watts) dissipated or 
utilized by the resistive load. Significance: Represents the "Real Work" done. 
When compared to p_src, it confirms that 100% of the paid-for energy is reaching 
the load.

17 
 
• 
tvind: V(vLind)=0. Definition: The exact timestamp when the voltage waveform 
crosses zero. Significance: Used as the reference point to measure the time delay 
of the current. 
• 
tiind: I(LLOAD)=0. Definition: The exact timestamp when the current waveform 
crosses zero. Significance: Used to calculate the lag between voltage and current. 
• 
phi_time: 360 * (tiind - tVind) * FREQ. Definition: The calculated Phase Angle (in 
degrees) of the inductive branch. Significance: Reveals the physical state of the 
load. A decreasing angle confirms the system is performing real work (Monotonic 
Phase Retardation). 
• 
g_ratio: S_internal / S_source. Definition: The Geometry Ratio (dimensionless). 
Significance: The defining metric of the invention. A value > 1.0 proves that the 
Internal Reactive Power exceeds the Source Apparent Power, confirming the 
"Geometric Phase Isolation" state. 
 
[0038] Table 2 - MASTER SIMULATION DATASET: LCFVR GPI PARAMETER SWEEP 
Master Configuration: 
LCFVR in GPI 
L=70H w 500R, C=0.1uF w 10R, F=60Hz, V=123.74Vrms, R=Base+FluxHindrance = 
500 to 25500 
 
Para
meter 500 Ω 
1500 Ω 
3000 Ω 
5500 Ω 
10500 Ω 
20500 Ω 
25500 Ω 
vrms_
src 
123.7423
144 
123.74231
44 
123.74231
44 
123.74231
44 
123.7423
144 
123.7423
144 
123.7423
144 
irms_
src 
9.33E-05 
0.0002675
845583 
0.0005292
291278 
0.0009538
318117 
0.001726
423745 
0.002863
317949 
0.003242
971315 
vrms_
ind 
123.7423
144 
123.74231
44 
123.74231
44 
123.74231
44 
123.7423
144 
123.7423
144 
123.7423
144 
irms_i
nd 
0.004688
34272 
0.0046816
27079 
0.0046591
7304 
0.0045905
39044 
0.004356
953785 
0.003703
095944 
0.003372
059524

18 
 
s_sou
rce 
0.011545
9815 
0.0331115
3254 
0.0654880
3712 
0.1180293
559 
0.213631
6698 
0.354313
5899 
0.401292
776 
s_inte
rnal 
0.580146
3789 
0.5793153
699 
0.5765368
551 
0.5680439
256 
0.539139
545 
0.458229
6626 
0.417266
4498 
p_src 
0.011207
40694 
0.0330926
0227 
0.0653384
5208 
0.1161145
036 
0.199531
8438 
0.281324
2216 
0.290165
3783 
p_ind 
0.010989
79477 
0.0328749
9695 
0.0651208
3837 
0.1158968
58 
0.199314
2331 
0.281106
6095 
0.289947
76 
tvind 
AT 
3.433333
33334 
AT 
3.4333333
3334 
AT 
3.4333333
3334 
AT 
3.4333333
3334 
AT 
3.433333
33334 
AT 
3.433333
33334 
AT 
3.433333
33334 
tiind 
AT 
3.437449
74754 
AT 
3.4373493
8665 
AT 
3.4371997
3823 
AT 
3.4369549
592 
AT 
3.436495
51098 
AT 
3.435748
10089 
AT 
3.435462
12861 
phi_ti
me 
88.91454
676 
86.746751
56 
83.514345
73 
78.227118
64 
68.30303
703 
52.15897
927 
45.98197
8 
g_rati
o 
50.24660
56 
17.495879
09 
8.8036972
93 
4.8127342
65 
2.523687
361 
1.293288
419 
1.039805
535

19 
 
[0039] CLAIMS 
1. A resonant electrical manifold comprising an AC source, a capacitive reservoir 
branch, and an inductive branch operably coupled in an effective parallel relationship 
such that they are subject to a substantially common boundary voltage, wherein the 
branches are configured according to a multi-parameter LCFVR tuning regime 
establishing a Geometric Phase Isolation (GPI) state, the LCFVR tuning regime defining 
the proportional relationship among inductance, capacitance, frequency, voltage, and 
resistance necessary to maintain the GPI state, such that the inductive reactance strictly 
exceeds the effective load resistance of the manifold, and an internal apparent power 
reservoir exceeds a boundary apparent power demand. 
2. The manifold of claim 1, wherein the circulating current magnitude in the inductive 
branch remains substantially constant across a range of load resistances. 
3. The manifold of claim 1, wherein the inductor phase angle decreases monotonically 
with increasing load resistance while flux amplitude remains proportional to the 
circulating current. 
4. The manifold of claim 1, wherein the effective load resistance comprises any real-
power extraction mechanism, including mechanical, magnetic, radiative, thermal, or 
environmental loads presenting electrically as a series resistance. 
5. The manifold of claim 1, wherein the manifold is scale-invariant, maintaining the GPI 
state under proportional scaling of inductance, capacitance, frequency, voltage, and 
resistance. 
6. The manifold of claim 1, wherein the inductive and capacitive branches comprise 
multi-coil geometries, capacitor arrays, or distributed asynchronous LC networks 
operating cooperatively. 
7. The manifold of claim 1, wherein the manifold transitions to classical resonant 
behavior only when the effective load resistance approaches the inductive reactance. 
8. A method of operating a resonant electrical manifold comprising: operably coupling a 
capacitive branch and an inductive branch in an effective parallel relationship configured 
to present a substantially common boundary voltage across both branches to a source, 
establishing an internal reactive power reservoir geometrically isolated from a boundary 
phasor, coupling a variable real-power load to the manifold, and maintaining a

20 
 
circulating current magnitude substantially independent of the variable load while 
allowing the inductor phase angle to decrease monotonically with increasing load. 
9. The method of claim 8, further comprising maintaining a Geometry Ratio greater than 
unity, defined as the ratio of internal apparent power to boundary apparent power. 
10. The method of claim 8, wherein magnetic flux amplitude is maintained 
independently of electrical phase angle under load variation. 
11. The method of claim 8, wherein the step of coupling a variable load includes 
extracting real power via mechanical work, thermal conversion, or radiative emission, 
demonstrating universal load equivalence. 
12. An electromechanical energy conversion system comprising a phase-isolated 
parallel resonant manifold coupled to a physical load, wherein the manifold operates in 
a Geometric Phase Isolation (GPI) regime defined by a proportional tuning of 
inductance, capacitance, frequency, voltage, and resistance such that internal 
circulating reactive power drives the physical load while presenting a reduced boundary 
apparent power demand to an energy source. 
13. The system of claim 12, configured as a grid-tied industrial drive providing leading or 
unity power factor to a utility grid, loaded or unloaded. 
14. The system of claim 12, configured as an inverter-coupled platform wherein the 
manifold isolates a DC/AC inverter from high internal magnetization currents. 
15. The system of claim 12, wherein the physical load comprises an electromechanical 
actuator, a rotary machine, or a multi-piston array. 
16. The system of claim 12, wherein the energy source comprises an autonomous 
generator. 
17. The system of claim 12, configured for deployment in mobile platforms or 
environmental energy recovery systems.

21 
 
[0040] ABSTRACT OF THE DISCLOSURE 
A Phase-Isolated LCFVR Energy Manifold is disclosed. The system utilizes a passive 
parallel resonant topology tuned to a "Geometric Phase Isolation" (GPI) state. When 
tuned within this support region, the manifold maintains high internal reactive power 
(Sinternal) while boundary real-power demand (Ssource) remains low, yielding a 
Geometry Ratio G > 1. The system acts as a Flux-Stable Resonant Source, allowing a 
variable mechanical load to extract real power via Monotonic Phase Retardation without 
collapsing the circulating magnetic flux. Data confirms the effect is maintained until the 
resistance exceeds the inductive reactance of the system.