Authors: O. Krishevich, V. Peretyachenko

Interpretation & Scope Clarification

System class: open electrodynamic system governed by classical laws. Medium: coupling and boundary medium, not a consumable source. Validation-first: TRL-stage work; no public performance claims in this document. Disclosure gating: implementation details are disclosed only through independent verification pathways. Terminology: the device is an energy conversion (transduction) system; “generator” is used in the patent/industry naming sense and does not imply creation of energy.

Classification of Evidence

This document constitutes operating regime validation evidence.

The procedures, measurements, and methodologies described herein are intended exclusively to:

• confirm the existence of repeatable operating regimes,
• assess regime stability under controlled laboratory conditions,
• verify bounded behavior and exclusion of trivial linear interpretations.

This protocol does not represent performance validation and does not establish energy balance, efficiency, or output capability.

All performance-related conclusions are explicitly deferred to subsequent validation stages and are subject to independent, integrated power and thermal measurement protocols.

Explicit Boundary of Non-Claims

The present protocol explicitly excludes the following interpretations and claims:

• net energy gain or energy amplification;
• self-sustaining or autonomous power generation;
• efficiency greater than unity;
• medium or environment acting as an energy source;
• substitution of calorimetric or integrated power measurements;
• conclusions derived from oscilloscope or spectral data alone.

Any interpretation extending beyond regime existence, stability, and repeatability falls outside the scope of this document and is considered invalid in the absence of dedicated, independent verification.

Where the Energy Comes From (Without Myths)

This system does not rely on fuel, does not extract energy “from air,” does not claim over-unity operation, and does not claim creation of energy. No consumable energy source is introduced beyond the system’s interaction with its environment as an open electrodynamic system under classical electrodynamics. In strict engineering terms, the system is an energy conversion (transduction) architecture that delivers electrical power by closing the measured external energy balance of an open electrodynamic system. In classical electrodynamics, a “source” is not defined as a fuel or reservoir, but as the complete external energy balance of an open system. For systems operating in nonlinear resonant regimes with internal circulation and feedback, energy exchange must be accounted for not only through wired inputs, but also through electromagnetic boundary interactions. Port (2) is introduced as an operational boundary interface term used to close the energy balance. It represents boundary-mediated energy exchange across the system boundary as described by the Poynting theorem and must not be interpreted as a discrete energy source, a generator claim, or a secondary battery. The term “external” refers to energy exchange occurring across the system boundary (external with respect to the system boundary), not to an identified external source. Linear input–output models fail in this context because they ignore internal energy circulation and phase-stabilized feedback. In such regimes, useful output power is sustained by maintaining a stable energy balance, not by continuous direct wired input proportional to output. Implementation details, internal parameters, and constructive solutions are treated as protected know-how and are intentionally excluded from this document. Verification is performed using standard engineering formats: sealed module validation and controlled disclosure under NDA. In both formats, an independent laboratory measures external inputs and outputs with its own instrumentation and applies controls to exclude parasitic coupling paths. Disclosure of implementation-specific details is gated by validation and certification milestones.

0. Document Status, Reproducibility, and Limits of Claims

This document is an engineering verification brief. Its purpose is to define verifiable energy behavior, formalize the energy balance, and specify an independent metrological test protocol. The document does not claim the status of a full academic publication with an openly reproducible design: part of the constructive implementation constitutes know-how and is protected by a patent portfolio. Independent verification is required in two acceptable formats:

• Controlled disclosure (under NDA): an independent laboratory is granted access to selected critical nodes strictly for verification purposes.
• Sealed module validation: an integrated module (including interface elements (2), if technologically inseparable) is provided sealed, and all measurements are performed by an independent party using its own equipment.

These formats are standard for engineering verification when implementation details are protected. The system is not treated as a “black box” in the evaluative sense: verification is metrological and is based on measured quantities, documented instruments, uncertainty, and mandatory control tests that exclude parasitic energy paths.

Methodology status under sealed module

This document defines measurable parameters, acceptance criteria, and test conditions. For configurations provided in the sealed module format, the test method may include elements protected as know-how. In this case, the test report contains a description of the measured quantities, the measurement instruments used, the test conditions, and the acceptance criteria, but does not contain a full description of the internal design or the implementation of the boundary interface associated with Port (2). The verification focus is strictly metrological: measurable quantities, uncertainty, and control tests — not disclosure of internal construction. The absence of full disclosure of the sealed module design does not affect the validity of test results, provided that all criteria defined in Section 9 of this document are met.

0.1 Methodological Boundaries and Interpretational Limitations

This document is an engineering specification for verification of the system’s energy behavior and does not assert the physical nature of the boundary-mediated energy exchange accounted for via Port (2) in Mode B. In particular:

• The document does not claim that the boundary-mediated energy exchange accounted for via port (2) is caused by any specific physical field, interaction, or environmental parameter (E, H, T, ρ, etc.).
• The document does not assume the existence of a new fundamental interaction or a violation of known laws of physics.
• The document does not require the verifying party to recognize any mechanism of energy generation beyond the experimentally measured energy balance.

Port (2) is introduced exclusively as an operational engineering designation of a boundary interface through which a reproducible energy contribution is observed under controlled test conditions and is tested against — and must not be attributable to — the following categories:

• wired input (port (1)),
• internal energy storage elements,
• recirculation of the system’s own losses,
• known parasitic paths (conductive, grid-based, or radio-frequency), including untracked return paths, shielding/grounding artifacts, and measurement reference errors.

The determination of the physical nature of this contribution lies outside the scope of this specification and pertains to a separate stage of fundamental research, which is not the subject of certification or investment verification.

1. Definitions and Energy Balance

1.1 Definitions and Energy Balance of the System

The VENDOR system is described by the Poynting theorem and standard circuit energy analysis as an open system with external energy exchange through defined ports and boundary interfaces.

1.1.1 Port (1): Wired Energy Interface

The average active power at port (1) is measured as: \[ P_{\mathrm{elec,avg}} = \frac{1}{T}\int_{0}^{T} v_{\mathrm{ext}}(t)\, i_{\mathrm{ext}}(t)\, dt, \] where the measurement includes all return current paths, reference conductors, shields, and cable assemblies associated with port (1).

1.1.2 Port (2): Boundary Coupling Interface (Installation Interface)

Definition note: In this document, “Port (2)” denotes a boundary/interface class for energy exchange across the system boundary (installation-dependent coupling), not a requirement for a dedicated electrical connector. Port (2) is an operational boundary interface term introduced to close the energy balance of an open electrodynamic system. It does not represent an energy source claim. Instead, it accounts for boundary-mediated energy exchange occurring through installation fixtures and electromagnetic boundary conditions. The formal representation of boundary-mediated exchange is expressed through the Poynting flux: \[ P_{\mathrm{field,avg}} = \oint_{\partial V} \langle \mathbf{S} \rangle \cdot d\mathbf{A}, \qquad \mathbf{S} = \mathbf{E} \times \mathbf{H}. \] Metrological note: in this specification, the boundary contribution associated with Port (2) is represented in classical form via the Poynting theorem; however, within the practical protocol it may be determined operationally as a residual of the measured energy balance, subject to mandatory control tests and uncertainty bounds (Section 9.2.2). This is a standard engineering approach when direct near-field flux integration is not practical for impulsive systems. The physical nature of the energy exchange associated with Port (2) lies outside the scope of this document and is addressed exclusively through metrological verification. No a priori assumptions are made regarding its physical carrier or underlying interaction mechanism. Important accounting note: Port (2) is an operational accounting interface, not necessarily a directly instrumented physical connector. It represents the boundary-mediated contribution required to close the measured energy balance under the control tests specified in Section 9. Port (2) must not be interpreted as an internal-only bookkeeping artifact. In particular, the boundary term is not reduced to:

• internal energy recirculation,
• reuse of the system’s own radiative or reactive losses,
• apparent output caused solely by detuning or transient discharge of stored energy,
• measurement artifacts due to untracked return paths, grounding, shielding, or reference conductors.

Changes in boundary capacitances/inductances may affect the operating regime and are treated as regime conditions; they are not, by themselves, an external energy source claim. Any energy leaving the system and not returned through an explicitly defined external interface is attributed to \(P_{\mathrm{loss,avg}}\). Thus, Port (2) represents a boundary-mediated external energy balance term defined exclusively on an experimental basis, without assumptions regarding its physical origin, and introduced solely to ensure a complete and non-contradictory energy balance of the open system.

1.1.3 Internal Quantities

• \(P_{\mathrm{load,avg}}\) — useful power delivered to the load.
• \(P_{\mathrm{loss,avg}}\) — total losses (thermal, dielectric, radiative, etc.).
• \(E_{\mathrm{buf}},\; P_{\mathrm{buf,avg}} = \left\langle \frac{dE_{\mathrm{buf}}}{dt} \right\rangle\) — energy and power of the internal buffer (if present).
• \(U_{\mathrm{circ,max}}\) — maximum recoverable stored energy in circulating fields/circuits (upper bound estimated from \(L,\; C,\; V_{\mathrm{peak}},\; I_{\mathrm{peak}}\)).

1.1.4 Full Balance

The full balance of average powers: \[ P_{\mathrm{elec,avg}} + P_{\mathrm{field,avg}} = P_{\mathrm{loss,avg}} + P_{\mathrm{load,avg}} + P_{\mathrm{buf,avg}}. \] In steady state with respect to the buffer: \[ P_{\mathrm{elec,avg}} + P_{\mathrm{field,avg}} = P_{\mathrm{loss,avg}} + P_{\mathrm{load,avg}}. \] The “not a power bank” criterion: in any claimed autonomous operating mode, the following must hold: \[ \int_{0}^{T} P_{\mathrm{load}}\, dt \gg \left|\Delta E_{\mathrm{buf}}\right| + U_{\mathrm{circ,max}} \] with simultaneous control of \(P_{\mathrm{elec,avg}} \approx 0\). Under these conditions, sustained delivered energy must be attributable to an external boundary term under the protocol classification (Port (2)), rather than internal storage, provided all exclusion controls are satisfied. Note: \(U_{\mathrm{circ,max}}\) represents the absolute upper bound of recoverable internal field energy at any instant and therefore bounds any possible storage-based explanation.

1.2 Why Linear Analysis Leads to False Conclusions

A typical critic’s argument: “How much power can be extracted from the Earth’s electrostatic field? The calculation shows \(P \sim 10^{-12}\ \mathrm{A/m^2} \times \text{area}\), which is negligibly small. Therefore, the system is impossible.” This criticism answers the question: “Can the global atmospheric field directly power a useful load through air conductivity?” But the system poses a different question: “What is the required total external balance \(P_{\mathrm{in,avg}}\) to sustain a regime with internal circulation and deliver power to the load under controlled conditions?” These are different problems. The critic implicitly models the environment as a direct power source, whereas in the correct model internal flows (including feedback) are a redistribution of energy within the device and do not form an additional external input. The external balance is fully defined by: \[ P_{\mathrm{in,avg}} = P_{\mathrm{loss,avg}} + P_{\mathrm{load,avg}} + P_{\mathrm{buf,avg}} \] (in steady state, the last term \(\to 0\)).

2. Resonant LC Circuits: Energy and Mathematics

2.1 Ideal Lossless LC Circuit

In an ideal (resistance-free) LC circuit, charge and current oscillate: \[ \omega_{0}=\frac{1}{\sqrt{LC}}, \qquad f_{0}=\frac{1}{2\pi\sqrt{LC}} \] \[ q(t)=q_{0}\cos(\omega_{0}t), \qquad i(t)=\frac{dq}{dt}=-q_{0}\omega_{0}\sin(\omega_{0}t) \] The energy of the capacitor and the inductor: \[ U_{C}(t)=\frac{q(t)^{2}}{2C}, \qquad U_{L}(t)=\frac{1}{2}L\,i(t)^{2} \] The total stored energy remains constant: \[ U_{\mathrm{tot}}=U_{C}+U_{L}=\frac{q_{0}^{2}}{2C}=\mathrm{const} \] Physical meaning: energy periodically transfers between the electric field of the capacitor and the magnetic field of the inductor at frequency \(f_{0}\). Note on sign and phase: the sign in the expression for \(i(t)\) depends on the chosen current direction; physically relevant are the amplitude and the phase shift of \(\pi/2\) between \(q(t)\) and \(i(t)\).

2.2 Real RLC Circuit with Losses and External Voltage

In reality, losses are present and are modeled by an equivalent resistance \(R\): \[ \frac{d^{2}q}{dt^{2}}+\frac{R}{L}\frac{dq}{dt}+\frac{q}{LC}=\frac{1}{L}v_{\mathrm{drive}}(t) \] where \(v_{\mathrm{drive}}(t)\) is the external driving voltage (in a practical circuit, it is formed by port \(v_{\mathrm{ext}}(t)\) through the appropriate connection topology). For a weakly damped regime \(\left(R \ll \sqrt{\frac{L}{C}}\right)\), the energy decays approximately exponentially: \[ U(t)\approx U_{0}\exp\!\left(-\frac{t}{\tau}\right), \qquad \tau \approx \frac{2L}{R} \] The quality factor (Q-factor) determines the decay rate and energy efficiency: \[ Q \equiv 2\pi \times \frac{\text{stored energy}}{\text{losses per cycle}}=\frac{\omega_{0}L}{R}\approx \pi f_{0}\tau \] A high \(Q\) means slow decay: energy circulates many times before being fully dissipated.

2.3 Spectral Structure of Instantaneous Power

In an LC circuit, current and voltage oscillate at the fundamental resonant frequency \(f_{0}\): \[ i(t)=i_{0}\cos(\omega_{0}t), \qquad v_{C}(t)=V_{0}\sin(\omega_{0}t) \] Energy at each instant: \[ U_{C}(t)=\frac{1}{2}C V_{0}^{2}\sin^{2}(\omega_{0}t) =\frac{C V_{0}^{2}}{4}\left[1-\cos(2\omega_{0}t)\right] \] \[ U_{L}(t)=\frac{1}{2}L i_{0}^{2}\cos^{2}(\omega_{0}t) =\frac{L i_{0}^{2}}{4}\left[1+\cos(2\omega_{0}t)\right] \] Current and voltage have the fundamental frequency \(f_{0}\), whereas instantaneous energy contains a DC component and a component at the doubled frequency \(2f_{0}\). Significance for coupled circuits: In coupled circuits, energy transfer is determined by the instantaneous power \(p(t)=v(t)i(t)\); for harmonic components \(v \sim \sin(\omega_{0}t)\), \(i \sim \cos(\omega_{0}t)\), their product contains components at \(0\) and \(2\omega_{0}\). Therefore, when analyzing power and losses in a resonator, it is essential to account for the component at \(2f_{0}\), even if currents/fluxes are dominated by \(f_{0}\).

2.4 Conditions for the Initiation and Sustaining of Oscillations in a System with Feedback and Dissipative Channels

To initiate oscillations in a system with feedback, the energy delivered to the circuit through port (1) over a period \(T\) must exceed the losses: \[ E_{\mathrm{ext,in}}(T) > E_{\mathrm{loss}}(T) + E_{\mathrm{load}}(T) \qquad \text{(start-up phase)} \] where \(E_{\mathrm{ext,in}}(T)\equiv \int_{0}^{T} p_{\mathrm{ext}}(t)\, dt\). In the steady-state (limit cycle): \[ E_{\mathrm{ext,in}}(T)=E_{\mathrm{loss}}(T)+E_{\mathrm{load}}(T) \] In this regime, the amplitude stabilizes at a level determined by system nonlinearities (discharger, saturation, breakdown diodes). This is described in Section 7.

3. VENDOR Generator Architecture

3.1 System Components

According to patent WO2024209235A1:

• Port-based energy interface / mode initiation node (1) — a physically defined bidirectional port through which port-based energy exchange is carried out during start-up and in steady-state operation. In a practical implementation, port (1) may be connected to a battery buffer via a BMS, enabling both energy delivery into the system and energy reception for recharging when reverse flow is present (recuperation).
• Discharge node storage element (3) — a capacitor charged from port (1).
• Multiple dischargers (14, 15, 16) — corona dischargers with different breakdown voltages and spectral characteristics.
• Primary winding (4) of transformer (5).
• Secondary winding (7) + capacitor (8) — forming a resonant LC circuit.
• Feedback path (internal coupling path) — returns part of the energy from the resonant circuit to storage element (3), enabling energy redistribution and sustaining a self-oscillatory regime.
• Output extraction stage (as in the patent) — transfers energy to the load (13) via an isolated extraction topology.

3.2 Operating Sequence

Phase 1: Charging of the Storage Element

Through port (1), external power \(P_{\mathrm{ext}}\) is delivered, charging capacitor (3) to a voltage exceeding the breakdown voltage of one or more dischargers.

Phase 2: Discharge and Impulse into the Primary

The discharger breaks down; capacitor (3) rapidly discharges through the primary winding (4). A current impulse with a high \(di/dt\) arises, determined by capacitance \(C_{3}\), parasitic inductances, and the discharge dynamics of the discharger. This impulse induces a voltage on the secondary winding (7) via magnetic transformer coupling.

Phase 3: Resonant Oscillation of the Secondary Circuit

The secondary winding (7) together with capacitor (8) forms an LC circuit. The induced voltage excites this circuit, and with a high quality factor \(Q\), the circuit oscillates for many cycles. The magnetic field of the transformer carries these oscillations.

Phase 4: Feedback and Regime Dynamics

Part of the energy from the secondary circuit (via the internal coupling path) flows into the storage element (3). This feedback:

• serves as a positive feedback mechanism for sustaining the regime,
• provides redistribution of energy between the storage element and the resonator,
• maintains the system in a limit-cycle regime (see Section 7).

In port-based terms, the feedback forms an internal energy transfer path from the oscillatory circuit to the storage element, modifying phase relationships and excitation conditions, but without adding external energy beyond the total external balance defined by the measured inputs and boundary terms. In steady-state operation, the total external balance compensates losses \(P_{\mathrm{loss}}\) and useful output power \(P_{\mathrm{load}}\) in accordance with the balance formula given in Section 1.1.

Phase 5: Power Extraction to the Load

The output extraction stage transfers energy to the load. The load receives power \(P_{\mathrm{load}}\), and its magnitude is reflected in a reduction of the overall quality factor \(Q_{\mathrm{tot}}\) and an increase in the required total external energy inflow \(P_{\mathrm{in,avg}}\), as described in Section 6.3.

3.3 Role of Multiple Dischargers and Spectral Stability

The dischargers have different breakdown voltages and spectral characteristics, offset in frequency. Engineering purpose:

• When operating conditions change (humidity, temperature, micro-gaps due to erosion), one discharger may lose optimal characteristics.
• Another discharger with a neighboring breakdown voltage then activates and sustains the regime.
• The collective action reduces sensitivity to parametric drift.
• This is an engineering redundancy, not a “magical” mechanism.

Regime stability as an architectural property: A multi-discharger structure with overlapping thresholds and conductivity dynamics implements “regime stability”: the system preserves the excitation conditions of the resonator under drift of discharge parameters (humidity, erosion, micro-geometry) by switching the active discharge channel, without changing the external balance principle \[ P_{\mathrm{ext,avg}} = P_{\mathrm{loss,avg}} + P_{\mathrm{load,avg}} + P_{\mathrm{buf,avg}}. \]

4. Corona Discharge as a Nonlinear Adaptive Element

4.1 Physics of Corona Discharge

Corona discharge occurs when the local electric field strength near an electrode reaches values sufficient to ionize the gas; the threshold is determined by geometry (radius of curvature), pressure, gas composition, and the operating regime (corona vs. streamer). Ionization mechanism:

• A high electric field gradient ionizes air molecules in the vicinity of the electrode tip.
• A cloud of weakly ionized plasma is formed.
• The plasma exhibits an effective conductivity \(\sigma(t,E)\), which depends on the electric field strength and time.
• This conductivity is nonlinear and nonstationary.

Corona discharge generates impulsive currents with a broadband spectral density, depending on electrode geometry, gas parameters, and the discharge regime (corona vs. streamer). The nonlinear conductivity affects phase noise, resonator excitation conditions, and regime stability.

4.2 Regime Adaptivity

Multiple corona dischargers connected in parallel with different breakdown voltages form an adaptive system:

• At low field levels, some dischargers remain in a state of weak ionization.
• At higher field levels, other dischargers trigger and draw the current.
• The overall regime remains stable over a wide range of conditions.

5. Environmental Medium as Boundary Conditions and a Reproducibility Factor

5.1 Influence of Environmental Parameters

The electrical parameters of the atmosphere (conductivity \(\sigma\), humidity, pressure, temperature) affect:

• Breakdown thresholds and regime transitions — for uniform gaps, a Paschen-type dependence \(U_{\mathrm{br}} = f(pd)\) serves as a reference; however, for sharp electrodes, local field enhancement and emission conditions become decisive.
• Corona discharge stability — the spectral characteristics of the impulse depend on pressure and gas composition; humidity can significantly modify breakdown thresholds and discharge stability.
• Parasitic losses — dielectric losses in air, leakage over contaminated surfaces, and induced currents.

5.2 Role in Test Protocols

In VENDOR, the atmosphere is considered exclusively as the working and boundary medium for discharge processes, not as an energy source. Independent verification protocols must:

• Record and control environmental parameters (\(P, T, RH\)).
• Evaluate regime sensitivity to their variations within the protocol (Section 9.5).

For reproducibility purposes, these influences are treated as experimentally measurable regime sensitivities, not as a priori explanations of the energy source.

6. Quality Factor and Energy Balance in Resonant Systems with Load

6.1 Q-Factor and Power Losses in a Resonator

For a resonator with stored energy \(U\) and angular frequency \(\omega_{0}\), the power dissipated in internal losses is: \[ P_{0} = \frac{\omega_{0} U}{Q_{0}} \] where \(Q_{0}\) is the equivalent unloaded quality factor, including all dissipative channels: \[ \frac{1}{Q_{0}} = \frac{1}{Q_{R}} + \frac{1}{Q_{C}} + \frac{1}{Q_{\mathrm{rad}}} \] Here, \(Q_{R}\) corresponds to ohmic losses, \(Q_{C}\) to dielectric losses, and \(Q_{\mathrm{rad}}\) to radiative losses.

6.2 Load as an Additional Dissipation Channel

When a load is connected (extraction stage), the load interacts with the electromagnetic field of the resonator and acts as an additional channel for energy extraction from the resonator (with the energy being converted into useful work at the load). This is equivalent to introducing a load quality factor: \[ Q_{L} = \frac{\omega_{0} U}{P_{\mathrm{load}}} \] The total quality factor of the system is: \[ \frac{1}{Q_{\mathrm{tot}}} = \frac{1}{Q_{0}} + \frac{1}{Q_{L}} \]

6.3 Required External Power in the Presence of Load

To maintain a specified level of stored energy \(U\) in the resonator with a connected load, compensation of total losses and energy extraction to the load is required. The corresponding total external average power is defined as: \[ P_{\mathrm{in,avg}} = \frac{\omega_{0} U}{Q_{\mathrm{tot}}}, \qquad P_{\mathrm{in,avg}} \equiv P_{\mathrm{elec,avg}} + P_{\mathrm{field,avg}}. \] An increase in useful load power \(P_{\mathrm{load}}\) is equivalent to a reduction of the total quality factor \(Q_{\mathrm{tot}}\) and requires an increase in the total external energy inflow \(P_{\mathrm{in,avg}}\). The contribution to \(P_{\mathrm{in,avg}}\) may originate from either the wired port-based channel or the boundary (field) term, depending on the operating regime and the configuration of the system’s electrodynamic coupling to its environment. Thus, an increase in load does not necessarily require an increase in the wired port power \(P_{\mathrm{elec}}\); it requires an increase in the total external balance, as determined by the complete system energy accounting.

6.4 Stored Energy Level as a Design Parameter

The level of stored energy \(U\) in the resonator is determined by the technical design: \[ U = \frac{1}{2} C_{8} V_{8}^{2} = \frac{1}{2} L_{7} I_{7}^{2} \] where \(C_{8}\) and \(L_{7}\) are circuit parameters. Increasing \(U\) requires either increasing the voltage \(V_{8}\) (with stringent insulation requirements) or increasing the inductance (more turns, larger physical construction). This is not an independent degree of freedom for increasing output power. The level of \(U\) and the required external power \(P_{\mathrm{in,avg}}\) are linked by the relation given in Section 6.3.

7. Nonlinear Dynamics and the Limit-Cycle Regime

7.1 Closed Systems with Positive Feedback

The equation for a closed resonant system with feedback: \[ \frac{dx}{dt} = f(x) + k \cdot g(x) \] where:

• \(f(x)\) — natural dynamics (losses, damping),
• \(g(x)\) — feedback signal,
• \(k\) — coupling coefficient.

System behavior:

• \(k = 0\) (no feedback): the trajectory converges to equilibrium (oscillations decay exponentially).
• Small \(k\): damping is slowed.
• Critical \(k\): the system enters a limit cycle — a periodic regime with fixed amplitude and frequency.

Physical meaning of the state vector: In the context of VENDOR, the state vector \(x\) may include: the voltage across the storage element \(V_{3}\), winding currents, the phase and amplitude of the resonant regime in the secondary circuit, effective discharge parameters (equivalent conductivity \(\sigma(t,E)\)), and the buffer state of charge (SoC).

7.2 Limit Cycle and Energy Balance

In the limit cycle, the system self-regulates its amplitude such that the energy supplied through port (1) over a period \(T\) equals the energy lost and delivered to the load: \[ E_{\mathrm{ext}}(T) = E_{\mathrm{loss}}(T) + E_{\mathrm{load}}(T) \] where \[ E_{\mathrm{ext}}(T) \equiv \int_{0}^{T} v_{\mathrm{ext}}(t)\, i_{\mathrm{ext}}(t)\, dt. \] When a battery buffer is present via a BMS, the quantity \(E_{\mathrm{ext}}(T)\) is interpreted as the total energy flow through port (1), rather than as a unidirectional battery discharge. In steady state (\(P_{\mathrm{buf,avg}} \approx 0\)), intervals of partial buffer recharging are possible due to internal energy redistribution and recuperation paths, without violating the overall energy balance \[ P_{\mathrm{ext,avg}} = P_{\mathrm{loss,avg}} + P_{\mathrm{load,avg}}. \] The amplitude neither grows nor decays — the system resides at an equilibrium point on the phase plane. This does not violate the law of energy conservation; it is simply a stable operating point where energy input is balanced by energy expenditure.

7.3 Role of Nonlinearities in VENDOR

Nonlinear elements (dischargers, transformer saturation, breakdown diodes) serve to:

• limit amplitude — preventing exponential growth of voltages,
• synchronize the regime — fixing frequency and phase,
• adapt to load — changes in \(Q_{L}\) lead to amplitude changes while the regime remains stable.

8. Energy Balance in Steady-State Operation: Strict Formulation

8.1 Full Power Balance

In steady-state (limit cycle), for the entire system (averaged over interval \(T\)): \[ P_{\mathrm{ext,avg}} = P_{\mathrm{Joule,avg}} + P_{\mathrm{dielectric,avg}} + P_{\mathrm{radiation,avg}} + P_{\mathrm{erosion,avg}} + P_{\mathrm{load,avg}} + P_{\mathrm{buf,avg}} \] or, in compact form: \[ P_{\mathrm{ext,avg}} = P_{\mathrm{loss,avg}} + P_{\mathrm{load,avg}} + P_{\mathrm{buf,avg}} \] where \[ P_{\mathrm{loss}} = P_{\mathrm{Joule}} + P_{\mathrm{diel}} + P_{\mathrm{rad}} + P_{\mathrm{erosion}} + \ldots \] is the total loss power, and \[ P_{\mathrm{buf,avg}} = \left\langle \frac{dE_{\mathrm{buf}}}{dt} \right\rangle \] is the average buffer power. In steady state with respect to SoC, \(P_{\mathrm{buf,avg}} \approx 0\), hence: \[ P_{\mathrm{ext,avg}} = P_{\mathrm{loss,avg}} + P_{\mathrm{load,avg}}. \] The left-hand side represents the energy entering through port (1) and other external inputs (including boundary terms defined in this specification). The right-hand side represents all channels of energy expenditure and buffering.

8.2 Control of Parasitic Inputs in the Test Protocol

The test protocol must include measures to control parasitic couplings (mechanical, thermal, electromagnetic) and to evaluate their contributions. The objective is to demonstrate that the measured balance \[ P_{\mathrm{ext,avg}} \approx P_{\mathrm{load,avg}} + P_{\mathrm{loss,avg}} + P_{\mathrm{buf,avg}} \] is preserved under controlled variation of external conditions and cannot be explained by parasitic inputs. A detailed protocol is provided in Section 9.

9. Metrological Verification Protocol

Theoretical analysis shows that the VENDOR architecture is physically consistent within the framework of classical electrodynamics. Final verification requires independent laboratory validation.

9.1 Classification of the Test Site and Low-EM Criteria

To exclude interpretations related to “50/60 Hz harvesting,” the test site must be quantitatively characterized.

9.1.1 Grid Background Metric (50/60 Hz)

The measurable metric \(B_{50}\) is defined as the amplitude of magnetic flux density at 50/60 Hz (and \(B_{150}\) at the 3rd harmonic) at a control point, measured using a calibrated induction loop and a spectrum analyzer / FFT recorder. A threshold low-EM criterion is established:

• \(B_{50}\) and \(B_{150}\) at the test site must not exceed 1% of the reference “urban” level, measured using the same equipment set in a typical urban laboratory (reference site), at the same height and with the same loop orientation.

Note: the reference value may be recorded prior to testing, with calibration logs retained.

9.1.2 Site Qualification and Grid Infrastructure Recording

The test site must simultaneously satisfy:

• site qualification based on measured \(B_{50}\) / \(B_{150}\) background and mapping; distance from grid infrastructure is recorded, but acceptance is determined by the low-EM criteria and field scans rather than a fixed radius;
• absence of unaccounted underground power cabling or transformers within the radius identified by preliminary scanning of \(B_{50}\), confirmed by site mapping and instrumentation logs.

9.2 Main Test: Energy Balance

9.2.1 Measured Quantities

During testing, the following time-averaged quantities are determined: \[ P_{\mathrm{elec,avg}} = \frac{1}{T}\int_{0}^{T} v_{\mathrm{ext}}(t)\, i_{\mathrm{ext}}(t)\, dt \] — average wired electrical power at port (1), including all return and reference paths. \[ P_{\mathrm{buf,avg}} = \left\langle \frac{dE_{\mathrm{buf}}}{dt} \right\rangle \] — average rate of change of internal buffer energy, determined via energy audit at the buffer terminals and/or independent state-of-charge (SoC) estimation. \[ P_{\mathrm{load,avg}} = \frac{1}{T}\int_{0}^{T} v_{\mathrm{out}}(t)\, i_{\mathrm{out}}(t)\, dt \] — average active power delivered to the load. \[ P_{\mathrm{loss,avg}} \] — average loss power, determined via thermal and/or calorimetric balance, including local hot spots and total heat dissipation.

9.2.1.1 Measurement Equipment Requirements and “External-Terminals (Black-Box) Method”

Because the system operates with non-sinusoidal, impulsive waveforms, power measurements shall be performed using instrumentation and methods demonstrably suitable for wideband, transient regimes. The objective is to obtain metrologically defensible active power on external terminals without requiring access to internal nodes. (a) Allowed measurement approaches (choose one or combine):

1. Wideband power analyzer method (if instrument capability is demonstrated for the measured waveform class), or
2. Oscilloscope-based method using simultaneous voltage and current acquisition with calibrated probes and documented processing of instantaneous power \(p(t)=v(t)\cdot i(t)\).

(b) Adequacy criteria (mandatory):

• The selected method shall demonstrate sufficient bandwidth, sampling, and dynamic range to represent the measured waveforms without aliasing or front-end saturation.
• The measurement chain shall include documented probe transfer functions (magnitude and phase where applicable) or manufacturer calibration data sufficient to bound amplitude and phase errors in the frequency range that materially contributes to active power.
• Deskew / time-alignment between voltage and current channels is mandatory, with a documented procedure and resulting residual timing uncertainty.
• The laboratory shall provide a measurement uncertainty budget for \(P_{\mathrm{elec,avg}}\) and \(P_{\mathrm{load,avg}}\) consistent with the overall energy-balance uncertainty defined in this protocol.

(c) External-terminals-only (“black-box”) constraint (IP protection): All electrical measurements are performed exclusively on external terminals:

• Port (1) terminals, including all return paths, shields, and reference conductors;
• Output/load terminals.

Connection of probes to internal nodes, PCB traces, component leads, or internal measurement points is not required and is not permitted under the IP protection rules of this protocol. (d) Anti-artifact controls: The verifying party shall document measures to exclude hidden return paths and reference errors (grounds, shields, chassis, auxiliary cables, instrumentation earth paths), and shall perform control checks specified in Section 9 to demonstrate measurement integrity. (e) Calibration and uncertainty requirements: Electrical power measurement instruments must be calibrated at least once every 12 months. Temperature measurements must be performed using sensors with accuracy no worse than ±0.5 °C, calibrated at least once every 6 months. The expanded uncertainty of the energy balance is taken as: \[ \delta_{A} = 5\% \qquad (k = 2), \] corresponding to the combined uncertainty of electrical, thermal, and stored energy measurements. Note: For low-power tests (\(P_{\mathrm{load,avg}} < 50\,\mathrm{W}\)), the laboratory may specify a tighter uncertainty bound or justify the applicability of \(\delta_A\).

9.2.2 Energy Balance Equation

In all operating regimes, the averaged energy balance must hold: \[ P_{\mathrm{elec,avg}} + P_{\mathrm{field,avg}} \approx P_{\mathrm{loss,avg}} + P_{\mathrm{load,avg}} + P_{\mathrm{buf,avg}}. \] Important accounting note: The decomposition into \(P_{\mathrm{elec,avg}}\) and \(P_{\mathrm{field,avg}}\) is an accounting decomposition of the total external balance, not a statement of two independent or additive sources. It represents a metrological partitioning of energy exchange across different interface types (wired vs. boundary-mediated), both of which contribute to the total external balance of the open system. Direct measurement of the Poynting vector flux integral \[ \oint \langle \mathbf{S} \rangle \cdot d\mathbf{A} \] in an impulsive near-field system is a complex metrological task. Therefore, \(P_{\mathrm{field,avg}}\) may be determined as the residual term of the energy balance, subject to mandatory control tests listed in Sections 9.2.3–9.2.7.

9.2.3 Control of Hidden Energy Storage (“Energy Stress Test + Negative Inspection”)

Because the Applicant does not disclose circuit topology, component nomenclature (BOM), or schematic implementation details (protected know-how), verification that the device does not contain hidden stored-energy sources (batteries, primary cells, fuel cells, supercapacitors, or equivalent) shall be performed using a two-stage protocol: Stage A — Energy Stress Test (duration requirement) The device shall operate continuously under a defined load with stable output such that the delivered energy \(E_{\mathrm{out}}\) exceeds a conservative upper bound on any plausible internal stored energy that could physically fit within the device enclosure. \[ E_{\mathrm{out}}=\int_{0}^{T_{\mathrm{test}}} P_{\mathrm{load}}(t)\,dt \] The minimum test duration \(T_{\mathrm{test}}\) shall be chosen such that: \[ E_{\mathrm{out}} \ge K_{\mathrm{safety}}\cdot E_{\mathrm{max,storage}} \] where:

• \(E_{\mathrm{max,storage}}\) is a conservative upper estimate of the maximum physically plausible stored energy within the sealed volume, based on established volumetric energy density bounds of known storage technologies (primary cells, rechargeable cells, supercapacitors, fuel cartridges, etc.).
• \(K_{\mathrm{safety}}\) is a safety factor (recommended \(K_{\mathrm{safety}}\ge 2\), unless the laboratory justifies a higher value).

Laboratory discretion (anti-dispute clause): The verifying laboratory defines and documents \(E_{\mathrm{max,storage}}\) using conservative industry bounds and publishes the basis as part of the test report. The protocol does not mandate a single chemistry value to avoid disputes over market maxima. Success criterion (Stage A): The device completes \(T_{\mathrm{test}}\) without a sustained decline of delivered load power that would be consistent with depletion of an internal storage source, and with buffer neutrality requirements in Section 9. Stability definition: The laboratory shall pre-define and document an objective stability metric for “no sustained decline” (e.g., allowable drift band and minimum duration window), appropriate to the selected load and measurement uncertainty, and apply it consistently throughout the test. Note: \(T_{\mathrm{test}}\) shall be no less than the characteristic thermal and buffer time constants of the system and, in any case, not less than several hours for power levels above \(P_{\mathrm{min}}\), unless otherwise justified. Stage B — Negative Inspection (post-test verification without IP disclosure) Immediately after Stage A, the device shall undergo negative inspection to confirm absence of prohibited stored-energy sources. Permitted inspection methods (choose one):

1. Witnessed opening of the enclosure under controlled conditions, or
2. X-ray / CT inspection where opening is not possible (e.g., full potting/compounding).

Inspection scope limitation (IP protection):

• The inspector is authorized only to search for prohibited inclusions: batteries/primary cells, fuel cartridges, electrochemical stacks, supercapacitor banks, hidden power modules, or other stored-energy subsystems.
• The Applicant may remove component markings, use opaque potting, and apply protective covers to PCB assemblies.

Prohibited actions (anti-espionage):

• No reverse engineering: no tracing or documenting PCB topology, no measurement of R/L/C values, no attempt to dissolve or remove protective compounds, no demand for BOM or schematics.
• Photo/video is limited to angles sufficient to confirm the absence of prohibited energy storage (overview documentation). Macro photography or imaging intended to capture PCB routing, component placement detail, or winding geometry is prohibited.

X-ray/CT limitations:

• Imaging interpretation is limited to identifying structures characteristic of stored-energy devices (cell geometries, electrode rolls/stacks, electrolyte volumes, supercapacitor cans, etc.).
• Analysis for reconstructing PCB layers, track routing, or internal construction beyond the purpose of negative inspection is not permitted.

Verdict rule: If Stage A is satisfied and Stage B reveals no prohibited stored-energy sources, the “hidden battery/storage” hypothesis is considered falsified without disclosure of the internal schematic or component nomenclature.

9.2.4 Exclusion of Wired and Parasitic Energy Inputs

In autonomous test mode, the following conditions must be met:

• wired input through port (1) is suppressed and measured: \[ P_{\mathrm{elec,avg}} \le \varepsilon_{\mathrm{elec}}; \]
• no hidden or unaccounted wired paths, including grounding, shields, signal and reference lines;
• absence of active wireless power injection confirmed by independent spectral monitoring over a laboratory-defined range appropriate to the site and device class, with results included in the test report.

9.2.5 Status of the Residual Energy Term \(P_{\mathrm{field,avg}}\)

Determining \(P_{\mathrm{field,avg}}\) as a residual term of the energy balance does not constitute proof of a new physical interaction. \(P_{\mathrm{field,avg}}\) must be interpreted as a boundary contribution whose physical nature lies outside the scope of this engineering specification and is subject to separate fundamental research. Any energy leaving the system and not returned through a defined external interface is attributed to \(P_{\mathrm{loss,avg}}\) and cannot be included in \(P_{\mathrm{field,avg}}\).

9.2.6 Classification of Operating Modes

Mode A (wired input): \[ \left| P_{\mathrm{elec,avg}} – \left(P_{\mathrm{loss,avg}} + P_{\mathrm{load,avg}} + P_{\mathrm{buf,avg}}\right) \right| \le \delta_{A}. \] Mode B (classified boundary-mediated operation via Port (2)): All of the following conditions must be satisfied simultaneously:

• \(P_{\mathrm{elec,avg}} \le \varepsilon_{\mathrm{elec}}\);
• \(\left|P_{\mathrm{buf,avg}}\right| \le \varepsilon_{\mathrm{buf}}\);
• \(P_{\mathrm{load,avg}} \ge P_{\mathrm{min}}\);
• control tests in Sections 9.2.3–9.2.7 successfully completed.

In this case: \[ P_{\mathrm{field,avg}} \approx P_{\mathrm{loss,avg}} + P_{\mathrm{load,avg}}. \]

9.2.7 Numerical Values of Tolerances

Parameter	Value
\(\delta_{A}\)	5 %
\(\varepsilon_{\mathrm{elec}}\)	≤ 1 % of \(P_{\mathrm{load,avg}}\)
\(\varepsilon_{\mathrm{buf}}\)	≤ 0.5 % of \(E_{\mathrm{buf,max}}\) over \(T_{\mathrm{test}}\)
\(P_{\mathrm{min}}\)	10 W

9.3 Resonant Characteristics

Resonant frequency: \[ f_{0}^{\mathrm{meas}} = \arg\max_{f} \left| \mathrm{FFT}\{i_{2}(t)\} \right| \] Expectation: \[ \left| f_{0}^{\mathrm{meas}} – \frac{1}{2\pi\sqrt{L_{7}C_{8}}} \right| < 10\%. \] Q-factor: \[ Q_{\mathrm{meas}} = \frac{f_{0}^{\mathrm{meas}}}{\Delta f_{3\mathrm{dB}}}, \] where \(\Delta f_{3\mathrm{dB}}\) is the bandwidth at the −3 dB level.

9.4 Load Verification via Quality Factor

\(Q_{\mathrm{tot}}\) is measured for different load resistance values \(R_{L}\): \[ \frac{1}{Q_{\mathrm{tot}}} = \frac{1}{Q_{0}} + \frac{1}{Q_{L}}, \qquad Q_{L} = \frac{\omega_{0}U}{P_{\mathrm{load}}}. \] Expectation: the load manifests as an additional energy extraction channel from the resonator (loaded Q), not as an external source. The plots of \(Q_{\mathrm{tot}}(R_{L})\) and required power \(P_{\mathrm{in,avg}}(R_{L})\) should follow theory linearly.

9.5 Control of Environmental Influence

• Pressure variation (within an available controlled chamber range, e.g., 500–1000 mbar): measure \(\Delta f_{0}\), \(\Delta U_{\mathrm{br}}\), \(\Delta P_{\mathrm{loss}}\).
• Humidity variation (20–90% RH): verify drift of breakdown voltage.
• Long-term test (≥ 24 h): regime stability under fixed load and monitoring of buffer SoC.
• Isolation from parasitic fields: Faraday shielding, verification of absence of induction from grid fields.

9.6 Exclusion of Additional Energy Inputs

• Mechanical vibration — system on vibration isolation; measure acceleration.
• Thermal gradients — control temperature within ±2 °C; exclude Seebeck and Peltier effects.
• Electromagnetic induction — shielding; verify residual fields with source (1) disconnected.
• Buffer state-of-charge monitoring — confirm that in steady state \[ P_{\mathrm{buf,avg}} = \left\langle \frac{dE_{\mathrm{buf}}}{dt} \right\rangle \approx 0 \] throughout the test, confirming absence of hidden energy sources.

9.7 Test Data Management

9.7.1 Primary data are recorded continuously with the following periodicity:

• \(P_{\mathrm{elec}}, P_{\mathrm{load}}\): at least once per minute;
• \(B_{50}, B_{150}\): at least once per second;
• Buffer SoC and temperatures: at least once every 5 minutes.

9.7.2 Data are stored in CSV format with metadata including date, time, equipment identification, and calibration information.

9.7.3 Minimum retention period for primary data is 5 years after completion of testing.

9.7.4 Data backup is performed at least once per day to an independent storage medium.

10. Safety Requirements and Limitations

10.1 Equipment Classification

Class I equipment (protective earthing).

10.2 Maximum Operating Voltage

Specified in the technical datasheet of the particular configuration.

10.3 Pollution Degree

Degree 2 (normal atmospheric environment).

10.4 Ozone Control

Continuous monitoring of ozone concentration \( \mathrm{O_3} \) with automatic system shutdown if the concentration exceeds \(0.05\ \mathrm{mg/m^3}\).

10.5 Electromagnetic Compatibility

Testing in accordance with EN 55011, Class A (industrial equipment).

10.6 Application Limitations

The equipment is intended exclusively for industrial use under controlled conditions. It is not intended for domestic or household applications.

Conclusion

The VENDOR generator is an open electrodynamic system whose behavior is described within the framework of classical electrodynamics and the theory of nonlinear resonant systems. The complete energy accounting of the system includes both wired (port-based) and boundary-coupled terms of external energy exchange, where “external” refers to energy exchange across the system boundary, not to an identified external source. In steady-state operation, the balance of average powers takes the form: \[ P_{\mathrm{elec,avg}} + P_{\mathrm{field,avg}} = P_{\mathrm{loss,avg}} + P_{\mathrm{load,avg}} + P_{\mathrm{buf,avg}}, \] with \(P_{\mathrm{buf,avg}} \approx 0\). Thus, useful power delivered to the load is sustained by the total external energy balance of an open electrodynamic system. In Mode B classification, the boundary-coupled contribution associated with Port (2) is treated as a residual term required to close the measured balance under the mandatory control tests in Section 9. This does not constitute a claim of a discrete “source,” and no physical carrier is asserted within this specification. The power class (watts / hundreds of watts / kilowatts) within the scope of this document is a parameter subject to verification under Section 9; any numerical values are considered claims only after an independent energy audit in Modes A/B with successful completion of the control tests specified in Section 9.2.

References

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