Mathematician review: Kelly, "The Practical Guide to Free-Energy Devices" (V32.9, 2018)

Reviewer: PhD mathematician (Step 2). Date: 2026-10-08. Tags: [read] from the project files (deep reads, facts.json, claims.md, sites.md, research notes) or the source text in _text/; [calc] my own arithmetic (Python, .venv); [web] with URL; [memory] with confidence.

Source note. The book is a compilation: the primary source for what Kelly and the people he reproduces claim, not for independent measurement. Kelly: "you are welcome to consider this a work of fiction" (p.11) [read: claims.md]. About 60 percent of the pages were deep-read in Step 1; I rechecked the arithmetic in the deep reads rather than re-reading the PDF, and went to the extracted text where a number mattered (Tesla distance figure, p.923). Interested parties (patentees, sellers, the inventors, Kelly as operator of an information site) are reported as their own characterisations.

Plain-language map: the four mathematical tools used here

1. Energy bookkeeping. Output energy over a time T cannot exceed input plus any stored energy released. If the claimed output cannot come from the stored energy of the parts, there must be a metered source. Example: a 500 W output for one minute is 30 kJ.
2. Units. Every formula must have the same units on both sides. A formula that gives watts-per-second where it claims watts is not a power law, whatever the numbers.
3. Real versus apparent power. For an AC circuit, V_rms x I_rms (volt-amperes) equals real power P only when voltage and current are in phase: P = V_rms I_rms cos(phi), with phi the phase angle. A coil or capacitor has phi near 90 degrees, so V x I there is mostly "reactive" power that sloshes back and forth and is not consumed. (Griffiths-level circuit theory.)
4. Resonance gain is not energy gain. In a series RLC circuit (resistor, inductor, capacitor) the quality factor Q = (1/R) sqrt(L/C) multiplies the voltage across L or C by Q at resonance. The circulating energy is Q times larger than what the source supplies per cycle, but the source still pays for the resistive losses each cycle.

Verdict summary (details below)

---

Claim 1. The "closed system" argument

Kelly's argument [read: pp.12-17, 422; claims.md]: conservation of energy applies to closed systems; real devices are open to an ambient or zero-point field; therefore COP (output power divided by the operator's input power) above 1 does not break the law.

a. Is the mathematics internally consistent?

There is almost no mathematics to check, only a definition and an inference.

• The definition COP = P_out / P_in(operator) is perfectly consistent, and Kelly is clear that "efficiency" above 100 percent is impossible while COP can exceed 1 [read: facts.json Basics essay; p.422]. A heat pump (COP about 3 [read: pp.38-41]) and a solar panel (COP infinite on this definition) show the definition is harmless. Nothing in it is wrong.
• The inference "open, therefore COP above 1" is true but empty until the inflow is identified. In classical field theory the energy balance for any region is Poynting's theorem:

d/dt (field energy in V) + (power dissipated or delivered inside V) = - (closed surface integral of S . dA), with S = E x H (watts per square metre).

"Open system" therefore has a precise meaning: a measurable net Poynting flux (or heat, mass, chemical or mechanical flow) across the boundary. A claim of extra energy from "the environment" is a claim that a surface integral of S, or another named flux, is non-zero and large. That is a specific, measurable statement, and Kelly never supplies the number. - Sweet's version of the same argument is "we are now dealing with an open-ended system and not the closed system within which all conservation and thermodynamic laws were developed" [read: p.266; A-817]. The passage first concedes that conservation applies to every system ("The laws of conservation of energy always apply to all systems"), then says the laws "need to be applied" to a changed system. That is consistent only if an inflow is identified. "Negative energy and negative time" are not defined, so the paragraph has no checkable content. - Utkin (reproduced Ch.16) argues that energy conservation "is the result of symmetrical interaction" and that Noether's theorem "just does not apply (but, that needs to be proved at a future date)" [read: p.1309, 1318]. This is a misstatement of the mathematics. Noether's theorem (1918) says that every continuous symmetry of the action gives a conserved quantity; invariance under time translation gives energy conservation. A pair of coils being "symmetrical" is not the relevant symmetry. If the laws governing the circuit (Maxwell's equations plus circuit elements) do not change with time, energy is conserved, symmetrical coils or not. The author himself says the proof is outstanding.

b. Consistent with established experiment?

The weak form is consistent with everything: heat pumps, solar cells, wind turbines, ram pumps and sailing boats take energy from an identified flow. The strong form needs a source, and the candidate sources can be budgeted:

So an ambient field in the ordinary senses (atmospheric electricity, radio, thermal background) cannot supply tens or hundreds of watts to a compact device. Nothing measured supports an inflow of the claimed size. The one ambient channel that is large (solar heat and light, or sources such as mains induction near power lines) is identified by ordinary physics and is metered when one looks (see Claim 6, Moray: Eyring's remark that the demonstration "might be induction", sites.md).

Kelly offers two specific physical statements for the inflow: - "A battery or generator makes a dipole that pours energy in from the environment" [read: Basics essay, pp.16-17]. A dipole (separated + and - charge) stores field energy but does not receive a continuing Poynting flux without a source. Kelly says the "tricky bit" of extraction "has been done" without a citation. - Lee and Yang (1957 Nobel Prize) are cited as proof of broken symmetry [read: facts.json]. Their result is parity violation in weak interactions [memory, high]; it does not bear on classical energy conservation.

c. Has it been tested?

No neutral test of "the environment feeds a dipole" is on record in the files. Kelly's own evidence is device anecdotes treated under Claims 2-6. His own light-meter test found a Joule Thief less efficient than direct LED drive (p.476) [read], which is a null result against his gain claim.

d. If true, what in mainstream physics would have to change?

For a non-trivial strong form: a new energy channel into a circuit that does not show up as a Poynting flux or any known field. That would contradict the local conservation law (continuity equation for energy) which holds in Maxwell theory and in quantum field theory to very high precision. The weak form requires nothing.

Verdict, Claim 1

• Weak form (an identified external inflow lets COP exceed 1): Established.
• Strong form (an unidentified ambient or zero-point inflow into battery, coil or spark circuits): Not testable as stated; for the named ambient sources at the powers claimed: Refuted by calculation (table above).

---

Claim 2. Sharp pulses, resonance and a tiny drive tap the ambient field

Principal examples [read: claims.md; Chapters 3, 5, appendix]: Don Smith, Kapanadze, Benitez GB 121,561, Joule Thief and Tseung's FLEET, Bedini, Ainslie, Prentice, Ace_Propulsion.

a. Is the mathematics internally consistent?

Don Smith and Mohamed formulas [read: deep read, Ch.3 pp.272-285; appendix pp.2354-2359; page image p.276 and p.2355]. I recomputed each.

The correct statement of what Smith may mean is in the book itself, in the parts he gets right: resonance raises circulating voltage and current by Q; a single spark gap is a fast switch; wire length for a quarter wave is 247/f(MHz) feet, within 0.5 percent of the free-space value (c/4f = 246 ft at 1 MHz) [calc]. Kelly's own arithmetic on coil turns (1.43 inch former, 458 V, divider 64 mW / 800 V) is correct [read: deep read p.2358, 2376; calc]. Errors by Kelly: 18 mm should be about 37 mm for the six-pipe bubbler (areas, p.2339); "998" for 988; reactance example read as 51 ohm, true 53.05 ohm; 5 psi is 0.345 bar not 0.36.

Transformer argument (Kelly, p.2374): "all of the electricity flowing into the primary winding ... flows back out ... where does the secondary current come from? ... from the surrounding local environment." In an ideal transformer V1 I1 = V2 I2 and primary current rises when the secondary is loaded (reflected impedance Z' = (N1/N2)^2 Z_load). That is verifiable with a wattmeter on the primary. The statement "none of it comes from the primary" is contradicted by the measurement.

Benitez GB 121,561 worked example [read: deep read Ch.5 section 6c, pp.456-458]. I recomputed it: - Circuit values from the patent: R = 15 ohm, C = 0.222 uF, L = 22.2 uH (0.0222 mH), spark every 1 ms. - f_0 = 1/(2 pi sqrt(LC)) = 71.7 kHz [calc], matching the patent's 71,900 Hz. - But the characteristic impedance Z_0 = sqrt(L/C) = 10 ohm, and Q = Z_0/R = 0.67 [calc]. A series RLC circuit is critically damped at R = 2 Z_0 = 20 ohm; at 15 ohm it is barely underdamped. The decay constant is alpha = R/(2L) = 3.4e5 per second, so the amplitude falls by a factor e^-7.1 in the first cycle [calc]. The patent's "72 oscillations per spark" cannot occur; the circuit rings for a fraction of one cycle. - Energy per spark: 0.5 C V^2 = 0.5 x 0.222e-6 x 1200^2 = 0.16 J [calc]; at 1,000 sparks per second 160 W, which is the power the transformer delivered (321 W less losses). The patent then needs 40 A through 15 ohm continuously, which is 40^2 x 15 = 24 kW; per cycle at 71.9 kHz that is 0.33 J, twice the entire energy of one spark and 72 times more over 72 cycles [calc]. The patent's argument is the water analogy ("one gallon moved 1000 times per second = 1000 gallons per second"): charge moved repeatedly is not energy created, because each pass through 15 ohm dissipates energy. - Also, 40 A through a 15 ohm resistor requires 600 V sustained; a 1200 V charged capacitor starts the discharge at 1200/10 = 120 A peak, which decays within about 3 microseconds. So the example is internally inconsistent (the ringing the energy gain depends on does not exist at the stated R, L, C) and is refuted by its own energy figures. The claimed COP 6 (400 W taken, 2,400 W available) rests on this calculation alone; there is no test data [read: summary table, Ch.5].

Ainslie, WO 99/38247 [read: deep read appended section]. Example 1: 12.28 V / 0.196 A = 62.7 ohm total, less than the 68 ohm resistor alone (plus a sensing resistor), so the stated voltage, current and resistance are not mutually consistent as printed [calc]. Output inferred from resistor temperature (93 versus 95 C), COP 1.086 = 1.141 x 0.95, with the test resistor 2 C cooler. Example 2: COP 2.45 is the ratio of a calibration current 0.0612 A to a measured average 0.025 A; the electrical reading of load power (0.169 W peak from 47 ohm x 0.06^2; about 0.056 W average for a triangular wave) is below the battery power 0.153 W, so the gain rests on the temperature equivalence only. Example 3: input is Vdc x Iavg, output is Vrms x Irms; at 50 percent duty Irms/Iavg = 13, meaning the shunt current is peaky or reversing, where V_rms x I_rms is not real power. The patent text itself says the load does not use less; the claimed benefit is routing the stored inductor energy (0.5 L I^2) to the load or back to the source [read: p.2419-2420]. The three results (1.086, 2.45, 0.976-1.176) are within or near what unmetered phase, shunt inductance and thermal-coefficient errors can produce. The headline "COP 17" has no protocol in the book (the Panacea 250-page document is not in the files) [read: Section T].

Prentice [read: Ch.5 section 1]: 500 W in, 50 sixty-watt carbon lamps "lit to full candle power" = about 3 kW; the 3 kW is a nameplate count, not a measurement. A passive coupling between two antennas cannot transfer more than it radiates and the energy is bounded by the transmitter: a 805 m wire at 500 kHz is 1.3 wavelengths and radiates [calc]. A net gain needs an extra source.

Ace_Propulsion Joule Thief [read: p.482]: 12.5 mA x 2.35 V = 29.4 mW in; 8 mA x 6.60 V = 52.8 mW out, "COP 1.8". Both are DC meter readings of a circuit whose output is a pulsed waveform; the average of a spiky current is not what a DC meter reads, and the base-current and LED-string power is not in the "input". No waveform or duration.

b. Consistent with established experiments?

Resonant transformers and spark-gap circuits are standard, tested technology (Tesla, radio). Established results: voltage gain Q at resonance; high-frequency AC lights bulbs more brightly than the same RMS at 50 Hz because of heating nonlinearity and filament thermal inertia is not it, but a bulb has strongly non-linear brightness and its brightness at high frequency and high voltage is a known poor power meter. Kelly himself warns, "bulbs ... are notorious for lighting brightly at low power levels, especially if the frequency is high" (p.314) and "This does not tell us very much about the actual output power" [read]. Nothing established shows output exceeding input in any such circuit.

c. Tested?

• Named measurements: none by a named independent party for Smith's 160 kW (8 kV x 20 A claimed, no instrument; 160,000/12 = 13,333) [read: p.2346; calc], the suitcase (28.8 kVA; a 12 V 7 Ah cell holds about 302 kJ, so 28.8 kW for about 10 s) [calc], Salty Citrus (12 V, 1-2 A in; bulbs bright; input figure only), Nick Giannopoulos (input only), Kapanadze (no measurement of a Kapanadze device in the book), Russian 2 kW lamp from a 12 V 0.8 Ah battery (9.6 Wh, about 17 s at 2 kW) [calc].
• Meyl, 0.5 mW in, 6 mW out (x12), reported second-hand via Mohamed (p.288), "a published result"; I could not trace Meyl's own publication in this review. At 0.5 mW a receiver with its own LED driver board is a typical case where the supply of the receiver board matters.
• Kelly's own tests: a swap of two lead-acid batteries on the FLEET toroid ("both batteries gained genuine, usable power") has no voltages, currents, durations or capacities [read: p.480]. Lux-meter test against the Joule Thief: null result against the claim [read: p.476].
• Lyden US 11,588,421 B1 (Investigator lead) cites Benitez as showing batteries can be kept charged "with relatively little or possibly no energy loss": the applicant's characterisation of prior art, not a measurement [read: sites.md].
• Replicated: no.

d. If true?

Output from a pulse or resonance circuit exceeding the metered input would require a new energy flux across the circuit boundary (see Claim 1). For Smith/Mohamed's formulas to be "power", they would need an extraction mechanism that is not paid for in the charging of the capacitor, which contradicts the 1/2 C V^2 cost.

Verdict, Claim 2 (split)

• Smith/Mohamed/Kelly power formulas (W = 0.5 C V^2 Hz^2 and kin): Internally inconsistent (units W/s or J/s^2; double counting; time constants called frequencies).
• Benitez GB 121,561 worked example (COP 6): Internally inconsistent and Refuted by calculation (Q = 0.67; 160 W of spark energy cannot support 24 kW dissipation).
• Smith 160 kW, Kapanadze 5 kW, Salty Citrus, Meyl x12, Ainslie COP 17, FLEET COP above 10, Ace_Propulsion 1.8: Never properly tested (no neutral input and output metered together; bulb brightness, V x I products, DC meters on pulsed signals).
• Resonance as a voltage or current amplifier: Established (not the claim, but the true core).

---

Claim 3. Permanent magnets, switching or conditioning, give large gains

Principal examples: Sweet VTA, Flynn, Annis/Eberly, Asaoka, Kunel, Kawai, Heins, MEG. Investigator material: Sweet's 1987 letter, hyiq.org, AboveUnity notes, Newman v. Quigg (see Claim 6 for Newman).

a. Internal consistency

Sweet VTA: the numbers. [read: deep read section A, J; research/2026-10-08-sweet-sources.md] - 10 V x 31.2 uA = 0.312 mW; 112.5 V x 4.7 A = 528.75 W; ratio 1.69e6 [calc]. Kelly's 0.31 mW and 500 W (COP 1.612 million) trace to this filmed 1987 demonstration as read by Bearden [web via Investigator: https://www.aboveunity.com/thread/my-notes-on-floyd-sweet/]. The load of five 100 W lamps at 112.5 V is 25 ohm, and 112.5/25 = 4.5 A: the output figures are mutually consistent for a resistive load. - Input and output figures differ across Kelly's own pages: input 0.31 mW / 1 mW (Sweet's 26 April 1987 letter) / 10 mW (Sweet's 1988 paper, 1 mA at 10 V); output 500 W / 1 kW / 5 kW. The gains therefore range from 1.6e6 (500 W / 0.31 mW) to 5e5 (5 kW / 10 mW) [calc]. - A real-versus-apparent-power problem on the input side: V x I for a coil is apparent power. If the input coil is nearly pure reactance, real power would be much smaller than 0.31 mW. That would make the quoted COP larger, not smaller, so it does not rescue the measurement; what matters is the power drawn from the oscillator's own supply. A signal source delivering 1 mW into a load typically draws far more from its own battery or mains (a linear amplifier stage at 9 V and 5 mA quiescent is 45 mW [calc, illustrative]). The book does not say that the oscillator's supply was measured. - The 1986 lab notes, via the AboveUnity notes cited by the Investigator, list "E-coil 1 input 10.41 V and 1.84 A (about 19 W)" and an output P-coil 12 V, 500 mA. Gray's notes as printed by Kelly give 10.4 V at 1.84 A as the OUTPUT (19.15 W) with INPUT 7.5 V at 3.1 uA. The two descriptions of the same numbers disagree on which side is the input. I cannot settle this from the files; the notes written by Roberts are not available. This matters: if 10.4 V x 1.84 A is the input, there is no gain at all in that run. Flag for the Investigator.

Gray's coil: the impedance does not fit the hardware. [read: deep read A4; calc] - Input 7.2 V and 143 uA: |Z| = 50.3 kohm at about 400 Hz, which for a pure inductor means L = Z/(2 pi f) = 20 H. - The input coil is 250 turns of #18 wire on a 1.5 inch diameter former [read]. An air-core estimate is L = mu0 N^2 A / l = 0.35 mH (reactance 0.88 ohm at 400 Hz). The coil needs an effective relative permeability of order 5.7e4 to reach 20 H. The hardware described is barium ferrite magnets (relative permeability about 1.05-1.1 [memory, medium]) in an aluminium housing. Gray: "impedance ... rises dramatically in the magnetic field to several hundred thousand ohms, while ... outside the magnetic field is only 2 or 3 ohms @ 400 Hz" [read: p.249]. Roberts, in the AboveUnity account, "admits" the in-device impedance is "millions of times greater" and has no explanation [web via Investigator]. No high-permeability soft-magnetic core (permeability 1e4-1e5) is described in the device. So either an unlisted core is present, or the microamp reading is not the whole current in the coil (the notes describe a diode that "divides the current ... puts a small microamp current into the power coil as well as the excitation coil", which implies parallel branches that the ammeter may not span), or the AC microamp measurement at 400 Hz on a distorted waveform is unreliable. - Output flux: 24 turns at 24.2 V rms and 388 Hz require a peak flux Phi = V sqrt(2)/(2 pi f N) = 0.58 mWb, which over the 1.5 inch coil area (1.14e-3 m^2) is B_peak = 0.51 T [calc]. That is above the saturation of ferrite (about 0.3-0.5 T [memory, medium]). To drive a flux of that size through a path of about 0.1 m with an effective relative permeability of 1.1 takes about 3.7e4 ampere-turns; the excitation winding supplies 250 x 143 uA x sqrt(2) = 0.05 ampere-turns [calc]. A factor of 7e5 is missing unless the soft-magnetic path has a large permeability. - Conclusion: the numbers in Gray's lab notes are inconsistent with a passive magnetic circuit built from the parts named. This is a measured-versus-hardware inconsistency, not proof of fraud: it needs the full circuit and a core description.

Energy bound, independent of any instrument reading. Output energy over time T needs a source. Take the two candidates available: the stored energy of the permanent magnets and the (stated) input. - Ferrite magnet 150 x 100 x 25 mm = 3.75e-4 m^3. The maximum energy product of commercial ferrite is about 7-30 kJ/m^3 [web: https://www.magnetexpert.com/magnetic-properties-of-ferrite-magnets; the search summary gave Y28 at 26-30 kJ/m^3]; the total magnetic field energy that could ever be released from it is of order 0.5 x 30e3 x 3.75e-4 = at most a few joules to 11 J [calc]. Even NdFeB at 400 kJ/m^3 [memory, high] would store 150 J. - Sweet's 500 W would drain 11 J in 0.02 s; Gray's 111 W for 10-12 hours is about 4 MJ, 3.6e5 times the ferrite's total [calc]. A permanent magnet is not consumed when it holds a weight or acts as a bias; it is a store of limited energy that can be released at most once. - Therefore the magnets cannot supply the output. For the book's claims the energy must come from the oscillator supply (not counted), from an unlisted source, or from a source Sweet attributes to "the Dirac Sea". The last is not defined: the Dirac sea is a 1928-1930 picture of negative-energy electron states that quantum field theory replaced by antiparticles; it has no extractable energy [memory, high]. - Contrast with a magnetic amplifier or transistor: a power gain of 1e3 or more is routine, but the output power is supplied by a visible AC or DC source (the "gate" supply); the control input only modulates it. The VTA has no such source. That is the single mathematical difference between a device with "COP 1.6 million" and an ordinary amplifier.

Sweet's paper (A-808 to A-817) [read: deep read C2]. Equations: motional E-field E = B x v; "E = (B x v) + (-B x -v) = 2 (B x v)" for bifilar coils. E = v x B is the textbook motional field (Lorentz force per unit charge); for charges moving through a static B field it exists only if the conductor moves. In a stationary coil in a stationary magnet nothing moves at the macroscopic scale. "Electrometer readings were always close to parabolic" with no axes. The superposition "2(B x v)" assumes the two velocity signs add rather than cancel, but (-B) x (-v) = B x v only because the product of two sign changes returns the same vector; physically a pair of bifilar coils carrying opposite currents produces cancelling fields, not summing ones. This is a hidden assumption: the "-B" and "-v" must be separate physical quantities, not the same fields viewed after reversal. "Cos theta = 1 Kvar = 1 under all load characteristics" [A-817] claims unity power factor and zero reactive power for every load; a coil-and-magnet device cannot, in general, present zero reactive power to an inductive motor load.

Annis/Eberly, Asaoka, Flynn, Kunel, Kawai. - Annis/Eberly: COP 200-400 "without the coupling circuit", defined as output over drive power of the switches [read: p.213, 219]. The exclusion of the coupling circuit makes the figure a ratio of power through two different parts of the circuit; the power needed to move the flux (reluctance switching, saturation of a segment by extra coil flux) is the drive. Their table is an image I did not see. Abandoned application [web: sites.md, Google Patents]. - Asaoka: the equation Eff = Wp/Win2 + alpha shows the arithmetic by which "Wp/Win2 > 1" would give efficiency above 1, but the patent measures only that input falls to 1/40 for equal flux density; it states that the inventor "considers it possible" [read: p.237]. An input reduction is not an over-unity measurement. - Flynn US 6,246,561: the real result is a factor of 2 in coil power for equal holding force when switching flux between two paths, with force F proportional to B^2 A (a halved flux gives a quarter of the force per path) [read: p.1684-1694]. That is a correct statement about the force per coil power of a holding magnet, a variant of the permanent-magnet latching relay. It compares coil power only, not the work to move armatures over a cycle; no COP above 1 is claimed in the patent text. Kelly's header "greater output power than input" is not supported by the pages [read: deep read Corrections]. Lapsed for an unpaid fee in 2007 [web: sites.md]. - Hayasaka: "1/5.2 of the driving torque" is a torque ratio versus another generator [read: p.1606]; with no output power stated, it says nothing about COP. - Kawai US 5,436,518: one run: 17 V x 1.15 A = 19.55 W; torque 60.52 kgf-cm = 5.935 N m at 100 rpm (10.47 rad/s) = 62.15 W; ratio 3.18 [calc; matches]. Arithmetic correct. The 19.55 W is a DC meter reading of switched coils (average versus peak unspecified), and the torque was measured by an unstated brake. The extra 42.6 W would have to be supplied by the ferrite magnet's stored energy; at 62 W that is exhausted in about a fraction of a second against a few joules. So either the electrical input was under-measured (switching currents, sensor power) or the mechanical output over-measured. Never properly tested. - Heins "forty times" [read: p.1307]: one sentence; no data. - MEG: the patent states 48 W out for 12 W in; Kelly says both that no one has replicated it with COP above 1 (p.1145) and that it "has been replicated ... COP>1" (p.1147). Lawton's only report: removing the magnet made no difference in the laminated-iron version [read: p.1147].

b. Consistent with experiment?

Magnetic amplifiers, saturable reactors and permanent-magnet latching solenoids work and are standard. They have power gain with an external supply. No experimental result shows continuing output without a supply.

c. Tested?

• Sweet: a single filmed demonstration (1987), a fund-raising letter (26 April 1987: "for a miniscule power input (one milliwatt), the unit produces over 200 watts", written to "approach selected potential financial backers") [read: research/files/rex-sweet-sparky1987.pdf p.1, via Investigator]. Funded by Mark Goldes (stake). hyiq.org "tried to replicate it for a number of years now, without any success" (Weyrich via Kelly, p.247) [read]; Kelly "not aware of anybody who has succeeded in replicating" [read: p.244]. Output in 1986: 6-19 W then 100-110 W per hyiq.org [web via Investigator]. No neutral instrument test on record; the two obvious absent records are Roberts's lab notes and the 1987 video's meter views.
• Annis/Eberly, Asaoka, Kawai: patentee data only.
• A named independent measurement: none.

d. If true?

A source of energy not stored in the magnets, not in the oscillator, and not in any metered line. Sweet's own proposal (negative energy, negative time, "more than four dimensions") would require a physical energy reservoir with a tap that standard field theory does not contain.

Verdict, Claim 3 (split)

• Sweet VTA, energy supplied by magnets or magnetic circuit alone: Refuted by calculation (stored energy 11 J against 500 W).
• Sweet VTA as a measured COP of 1.6 million: Never properly tested (one filmed demonstration, no oscillator supply measurement, no published protocol). Gray's data additionally Internally inconsistent with the described hardware (20 H and 0.5 T).
• Flux-switching COP 200-400 (Annis/Eberly), Asaoka, Kunel cascade (1000 W in to 1000 MW), Kawai 3.18: Never properly tested.
• Flynn: coil power halved for equal holding force: Plausible, untested as an energy-gain claim; no COP above 1 is claimed in the patent.

---

Claim 4. Impulse, gravity and buoyancy devices give excess mechanical energy

a. Internal consistency

The "2mgr" impulse theory (Tseung via Kelly, p.366) [read: deep read Ch.4]: a pulse on a flywheel adds "excess energy equal to 2mgr" (m mass, r radius of the centre of mass, g gravitational acceleration); "no energy gain" for a smooth drive; gain grows with pulse rate. No derivation is given. - 2mgr is the potential energy of raising mass m by one diameter 2r in a uniform field. For a rotating flywheel about a horizontal axis whose centre of mass is at distance r from the axis, the gravitational potential energy returns to its starting value after each full turn. Gravity is a conservative force (curl of g is zero); the work over a closed loop is zero: integral of F . dl = 0 around any closed path. So over a revolution gravity gives the wheel exactly zero net energy [calc: textbook, Griffiths mechanics]. The same holds for any impulse timing: energy is gained from gravity during the falling half only to be spent in the rising half. - For m = 50 kg, r = 0.5 m: 2mgr = 490 J. If it were gained per revolution at 1,000 rpm it would be 8 kW from a loop with no input. The existence of such a term would mean the gravitational field does net work on a closed cycle, which contradicts conservative-force theory. - Kelly's own gravity theory [read: pp.924-926]: a flow of tiny particles, shadowed by the Earth, produces gravity as push gravity (Le Sage). It has no equations. Le Sage's pushing particles would heat bodies (energy absorbed from the push) at a rate that exceeds observation by many orders of magnitude [memory, high]; no number is given by Kelly.

Campbell: 750 W in, 2,340 W out, ratio 3.12 [calc]. The replication video "does not appear to have a heavy flywheel" [read]; no instrument details; the claimed self-powering is "switching the drive motor input to the output generator". If it ran for a stated duration at a stated load, the flywheel's kinetic energy would not account for it (a 50 kg flywheel of radius 0.5 m at 100 rpm has 685 J [calc], 0.3 s of 2.3 kW). The key datum, run time after switch-over, is not given.

Skinner: the 1939 newsreel says "1200%" [read: Ch.4 section 14]. Two readings: (1) COP 12 (1200 percent), supported by the United Press text "increase the horsepower of a motor about 1,200 per cent" [web via Investigator: https://rexresearch.com/skinner/skinner.htm]; (2) COP 1,200 (Kelly's reading). The newsreel's other numbers discriminate: a 1/8 hp (93 W) motor drove a 12-foot lathe, a six-foot drill press and a hacksaw. With COP 12 the output is 1.1 kW (1.5 hp), plausible for the three tools in light use; with COP 1,200 the output is 112 kW (150 hp), clearly not what a small lathe uses [calc]. The "3,500 homes" figure: 746 W x 12 / 3,500 = 2.6 W per home (Kelly: "clearly wrong"), 746 W x 1200 / 3,500 = 256 W per home (Kelly's choice) [calc; read: p.406]. Since the newsreel text was a promotional commentary, the "3,500 homes" sentence is more likely loose than quantitative. The UP text and the tool list favour 1,200 per cent = COP 12 read as an estimate by Skinner; "Estill's check was not complete enough" [web via Investigator]. A COP of 12 still demands a source: mechanical power from a 93 W motor cannot yield 1.1 kW without an energy store or an unmetered input. In the machine described (a weight moved by a small circle at the top of a tilted shaft), Kelly's "spinning chair" argument ignores that the weight's kinetic energy comes from the driver and the output equals friction and drag, not gravity [read: deep read].

Buoyancy (Kwok "Hidro", Ribero, Kelly's design): Kelly's claim that once an air column is established the pump "does not have to push against the head of water" because a vortex "negates the water head" [read: pp.400-401]. Hydrostatics: the pressure at depth d is p = rho g d; pushing air out at the bottom of a tank of depth d needs the gauge pressure rho g d (about 0.1 bar per metre). The work to push a volume V of air down to depth d is rho g d V, exactly the buoyant work recovered when the same volume rises; so the best case is zero net work, minus friction and air-compression losses. The patent for Hidro itself includes a solar collector supplying part of the energy [read: p.390-394]. Kelly himself doubts Ribero's pressure-reduction mechanism and says the generator "has never been built" [read: p.404]. Bessler 1712: 70 lb x 80 ft = 5,600 ft-lb is the work done on the lifted weight, an output; no input figure is given [read: p.384].

Newton's laws / Tseung COP 3.3 versus 3.4 (heading versus text): an unexplained internal inconsistency [read].

Tesla MHD and the 2.2e39 figure [read: pp.923-924; _text line 34461]: the ratio of the Coulomb force to gravitational force between a proton and an electron is k e^2/(G m_p m_e) = 2.27e39 [calc]. Kelly then says that the energy used mechanically to lift an object 1/100 inch, used electromagnetically, would lift it "more than 3,472,222,000,000,000,000,000,000 miles". A force ratio between two different particles is not an energy-to-height ratio. And even on his own premise 0.01 inch x 2.2e39 / 63,360 inch per mile = 3.47e32 miles [calc]: the leading digits 3.4722 match, so the printed number has 8 zeros too few (and the kilometre figure likewise). That is a transcription slip; the physical argument is the larger error. "Thrust rises with the fourth power of the frequency" has no derivation.

b. Consistent with experiment?

No experiment shows energy extraction from a closed cycle in a uniform gravitational field; this is the content of the conservative-force law, tested in countless mechanical cycles (pendulums, flywheels) and by Eotvos-type experiments for the field itself [memory, high].

c. Tested?

Tseung's public demonstrations in October 2009 (COP 3.3, video link, no instrument readings) [read]; Campbell replication video; Hardy video; Dmitriev and Milkovic (COP 12 is a force ratio "12W thrust", not an energy ratio) videos; Kwok sells 50 kW to 1 MW units (seller's claim) [read]. No input and output meters with a named independent party. Kelly himself calls the Tseung YouTube prototype inadequate (stops after five minutes).

d. If true?

Gravity would have to do net work on a closed cycle, i.e. g could not be derived from a potential; or an energy store must be found. This would overturn the Newtonian and general-relativistic treatment of the field as conservative for static sources.

Verdict, Claim 4 (split)

• "Excess energy from the gravitational field" mechanism (2mgr, spinning chair, hydrostatic vortex): Refuted by calculation (conservative field; hydrostatic work balance).
• Campbell, Hardy, Tseung 3.3, Dmitriev, Milkovic 12, Kwok: Never properly tested (videos and statements; no neutral metering).
• Skinner 1939: Never properly tested; reading "1200 times" implausible against the tools shown; reading "1200 per cent" (COP 12) is possible for light tool use but still needs a source.

---

Claim 5. Water splitting and engines on water beat the textbook energy

a. Internal consistency (the cleanest mathematics in the book)

What "Faraday" means in the book. Kelly defines it as 2.34 Wh per litre of HHO per hour [read: p.846]. Faraday's laws are about charge: 2 F = 192,971 C per mole of water split; one litre of mixed gas (H2 + 1/2 O2, 1.5 mol gas per mol water) at 0 C needs 5,740 C [calc]. Energy per litre = 5,740 C x V_cell. At the thermoneutral cell voltage 1.481 V that is 2.36 Wh; so Kelly's 2.34 Wh/L is the thermoneutral energy figure (about 1.47 V per cell), a good textbook value [calc; constants: memory, high]. The reversible (Gibbs) minimum, 1.229 V, is 1.96 Wh/L. Between 1.229 V and 1.481 V a cell can absorb heat from its surroundings, so a cell can be cold and use up to about 120 percent of the thermoneutral figure per energy input [calc; memory, high]. That is within textbook physics.

Converting the book's claims to the voltage per cell they imply (energy per litre / 5,740 C per litre per cell):

[calc; the deep read's figures reproduced]. Values below 1.229 V per cell per mole are below the reversible minimum and require either more than 1 H2 per 2 electrons (Faraday's law violated), an energy input not metered, a chemical energy source (Boyce: "relies mainly on a chemical reaction ... between the electrolyte used and the metal plates", p.807; if that consumes the plates it is a fuel), or measurement error (gas flow with entrained electrolyte or vapour; average versus peak current for pulses).

Kelly's description of Faraday's law as limiting gas "per amp" is itself loose: in a series stack of n cells, gas per ampere scales with n; the book's wording "Faraday's gas output for less than half the current" [read: p.2331] claims a current efficiency above 100 percent per cell, which Faraday's law does not allow; whether Boyce's "216 percent" meant per ampere or per watt is not stated [read: deep read].

Zigouras: 17,500 L/min x 2.36 Wh/L x 60 = 2.48 MW at the thermodynamic floor against 190 A x 14 V = 2.7 kW peak or 140 W running; a ratio of 17,700, not the "COP 5-10" printed on the same page [calc; read: p.916-918].

Meyer water capacitor [read: pp.1836-1893]: WO 92/07861 "about 5 US gallons (19 litres) of water per hour" [read: p.1893]. That is 1,049 mol per hour, a thermodynamic floor of 83 kW and a Faraday current of 56 kA; the patent's own electrical numbers are 1-2 mA at resonance (25 mA at start-up) and 360-650 V, about a watt: a factor of about 60,000 below the floor [calc]. The patent's explanation, "electrons are not consumed" [read: p.1841], means it is claiming a non-electrolytic route. The water in a 3-inch cell gap (about 12 mL) would have to be replaced 1,570 times per hour. Example 1 in US 4,936,961 gives geometry and a 26 V drive (frequency "0 KHz", a typo for 10 kHz, confirmed by the parallel patent) but no gas volume, power or run time; the capacitance of the 4-inch coaxial water capacitor is about 2.0 nF [calc]. The patent is one-source. The 1996 Ohio court finding of "gross and egregious fraud" after three expert witnesses found conventional electrolysis is reported by Wikipedia (secondary; court record not reached) [web via Investigator: https://en.wikipedia.org/wiki/Water_fuel_cell].

Generators on water. Kelly: "3 lpm (180 lph) is sufficient to run a generator which produces 5,500 watts" [read: p.846]. At 0.36 kW chemical energy in 3 lpm of HHO (0.120 kW per lpm; H2 LHV 241.8 kJ/mol; HHO is 2/3 H2 by volume) [calc; memory, high], a 4 kW electrical output would exceed the fuel's chemical energy by 11 times even at 100 percent engine efficiency. Kelly's resolution is "an internal combustion steam engine" with cold-water fog [read: p.847]. A water droplet converting to steam absorbs latent heat from the combustion gases and the expansion work is paid for by that heat; it cannot add energy beyond the combustion heat [memory, high]. The UK account itself does not mention fog [read: p.838]. For Cramton's 6 lpm (0.72 kW chemical), the claimed saving of 1.4 gal/h of diesel is 52.7 kW of fuel, about 73 times the HHO's energy [calc; diesel 35.8 MJ/L, memory, high]. Cramton's graph has four points per line and no protocol [read]; the 10 tests "within 1 percent" are about repeatability, not about the gain.

Harris (Honda GX4000i): 5 lpm carries 708 W at the thermodynamic floor against the stated 115 W (Hogg cell) input; the book does not comment [calc via deep read]. In his case the printed GX4000i rating is 2.7 kW; no output power was measured.

Other: Lawton's 300-900 percent "assessed" by no named person; Lawton's tube positions at "22.4 percent of the length" correspond to the nodal points of the first free-free bending mode of a uniform beam (0.224 L) [read: p.814; memory, high], which hints that what is being tuned is mechanical bending resonance of the tubes; but "smaller diameter resonates at a higher frequency" is the wrong way round for bending modes (frequency scales with radius over length squared, so a smaller tube of the same length rings lower) [read: deep read; memory, high]. This is a side error, flagged for readers.

b. Consistent with established experiment?

Water electrolysis has been measured for two centuries; the energy per mole is a calorimetric quantity known to high precision (285.8 kJ/mol higher heating value) [memory, high]. Pulsed or high-frequency drive can lower the average voltage somewhat but not below the reversible minimum. Brown's Gas / HHO measured by Eckman (Idaho State 2008) found little additional hydrogen and flame at 266 F, 130 C [read: Ch.10 inventory; Kelly's 130 F versus 130 C slip is internal]. The Navy "seawater fuel" clipping describes a CO2 + H2 to liquid fuel process; it says nothing about self-powering [read: deep read p.837; memory, medium on the underlying NRL work; not checked on the web].

c. Tested?

No neutral test. Everything is forum, video, patentee, or inventor statements: Boyce via Kelly, Lawton videos, Cramton team, the UK men's representative, Meyer's patents, and one demonstration of a 1,000-mile Chrysler bench run with currents 4-4.3 A (idle) and 10.9-11.6 A at 13.8 V and no gas rate recorded [read: p.806]. The Meyer expert-witness examination (1996) is the one adversarial test on record, reported by a secondary source (Wikipedia) and not yet read from the court file [web via Investigator]. The coroner's finding on Meyer's death (aneurysm, hypertension) and the brother's report of "They poisoned me" are both in the record [web via Investigator: Columbus Dispatch 8 Jul 2007].

d. If true?

Either Faraday's law (2 electrons per H2) fails, or the first law fails for electrolytic cells, or the cell absorbs ambient energy of the order of 10 times the input, which requires a flux not found in calorimetry. Textbook thermodynamics of electrolysis (Gibbs energy minimum) would have to be rewritten.

Verdict, Claim 5 (split)

• Over-Faraday gas for the electrical input (211 percent to 2,340 percent) and Zigouras: Refuted by calculation unless the input or the gas rate was mis-measured; the measurements offered are Never properly tested.
• Generators and engines running on 3-6 lpm of HHO and water mist at kilowatt loads: Refuted by calculation (chemical energy bound).
• Meyer water capacitor at 5 gal/h on milliwatts: Refuted by calculation; Meyer's own invitations to examine were not taken (Laughton) per secondary source: Never properly tested in an open protocol.
• Cell running cold and using up to 120 percent of 2.34 Wh/L: Established (textbook).

---

Claim 6. Aerial, passive and fuel-less devices deliver power

Includes Moray, Plauson, Tesla's aerial plate, Prentice, Papp, Coler, pyramids, Joe Cell, Gritskevitch, Hyde, Newman (which Kelly puts in Chapter 11), Rossi and Cater.

a. Internal consistency

Moray [read: Ch.7 summary table]: witnessed outputs of 635-675 W from lamps and an iron by their ratings, not measurement. The 635 W figure appears with "0.878 hp" (655 W) in the same account (655 [calc: 0.878 x 745.7]), so the book's own numbers differ by 3 percent. Hayes (PhD) says he could not measure voltage or current. Moray: "the frequency is so high that I have no instrument in my laboratory that is able to measure" it [web via Investigator: http://www.rexresearch.com/moray2/morayrer.htm]. Eyring (BYU physicist) "found no fault with the demonstration and the worst he could say was that it might be induction" and asked for a test 3 or 4 miles from power lines [same source]. Ambient budget (Claim 1 table): 675 W from an antenna in Utah in 1929 would need about 2.6e12 square metres of atmospheric-electric collector, or a matched dipole in a field of about 1 V/m (strong, within a few km of a transmitter) at best a few watts; near mains lines, induction at 50-60 Hz can supply hundreds of watts to a coil on a short run [calc: unmetered]. The witness record cannot tell these cases apart because neither current nor voltage was recorded. The device's frequency claim ("so high no instrument") is itself unusual because 1929 radio engineering already measured up to tens of MHz [memory, high].

Plauson, US 1,540,998: 100 kW "small" installation from over 100 aerials [read]. An elevated aerial of area A at 100 m height in a 130 V/m field has a potential of 13 kV; current is limited by conduction in air of 2 pA/m^2 times area. For 100 aerials of 100 m^2 each, 2e-12 x 1e4 = 2e-8 A, 2.6e-4 W [calc]. The patent claims 5-6 orders of magnitude above this. Corona and storms at the aerial can give bursts; no continuous kW.

Prentice (Claim 2) and Tesla's 685,957 ("indefinite accumulation until the dielectric ruptures") are consistent with a capacitor charged by a small leakage current (E = 0.5 C V^2), which is just stored energy.

Papp: inert-gas engine; no mathematics in Kelly's text; the 1968 demonstration, per Ansley and Feynman accounts (injury count differs: "eight others badly wounded" versus "three men injured") [web via Investigator: hoaxes.org]. Both accounts have a stake (Feynman as defendant in Papp's suit, Papp's partner Roser). I have no calculation to apply without an energy figure.

Gritskevitch dynamo [read: Section U]: arithmetic 220 V x 6,800 A = 1.496 MW is right; the sustaining input 14,400 W is a nameplate product (8 x 12 V x 150 A) rather than a measured current [calc]. The start-up figures are mutually impossible: "two 10-farad capacitors ... total of 20,000 Joules ... 100,000 volts at 0.05 amperes for 3 to 5 minutes". Two 10 F capacitors at 100 kV store 2 x 0.5 x 10 x (1e5)^2 = 1e11 J; 20 kJ at 100 kV is 4 uF in total; 100 kV x 0.05 A for 180-300 s is 0.9-1.5 MJ [calc]. "500 kJ/mole" of D-D fusion is chemical-bond scale; fusion releases of order 1e8 kJ/mole [memory, high]. The resistivity "18,000,000 Ohm/cm" is ohm-centimetres. Durations and dates conflict inside the account. The device was said to be destroyed in January 1997 "during the war", and no test report of the State Commission (document 14-451) is in the record (an absence-of-evidence anomaly in the sense of SOURCE HONESTY: competing explanations are device loss in war, the inventor's stated practice of "misleading information", and loss of archives; the Investigator's list of records applies) [read].

Hyde US 4,897,592: the patent says the mechanical input is "less than ten percent of the electrical output" and a prototype of 300,000 V; "10 kW" and "COP 10" are Kelly's headings, not in the patent text [read: deep read]. The output electrodes are charged by an external source not counted in the COP. For an electrostatic machine with rotating shielding segments, moving charge between plates of different capacitance does mechanical work against the field force; the patent claims the forces cancel (perpendicular). Without a drawing and numbers I cannot confirm that; the energy delivered to the output must come from the charging source plus mechanical input.

Newman [read: WO 83/00963, Ch.11]: the only measured ratio is 12.47 W in, 12.80 W out, "102 percent": 126 V x 0.099 A and 640 V x ">20 mA" [calc]. V x I is apparent power; the secondary voltage and current of a coil with 300 pounds of 24-gauge wire and a rotating magnet are strongly out of phase, so V x I overstates the real output unless the phase was measured; no waveform is given. The rotating magnet's kinetic energy (400 lb, assumed 0.25 m radius, 120 rpm) is about 440 J, which would cover a 12.8 W output for about 35 s [calc; assumption flagged]. The National Bureau of Standards, in 77 measurements, calculated efficiency 27 to 77 percent; Hastings had counted "anomalous back spikes" in the MHz range (observed on an oscilloscope, used to heat water) as output and "advanced no explanation" [web via Investigator: https://law.justia.com/cases/federal/district-courts/FSupp/681/16/1800217/; both parties to the suit are interested parties]. Newman's coil arithmetic (0.5 L I^2 = 116 J versus 1.4e-5 J for equal 9.5 W input) is correct; the point he draws (stored energy 8 million times larger at the same power) is a statement about stored energy that is returned, not a gain [calc; read: p.945]. The 1,905 versus 1,975 gauss ratio and the 90,000 versus 106,000 turns are small inconsistencies.

Rossi (US 9,115,913): patent text states 6 kWh out per 1 kWh in for 180 days; no test report in the book [read]. A 6 times energy ratio over 180 days for a wafer of lithium aluminium hydride and nickel exceeds the chemical energy of the fuel by a large factor; the book gives no mass. Not computed here for lack of the quantity.

Eskeli "no work" heat pump [read: p.954-962]: cycle table with compression total 66.7 B/lb and expansion 67.0 B/lb (the three expansion legs add to 66.9). A cycle with zero net work is a Carnot heat engine at zero temperature difference or a reversible heat pump with infinite COP at zero lift; it does not violate the first law, but the table is a design calculation of a cycle, not a built-unit measurement [read]. Plausible only as an idealised cycle; no test.

Pyramids, Joe Cell, Ighina, Coler: the book reports effects (razor blades, "orgone", Joe Cell trucks running in "shandy" mode with the fuel line connected [read: claims.md]); no quantity to check.

b. Consistent with experiment?

Atmospheric electricity and ambient RF are measured, and the budgets above stand. Coler's reported current drop (104 to 27 mA) is a loading change on a circuit; the claim 6 kW from dry cells has no measurement [read].

c. Tested?

• Moray: witnessed public demonstrations of unspecific type; the application file jackets remain at the Patent Office with contents missing (family statement) [web via Investigator]; this is an anomaly to analyse: competing explanations for the missing contents include loss, transfer, or removal; the USPTO and National Archives application record would decide. His only granted patent found is US 2,460,707 (1949, electrotherapy) [web via Investigator].
• Papp: demonstrated in 1968; engine destroyed; investor suits [web via Investigator].
• Hyde, Gritskevitch, Rossi, Newman: patent text or inventor statements; Newman has a court-record NBS test with result below unity (27-77 percent) [web].
• No replication that I can verify for any of these.

d. If true?

A continuous kW-class energy inflow through an elevated wire or through a coil would have to exceed the measured atmospheric and broadcast budgets by 5 to 12 orders of magnitude. A fuel-less engine would violate the first law; a source that has no signature in calorimetry is required.

Verdict, Claim 6 (split)

• Moray's 635-675 W: Never properly tested (witnessed by ratings, not meters; ordinary induction not excluded); the claim that the power came from the atmosphere at that size: Refuted by calculation for atmospheric electricity.
• Plauson 100 kW, Prentice 3 kW: Refuted by calculation for the named ambient sources; Never properly tested as devices.
• Gritskevitch COP 100: Internally inconsistent (start-up energy, resistivity unit, dates) and Never properly tested.
• Newman 102 percent: Tested, not supported in the one neutral test on record (NBS 27-77 percent) and Never properly tested by Hastings's method; Hyde 10 kW: Never properly tested (figure not in the patent).
• Papp, Joe Cell, pyramids, Coler, Eskeli's cycle: Not testable as stated or Never properly tested.

---

Claim 7. Suppression

Mathematically there is nothing to check. The numbers are 10,000 builders, 40,000 confiscated patents, "some are murdered" [read: pp.17, 22, 993-1005]. The passage has "I am reliably informed" and no named case or record [read: deep read section E]. Kelly is an interested party (he operates an information site). The counts are uncited and I have not found the basis; the Investigator's records on Moray's missing file contents, the Meyer coroner's ruling and court file, and Papp's suits are the checkable cases, and each is stated beside the claim above. Silence in other sources is not contradiction.

Individually checkable pieces with arithmetic: none. The statement "not a single electron of the current you use comes from the power station but is collected locally" [read: p.998] is also mistaken as stated: in AC supply electrons oscillate in place while energy is transmitted by the fields (Poynting vector); the sentence mixes carrier identity with energy source. The energy still comes from the station.

Verdict: Not testable as stated (uncited counts). Individual cases are open records (see Investigator leads).

---

Investigator leads: pertinent items kept

Weighed by claim above; kept in the record whatever the verdict:

1. Later editions V34.5 (June 2019) and V34.8 (26 Feb 2020); preface wording unchanged; new sections "Buie-Morin Power System", "Art Porter's Magnetic device" [web via Investigator]. I did not re-read V34.8 for changed figures.
2. Pen name: real name Edward Dickson Williams, died 11 July 2020 (forum snippet, memorial video) [web via Investigator]. Relevant to the "end of the record": explained by death, not an anomaly.
3. Sweet: 10 V x 31.2 uA / 112.5 V x 4.7 A / power factor 1 (AboveUnity notes); Sweet's 26 April 1987 letter (fund-raising); hyiq.org 6-19 W then 100-110 W (1986); Goldes funder; 29 Dec 1985 agreement; lab notes by Roberts with an impedance "millions of times greater" unexplained. These bear on Claim 3; my energy bound and the Gray impedance and flux calculations apply to all three versions of the figures.
4. Newman v. Quigg (D.D.C. 1988) and the NBS 27-77 percent result (Claim 6).
5. Tseung's principle: "X units supplied ... Y units of existing energy from the surrounding ... effective total input X+Y" [web via Investigator: Energetic Forum 7530]; it is the open-system argument in his words, and it makes my Claim 1 point: Y must be an identified flux.
6. Benitez family of four GB documents; the patent examples are the 1918 worked example; the Lyden 2023 patent cites Benitez (applicant's characterisation).
7. Patent status: Annis/Eberly abandoned, MEG lapsed 2006 (assigned to Magnetic Energy Ltd), Flynn lapsed 2007: abandonment and lapse are facts of the record; reasons not stated (commercial, cost, or other), not evidence of falsity or truth.
8. Papp 1968, Skinner 1939 (United Press 1,200 per cent, Estill and Michaels), Moray witness excerpts, Meyer court and coroner: weighed in Claims 4-6.

Corrections to Step 1

1. claims.md, claim 2: "Don Smith's resonant Tesla devices (output rising as V squared and f squared ...)". What Kelly prints (p.2355, page image) is W = 0.5 C V^2 Hz for a general circuit (first power of frequency) and W = 0.5 C V^2 Hz^2 only "at resonance". Both are dimensionally power (W) or J/s^2, not as stated; the "f squared" form has no consistent unit. Also Smith/Mohamed use "V squared" in a way that is just P = V^2/R. Evidence: deep read section 3.1-3.2; my table in Claim 2.
2. claims.md, claim 2 and facts.json: "Benitez GB 121,561 (400 W in, 2,400 W battery power)". This figure comes from a worked example in the patent that is internally inconsistent: Q = 0.67 at the stated R, L, C, so there are not 72 oscillations per spark; the spark energy is 0.16 J (160 W at 1,000 per second); the example then requires 24 kW dissipation. So it should be recorded as a paper calculation by the patentee with no test, and with the inconsistency noted. The deep reader already flagged the energy mismatch; the Q = 0.67 point is new.
3. claims.md, claim 4: Skinner "1200 percent". The Investigator's United Press quotation ("about 1,200 per cent", Skinner's own estimate) plus the tool list (1/8 hp motor driving lathe, drill press and hacksaw) favours COP 12; Kelly's reading as COP 1200 gives 112 kW from a 93 W motor. The deep read reports Kelly's reading but not this check.
4. claims.md, claim 5: Cramton "2,340 percent". The 2,340 percent is computed from 36 W (24 W alternator motor + 12 W rotor, p.830); using 12 W (p.827) it is 7,020 percent; and p.808 says 3 A at 12 V (36 W). Quote all three, as the deep read does.
5. claims.md, claim 5: "Faraday". The deep read (Chapter 10 second section) already corrected the earlier statement that the basis was undefined: it is Kelly's 2.34 Wh/L, an energy figure (thermoneutral voltage). I confirm: any text reading "% of Faraday" as gas per coulomb should be revised; the charge-law equivalents are in my Claim 5 table. In addition, up to about 120 percent of that energy figure is textbook-possible for a cell that absorbs heat; claims of 211 percent and above are not.
6. claims.md, claim 3: "Annis and Eberly COP 200-400 for the switches". The COP is defined "without the coupling circuit" and refers to the control switches, so it is not a device-level COP [read: p.213, 219]. Flynn's patent makes a factor-2 coil-power claim, not a COP above 1 (deep read Corrections; confirmed).
7. sites.md "Leads for review", Sweet. The AboveUnity notes list "E-coil 1 input 10.41 V and 1.84 A (about 19 W)" and describe Roberts's 1986 gain as 6-19 W; Gray's notes as printed in the book give 10.4 V at 1.84 A as the OUTPUT (19.15 W) with an input of 7.5 V at 3.1 microamps. The two accounts attribute the same numbers to opposite sides. The research note says "in one reading, an input of 10.41 V x 1.84 A"; this cannot be resolved without Roberts's notes and should be marked an open conflict, not a fact in either direction.
8. Deep read Ch.11 (Tesla MHD): the 3.47e24 miles figure. The printed digits match 0.01 inch x 2.2e39 / 63,360 inch per mile = 3.47e32; the printed exponent is 8 powers of ten too small (24 versus 32). I verified in the extracted text (line 34461). The ratio 2.2e39 itself reproduces the proton-electron Coulomb-to-gravity force ratio (2.27e39 [calc]). The deep read did not check.
9. claims.md, claim 1: "Conservation of energy only forbids ...". Kelly's own text and Sweet's quotation both state that conservation applies to all systems; the claim that they hold only for "closed" systems is a restatement of the need for an identified inflow. This is a wording point; no verdict change.
10. Utkin and Noether (Chapter 16). The deep read notes "Noether's theorem is about continuous symmetries of the action ... not about symmetrical interaction between coils"; I confirm and add that time-translation invariance alone gives energy conservation (Claim 1a).

No changes to Step 1 page references were needed beyond those already in claims.md.

Web checks (budget: 2 of 6 used)

• Ferrite (BH)max about 7-30 kJ/m^3 (barium grades weaker than strontium; best commercial Y28 at 26-30; theoretical limit about 45) [web: https://www.magnetexpert.com/magnetic-properties-of-ferrite-magnets; https://arxiv.org/pdf/2310.02106]. Retagged from [memory, medium].
• Fair-weather atmospheric electricity: field and current density vary by factors of 3 to 6; the exact pair 130 V/m and 2 pA per square metre was not confirmed in the snippet, though their ratio gives a plausible fair-weather conductivity of 1.5e-14 S/m [web: https://dspace.ut.ee/bitstream/handle/10062/50334/Dolezalek_Tammet_Latham_Uman_Atmospheric_Electricity_2006_CRC.pdf]. The conclusion (10^-10 W per square metre) is robust to a factor of 10.
• Not web-checked (the verdicts do not turn on them): barium ferrite relative permeability about 1.05-1.1 [memory, medium]; ferrite saturation about 0.3-0.5 T [memory, medium] (the Gray flux argument also holds with a larger limit, because the excitation ampere-turns are 7e5 times short); the Navy seawater-fuel background [memory, medium]; Dirac sea history [memory, high].

What would settle the main open points

1. Sweet and Gray: a power-meter measurement of the oscillator's battery or mains supply as well as the coil input, with the output load measured by a true-RMS wattmeter with phase; the 1987 video meter views; Roberts's 1986 notes. The calculation above shows the magnets cannot be the source.
2. Benitez: a SPICE or bench build of the 1918 circuit with its stated R, L, C, 1000 sparks per second, measuring the battery energy over hours.
3. Water: a calorimetric measurement of heat plus gas energy output against electrical input, with a mass-flow gas meter and a true-power (not V times I peak) input measurement on the pulsed supply; the Meyer cell at 5 gal/h would need 83 kW.
4. Smith: measure input power at the 12 V battery terminals (integrated, with a battery log over hours) and output with a wattmeter or calorimeter; the 160 kW figure needs 8 kV x 20 A of resistive load, which a calorimeter would show immediately.
5. Moray-type devices: log antenna current and voltage, and test away from mains lines, as Eyring suggested in 1920s Utah.

(End of mathematician.md)