Meyers-Stan (Stanley A. Meyer, "Water Fuel Cell"): Mathematician review (Step 2)

Reviewer: PhD mathematician role, 2026-10-09. Reads facts.json, claims.md, deep/, and the Investigator's findings (sites.md "Leads for review", research/ notes, research/files/). Tags: [read: p.N] from the source text; [calc] my own arithmetic (scripted with Python, reproducible from the numbers shown); [web] with URL; [memory] with confidence. Meyer's patents, newsletters and brief are his own characterisation (stake: patent holder, seller of dealerships and profit-sharing certificates).

Source gap (repeated from claims.md). The folder holds no measurement, test report or witness statement about any Meyer device. No digests exist. The Birth brief pp.1-56 were deep-read by Step 1b; I read pp.117-125 (Memo 424), 142-146 (Memo 426) and 220-221 (Appendix A) myself in the extracted text. The 1989 New Zealand video was not transcribed when this was written (it has since been; see deep/ and arbiter section 14) [corrected 2026-10-09 after QE: was "not transcribed and not read"] Anything below that rests on the Investigator's second-hand finds (Perkins, Nagypal, NIST, Hindley, court records) is stated as such.

0. How to read this review (for the reader)

Meyer's technical story has four mathematical parts: (i) an LC "resonance" that is supposed to multiply voltage across a water-filled capacitor; (ii) an energy claim far beyond combustion; (iii) a vehicle fuel budget; (iv) a few efficiency numbers inside the Puharich patent that he cites. Each can be checked with arithmetic you can do by hand. Where the documents give no numbers at all (claims 4 and 5) there is nothing to check, and that absence is itself the finding.

1. Corrections to Step 1

1. claims.md claim 1, "current minimised at resonance." In a series LC circuit, which is what Meyer's Eqs 1-7 describe [read: p.8-9, page images p.8, p.10], current is maximal at resonance (impedance Z = Xc - Xl goes to zero apart from losses). "Current minimised" is a property of a parallel (anti-resonant) circuit, or of a capacitor that has charged and then passes only leakage. Meyer uses both pictures: series-resonance formulas (Eqs 4, 6, 7) and a diode "step-charging" picture [read: p.9, p.54]. The claim as phrased in claims.md mixes them; I restate it in section 3.
2. Birth deep read, "Memo 424 unread." I read Memo 424 (PDF pp.117-125). It contains no calculation at all: no energy balance, no equation, no number except the sentence "exceeds 2.5 million barrels" repeated three times [read: pp.118, 121]. It is a narrative about an "Energy Aperture" in each atom that admits "Universal Energy"; only Eqs 31-32 (E = hv and photon momentum) appear, with Planck's constant printed as 6.547 x 10^-27 erg-s (the accepted value is 6.626 x 10^-27 [memory, high]) [read: p.123]. The claims.md request for a deep read of "the full energy calculation behind 2.5 million barrels" can be closed: none exists in Memo 424.
3. Birth deep read note on 78.54. The deep read flags the dielectric constant being added to ohms in Eq 9. It is worse than one equation: Memo 426 states "dielectric value of water ... being 78.54 ohms" three times and "a resistive liquid (having an ohmic value of 78.54 ohms)" [read: pp.142-143]. The dielectric constant is a pure number (relative permittivity), not an ohmic value; the stated reason (eight electrons in the L shell) has no mathematical link to either quantity. 78.4-78.5 at 25 degC is the accepted static value [web: https://bionumbers.hms.harvard.edu/bionumber.aspx?id=115815, 78.4 at 25 degC].
4. Birth deep read, 2.5 million barrels vs mc^2: confirmed (4.48 % of mc^2, [calc] below).
5. Puharich deep read, section 7: I confirm its 22,400 vs 33,600 cc point and push it further: the headline "114.9 %" is itself an artefact of the same slip (section 3, claim 6). The deep read's "~63 %" is the right-sized correction for the Gibbs-energy figure; for the enthalpy figure the corrected value is about 77 %.
6. Investigator, Electronics World (sites.md). The Wireless/Electronics World text says "pure water apparently possesses a dielectric constant of about 5" [read: Electronics-World-1991-01.pdf pp.10-12]. That is wrong at the kHz-range frequencies in question: the static value is about 78 and stays near that up to roughly 1 GHz; the main Debye relaxation is near 19-20 GHz [web: https://arxiv.org/pdf/1704.01667]. A value near 5 applies only at far higher (THz-to-optical) frequencies [memory, medium]. Do not use "5" in any estimate.
7. Appendix A slips (new, for facts.json if it quotes them): the page prints ".740 ml /sec" (decimal point lost in OCR; not a slip by Meyer) [corrected 2026-10-09 after QE: was "740 ml/sec" should read 0.74 ml/s]; the 3.3 amp/hr slip stands. "3.3 amp/hr" should be 3.3 A (a current, not a charge); the same table gives 7.4 microlitres per injection cycle and 40 kV x 1 mA = 40 W, both arithmetically right [read: p.221; calc].

2. Common tools (worked numbers used below)

A. The cell as a circuit element. For concentric tubes of length L, inner radius a, outer radius b, filled with water of relative permittivity er = 78.5 and conductivity s (siemens per metre), the cell is a capacitor and a resistor in parallel: - C = 2 pi e0 er L / ln(b/a), G = 1/R = 2 pi s L / ln(b/a). Their ratio does not depend on geometry: G/(omega C) = s/(omega e0 er). - Meyer's 3 in cell with a 0.5 in rod in a 0.75 in tube [read: US 5,149,407, per claims.md]: L = 7.62 cm, a = 6.35 mm, b = 9.53 mm, ln(b/a) = 0.405, so C = 821 pF [calc]. At 5 kHz the series-resonant inductance would be L = 1/((2 pi f)^2 C) = 1.23 H [calc] (Nagypal used about 0.8 H and about 10 nF, [web via Investigator: stanslegacy Nagypal letter]), a reasonable coil. So a resonance frequency is easy to hit. The question is how large the voltage gain is.

B. Water's conductivity. Chemically pure water: 5.5 microsiemens/m at 25 degC [web: https://en.wikipedia.org/wiki/Self-ionization_of_water and the sources the search returned; 0.055 uS/cm]. Meyer's own text says tap water has "less than 20 ppm" contaminants [read: Birth p.142]; typical tap water is of the order 0.01-0.05 S/m (100-500 uS/cm) [memory, medium; a stated assumption, tested over a range below].

C. Cell quality factor. For a series coil driving a lossy capacitor, the best voltage gain across the cell is bounded by the cell's own Q: Q_cell = omega e0 er / s. At 5 kHz (omega = 3.14 x 10^4 rad/s):

[calc] Even perfectly pure water cannot give a resonant voltage gain above about 4 at 5 kHz, and tap water gives a "gain" of a few parts in ten thousand. For a voltage gain of 1000, the water would need s about 1e-8 S/m, more than 500 times purer than the theoretical limit set by water's own self-ionisation. (A gain of 20,000 V from 12 V, Meyer's range, needs about 1700.)

3. Central claims

Claim 1. Water capacitor splitting (resonant charging choke, pulsed unipolar high voltage, "without electrolysis")

a. Is the mathematics internally consistent? Partly, and where it is not, the error is in the claim's core. - Consistent: Eqs 2-4 (reactances, F = 1/(2 pi sqrt(LC))) are textbook-correct [read: page image p.8]. Eqs 6-7, V_L = Vt Xl/(Xl - Xc) and V_C = Vt Xc/(Xl - Xc), are correct for a lossless series LC (I = Vt/(Xl - Xc)) [calc], but lack the absolute value and the resistance. - Inconsistent: (1) Eq 9 "Z = R1 + Z2 + Z3 + RE, where RE is the dielectric constant of natural water" adds a dimensionless number to ohms [read: page image p.10]; Memo 426 states the dielectric constant in "ohms" [read: pp.142-143]. (2) Impedances in Eq 9 are added as scalars, ignoring the 90-degree phase between reactances and resistances. (3) Eq 14 is printed V = q/e^R (R as an exponent); the definition beneath it shows V = q/(eR) was meant [read: page image p.12]. (4) Eq 17 "Le = (I_ON)^2 T1/(T1+T2), Le is light intensity in watts" has units of A^2, not W [read: p.15; calc]. - The key sentence is "at resonant frequency, the voltage across both the inductor and the capacitor are theoretically infinite" [read: p.9]. True only for zero resistance (infinite Q). Meyer then deliberately adds resistance: chokes wound from "resistive wire" (stainless 430F, 60 micro-ohm/cm) [read: p.7, p.144], plus a lossy water load. The finite Q set by these is never given. Section 2C supplies it for the water: Q_cell between 0.0004 and 4. - The "step-charging" alternative (a diode charge pump building a staircase voltage) [read: p.9, p.54; Electronics World p.10-12 describes the same] does not need a high Q, but it is limited by leakage: in steady state the supply must replace the leakage power V^2 G on every cycle. Holding 20 kV across a 17-ohm tap-water cell costs 24 MW (table above). Holding it across pure water costs 2.6 kW. - The 40 kV at 1 mA figure (newsletter, and Appendix A Tab 38: "40,000 volts @ 1 ma = 40 watts") [read: p.221; claims.md] implies a cell resistance of 40 Mohm; for the 3 in cell that corresponds to s = 2.1 x 10^-8 S/m, 260 times below water's self-ionisation limit [calc]. The arithmetic 40 kV x 1 mA = 40 W is right; the cell it describes cannot exist as water-filled concentric tubes. - There is one escape that the mathematics leaves open and I record it as such: the voltage across the water might be a short transient (microsecond pulses, with the cell charging faster than it can leak; the water relaxation time e0 er / s is about 14 ns for tap water at 0.05 S/m [calc], about 0.13 ms for pure water). The pulse then has to be shorter than that relaxation time for the water to behave as a capacitor and not a resistor; at 5-10 kHz the drive period (100-200 us) is longer than the relaxation time of any practical water except near-pure water. Meyer's stated pulse lengths are not given, so this cannot be checked. The Hindley account of "tens of thousands of volts" is by oscilloscope-like appearance, not instrument [read: Electronics World, Jan 1991].

Restated claim. The testable core is not "current minimised at resonance" but: the energy needed per unit of hydrogen is less than the energy needed by ordinary electrolysis. That is an energy-per-mole claim, and the mathematics above says nothing for or against it except that resonance cannot supply the 20-40 kV the story relies on in conducting water.

b. Consistent with established experiment? Faraday's law of electrolysis: moles of H2 = Q/(2F), a result tested for almost two centuries; the minimum electrical energy to split water is the Gibbs energy 237 kJ/mol [memory, high]. Nothing in the folder or the Investigator's finds measures an energy input against a gas output on a controlled bench. The mainstream pulsed-electrolysis literature (Puteanus et al. 2025, in research/files) reports that pulsed operation cannot beat steady DC for the standard cell model (Jensen's inequality) and that earlier "improvements" often came from computing power as mean current x mean voltage, which is wrong for a pulsed waveform [read: Puteanus 2025, Introduction, citing Puranen et al.]. This bears directly on Meyer: his witnesses report an "average current measured only in milliamps" while the voltage is pulsed [read: Electronics World, Jan 1991]. Mean(I) x mean(V) is not the input power. Interested-party note: Puteanus et al. study PEM cells; the authors "expect similar results for other models", not proof for Meyer's geometry. The opposite camp (Shimizu et al.) is cited there, not read here.

c. Tested? By whom? Replicated? (From the Investigator; all second-hand, none in the folder.) - Hindley et al., Oct 1990, eyewitness [read: Electronics World Jan 1991 pp.10-12]: ammeter "no greater than a tenth of an amp"; gas rate rose as plates moved closer; cell stayed cold; steel bar melted by the burner; the editor's own caveat: "the experimental technique has more holes in it than a sieve ... what is the precise total cell energy input required to deliver a unit volume of dry gas mixture?" No input-power measurement. Hindley's claim that Section 101 patent grants are "independent confirmation" is his characterisation (and an interested view); a patent grant checks novelty and utility on the written description, not a measured energy balance [memory, high; for the physicist to confirm]. - Perkins Technology bench observation, 8 Oct 1992 (Investigator, via stanslegacy, Meyer's own 1995 binder): dissociation from about 10 V, current under 1 mA, vessel at room temperature, no gas volume stated. Perkins's own later note: on none of three UK visits was a water-fuelled engine shown. - Nagypal (Vienna), 4 Jun 1991, a distributor applicant (interested party): plates 3 x 2 in with 1.6 mm gap, 12 V raised to about 600 V, about 0.8 H, about 10 nF, about 20 mA, 0.5-1 cc gas per minute, "can't reproduce" Meyer's waveforms, "relative effectivity about 300%" against his own 10-12 W ionic cell. I checked his number against Faraday: 20 mA of true DC electrolysis current gives 6.2 x 10^-6 mol H2 per minute = 0.15 cc H2, or 0.22 cc/min of H2 + O2 mixture at 24 L/mol [calc]. His 0.5-1 cc/min is 2 to 4 times that. This is single-source data and I report it at face value: it is either (a) a measurement of the mean cell current that understates the true current (clamp or averaging meters on spiky pulsed current are a known trap; the type of meter used is not stated), (b) gas other than electrolysis products (dissolved air driven off by the field, vapour, heating), or (c) a real excess. The letter does not distinguish them, no repeat or control run (same cell, plain DC) is reported, and the 300% is relative to a different cell's power. Gas energy content for 0.75 cc/min is 0.10 W (HHV) [calc]; his input power is not given (20 mA at 12 V would be 0.24 W; at 600 V, 12 W). It deserves a controlled repeat, which has not been done on record. - Sussex University breadboard (reported only in a Perkins note), DTI-sponsored Queen Mary & Westfield report (summarised by Perkins as unable to reconcile Meyer's descriptions with established science, though leaving open a new development), NIST Office of Energy-Related Inventions (Spy, Dec 1991: the WFC "would be a net consumer of energy, not an energy producer"; the NIST file is not obtained). The NIST finding is a government agency's characterisation; I have not seen its calculation. - Court: Fayette County CVH19930292, Willis and Harper v. Meyer (a dealership-fraud suit; the plaintiffs and the judge, not neutral scientists, set the question); Meyer's own account quotes the ruling as "only electrolysis". Exhibits were destroyed 18 Jun 2014; the decision transcript (filed 11 Sep 1996) is not obtained. I give no weight to the ruling as science and none to Meyer's account of it as fact. - Builders' replications (Lawton 2006, etc.): currents of about 1-2 A reported, no gas-rate or energy figures; not controlled tests. - Result: no neutral, instrumented energy-per-mole measurement is on record, for or against.

d. If true, what would mainstream physics have to change? For "electrolysis at less than the thermodynamic minimum": the second-law bound (Gibbs energy 237 kJ/mol at 25 degC; with heat from surroundings, up to the enthalpy 286 kJ/mol) would have to fail; no change is needed if Meyer's cell merely uses heat or is more efficient than a poor electrolyser (it only needs to reach, never to beat, about 1.23 V per electron pair). For "splitting by field alone with no current": the Faraday relation between charge and gas would need an exception.

Verdict, split: - 20-40 kV on a conducting water gap through LC resonance: Refuted by calculation (Q_cell at most 4; leakage power 2.6 kW to MW). - Splitting with less energy than ordinary electrolysis, without electrolysis: Never properly tested (no neutral controlled test; not dismissed without testing by a lab, but the one court proceeding was a fraud suit, not an energy-balance test). Nagypal's 2-4x excess over Faraday on one letter should be re-run. - The notation and equations as printed: Internally inconsistent (Eq 9, "78.54 ohms", Eq 17).

Claim 2. "Hydrogen fracturing": energy beyond combustion (barrels of oil per gallon of water)

a. Mathematics. There is none. Memo 424 (the "Atomic Energy Balance of Water") gives no derivation [read: pp.117-125]. The cover equation E = M_d C^2 is printed but no mass defect M_d is ever evaluated [read: p.1, page image p.22]. Meyer says both "complies with the Laws of Thermodynamics" and releases "atomic energy" and a "Universal Energy" through an "Energy Aperture"; those two cannot both be taken at face value, because an energy source from "Universal Energy" is a source external to the water and the circuit, a claim about physics, not a calculation.

Worked energy budget [calc] for one US gallon (3.785 kg) of water, 1 barrel of oil = 6.1 GJ [memory, high]:

Meyer's figure is 2.5 x 10^8 times the chemical energy, 4.5 % of complete matter-to-energy conversion, and 6 x 10^5 times the energy of fusing all the deuterium in the gallon. The only nuclear source of energy that "water" offers is the deuterium. Even that is four barrels. His phrase "atomic energy" cannot be rescued by any known nuclear reaction of hydrogen or oxygen at the 5-20 kV scale: hydrogen and oxygen-16 are at or near the bottom of the binding-energy valley for decay or fission and need fusion barriers of MeV scale [memory, high; physicist to confirm]. The earlier figures in the newsletters (44,000-108,000 barrels, 1987-88) are smaller but still 10^6-10^7 times the chemical energy.

b. Experiments. No measurement of the heat released per gallon is in the folder or the Investigator's finds. Kucherov US 5,632,870 (cites Meyer) is a patent on drawing ambient heat into an electrolytic split; a patent, not a result. The electrical-explosion papers Meyer cites (Graneau et al., Phys. Lett. A 1986; Johnson, Kansas State) are filed in his binder; the physicist should read them; they report energy in an electrical discharge, which is not evidence of nuclear release.

c. Tested? No test of the energy yield on record; the NIST evaluation (net consumer) is not obtained.

d. If true: conservation of mass-energy and the whole of nuclear physics would need revision for hydrogen and oxygen.

Verdict: the quantitative claim (2.5 million barrels per gallon, and the earlier 10^4-10^5 barrel figures): Refuted by calculation (energy budget above; no experiment needed). Meyer's "does not create energy / complies with thermodynamics" statements are Not testable as stated (no measurable prediction). The self-contradiction between "complies with thermodynamics" and "atomic energy beyond combustion" makes the claim, as a whole, Internally inconsistent.

Claim 3. Water-fuel injection and vehicles

a. Mathematics. Appendix A gives the only arithmetic in the folder, and it is checkable [read: Birth p.221; calc]: - 111 ml/min gasoline "on-road" at 65 mph, "2.5 hydrogen-fuel of water" so 44.4 ml/min water; /60 = 0.74 ml/s; 3,000 rpm gives 100 injection cycles/s; 0.74/100 = 7.4 microlitres per cycle. (Correct, apart from the "ml/sec" and "amp/hr" slips.) - Energy check. 44.4 ml/min of water is 2.46 mol/min. Even if every molecule is split and every hydrogen burned, the enthalpy is 2.46 x 285.8 kJ = 705 kJ/min = 11.7 kW. The 111 ml/min of gasoline he equates it with carries about 3.5 MJ/min (at 32 MJ/L [memory, high]) = about 59 kW. The water is at best one fifth of the gasoline's energy. His "2.5 times more powerful than gasoline" holds only per kilogram of pure hydrogen (about 120 vs 44 MJ/kg [memory, high]); water is 11 % hydrogen by mass, so per kilogram of water it is about 16 MJ/kg, about 0.36 of gasoline. - A 50 hp engine delivers 37.3 kW at the shaft. At a typical 25-30 % thermal efficiency [memory, high] it needs 125-150 kW of fuel energy, 11-13 times the 11.7 kW the water could provide even by perfectly efficient burning of the hydrogen. Per injection that is 117 J available vs about 1.5 kJ needed [calc]. Whatever the injector does, a chemical-energy source cannot produce this; it requires the "beyond combustion" release of claim 2. - Electrical side. Splitting 2.46 mol/min needs at least 237 kJ/mol x 2.46 /60 = 9.7 kW of electricity (Gibbs energy; up to 11.7 kW with heat supplied), against the "40 watts" in Tab 38. The ratio is 240-290 to 1. At the 40 W quoted, the electrolysis could make at most about 0.005 mol/min of water-equivalent gas, i.e. 0.2 % of the stated demand. - Scaling in Tab 39 ("148 ul = 20 x 7.4 ul = 20 x 50 bhp = 1000 bhp") is simple proportionality of power to droplet volume, consistent with his own premise, so it inherits the failure above.

b. Experiments. The dune buggy on "hydrogen power" appears in an ABC TV news segment (1985) and in witness recollections (Hughes, Columbus Dispatch 2007: a tractor ran 15 minutes on well water; single source, no measurement) [per Investigator]. Perkins's note records no water-fuelled engine demonstrated on three UK visits (Oct 1990, Aug 1992, Oct 1992); Meyer's 1994 newsletter says the buggy was still being retrofitted "to match the acceleration of gasoline cars" [read: claims.md]. A running engine on a gas mixture from electrolysis is not itself impossible (hydrogen-oxygen mixes burn, and a vehicle can carry a battery that electrolyses water); what fails is the energy accounting at 40 W, not the idea of a hydrogen engine.

c. Tested? Not under any measurement I can find: no fuel flow vs power log, no dynamometer, no neutral witness with instrumentation. Not dismissed without testing in the sense of refusal: Perkins's Project TACO (VW engine, then a ferry diesel) was proposed, and the record (as the Investigator found it) does not show it was completed [leads: Perkins notes, 1992-93].

d. If true: as claim 2.

Verdict: the quantified version in Meyer's own Appendix A (44.4 ml/min of water, 40 W, 50 hp): Refuted by calculation. A modest version (a hydrogen/oxygen on-demand generator running an engine at the energy cost of electrolysis, powered by a battery): Plausible, untested as physics, with no demonstration on record; this is not Meyer's claim.

Claim 4. Electrical Particle Generator (EPG), "voltage amplification"

a. Mathematics. None: the patent gives no voltages, currents, turns, velocities or materials [read: deep read CA 1,213,671]. A voltage gain by itself is not a violation (a transformer has one). Faraday induction for moving magnetised particles through a pickup coil is real. Without numbers, "output exceeds input" is never stated either, and the energy for the secondary must come from the kinetic energy of the particles supplied by the primary or a fan (claim 15), so power out cannot exceed power in on the stated structure.

Scale estimate [calc, memory medium for susceptibility]. Gases are at most weakly paramagnetic: oxygen has a volume susceptibility of about 2 x 10^-6 (SI) [memory, medium]. In a 1 T field, magnetisation M = chi B/mu0 is about 1.5 A/m, so the gas's own field is about 2 x 10^-6 T, six orders of magnitude below an ordinary magnet, and it relaxes away when the gas leaves the magnetising region. A secondary coil of N turns sees emf = N dPhi/dt of the order of millivolts at best, not amplification. "Preferably gas" therefore weakens the device, not strengthens it.

b-c. No experiments on record in the folder or the Investigator's finds. Later newsletters call it a "gas battery" producing "electric energy directly from fuel cell gases without chemical interaction" (no numbers).

d. If gain in power were real: conservation of energy.

Verdict: Not testable as stated (no numbers); the weak form (voltage gain, power-limited) is Plausible, untested, but the scale estimate suggests the output would be negligible. Never properly tested.

Claim 5. Resonance in the electrode gap (1982 form: EP 0 103 656, CA 1,234,773, US 4,798,661)

a. Mathematics. None: "no sphere diameters, no gap, no frequency in hertz, no wave speed, no equation, no data" [read: deep read EP 0 103 656]. The only physical quantity that does link a gap to a frequency is an ion transit time: f is about mu V/d^2, with mobility mu. For hydrogen ions in water mu = 3.6 x 10^-7 m^2/(V s) [memory, high], V = 12 V, d = 1 mm, f = 4 Hz [calc]. That is a sub-10 Hz rate, not a kHz resonance, and the same calculation would need about 140 kV for a 5 kHz match across 3.2 mm. Water itself has no resonance at kHz: its dielectric relaxation is at about 19 GHz [web: https://arxiv.org/pdf/1704.01667]. Meyer's "velocity increasing geometrically" has no equation.

US 4,798,661 gives a ladder of breakdown voltages (2.5, 4, 5.5, 7, 8.5 V) in a "given size apparatus" with distilled water, 0-45 V "one typical structure" and a "negligible" current [read: deep read]. The ladder is the only quantitative data in the 1982 family; it is consistent in kind with the onset voltages of ordinary electrolysis (about 1.23 V thermodynamic plus overpotentials) but no current or gas rate is given to compare.

b-c. No data. d. Nothing specific.

Verdict: Not testable as stated (no dimensions, frequency or data); a nearby testable version (does DC-pulse frequency vs gap change gas yield per joule?) is Never properly tested.

Claim 6. Puharich (US 4,394,230, 1983), the folder's only related work

a. Mathematics: the arithmetic is wrong. I checked the efficiency table [read: deep read §5, Puharich pp.18-20]: - The patent divides Gibbs energy 236,954 J/mol by 22,400 cc (one mole of gas) to get 10.58 J/cc. But splitting one mole of liquid water gives 1.5 mol of gas (1 H2 + 0.5 O2), 33,600 cc at STP. Correct: 7.05 J/cc [calc]. - With the correct figure, 180 J of input should yield about 25.5 cc of mixed gas (17.0 cc H2) at 100 % efficiency; the measured 16.2 cc total (10.8 cc H2) is 63 %, not 91.3 % [calc]. (The patent's 22,400 appears once as "33,400".) - The headline "114.92 %": 16.2 cc x 12.77 J/cc = 206.9 J / 180 J. With 33,600 cc per mole of water the energy is 16.2/33,600 x 286,021 = 137.9 J, which is 76.6 % of 180 J [calc]. The "surplus of 15 %" disappears. - The thermodynamic fact the patent quotes (Penner & Icerman: about 120 % attainable at 300 K) is real: electrolysis can take up to T dS = 49 kJ/mol of heat from the surroundings (286 vs 237 kJ/mol, ratio 1.21). But that is a ceiling and is realised only if the cell runs at the thermoneutral accounting with heat coming in from the room; 114.9 % was not a measurement of that. - The power was taken as rms V x rms I (100 mW) while the same patent says capacitive and inductive reactance are "almost exactly 180 degrees out of phase" [read]: with a phase angle, real power is V I cos(phi), not V I; the cos(phi) is not stated. - The 0.1 cc H2/min at 100 mW (a different run) is 0.020 W of hydrogen enthalpy [calc], 20 % of the input.

b-c. Claimed measurements by gas chromatograph and mass spectrometer "in two laboratories", unnamed, standard error +/-10 %, no raw data, no replication on record. Interested party: the inventor's own patent text.

d. If true as stated (more than 100 %): a heat source from the surroundings (permitted) or a violation of the first law.

Verdict: the 114.9 % and 91.3 % figures: Internally inconsistent (they depend on a unit slip; corrected, 77 % and 63 %). The underlying claim (resonant splitting at 80-100 % efficiency) in corrected form is Never properly tested by neutral parties; the 0.16 mW book-level statements were not in my reading.

4. Meyer's statements of outside confirmation

Not a technical claim, but the Investigator's finds bear on it, so I keep them in view: Hindley (witness, 1990), Perkins (bench, 1992, current under 1 mA, no gas volume), Nagypal (2-4x Faraday, distributor applicant), Griffin's Warsash lecture (Sep 1993: 10 W in, gas at 10 psi within 10 s, vessel cold; per stanslegacy, not read), Nieper (14 Dec 1996: "the tested overunity effect", not read), and the negative NIST/DTI/court records. Silence elsewhere is not contradiction (SOURCE HONESTY): the neutral record is thin, partly because the one court proceeding destroyed its exhibits (2014), partly because the QMW/DTI and NIST files are not obtained. Each of those is listed as a deciding record in the Investigator's leads.

Absence-of-evidence anomaly (maths angle). The record contains no gas-per-joule figure from any witness. A hundred-second measurement (cell, wattmeter that reads real power on a pulsed waveform, gas collected over water, plain-DC control cell) would settle claim 1. That nobody reported one in 1982-1998, with two decades of visits by engineers, is itself an anomaly; competing explanations: Meyer declined to release details (Electronics World: "Meyer declines to release details"); trade secrecy; the measurement was done and unfavourable (NIST); or his instruments could not capture pulsed power. The folder cannot choose between them.

5. What would settle each claim (mathematician's view)

1. Claim 1: input real power (integral of v(t) i(t) dt, with a fast scope or a power analyser) vs hydrogen moles collected, against a DC control in the same cell. Pass line: energy per mole below 237 kJ/mol (Gibbs) would be anomalous; between 237 and 286 kJ/mol is ordinary.
2. Claim 2: a bomb calorimeter on the burned gas of a measured water volume with the electrical input logged. Pass line: more than 286 kJ/mol out.
3. Claim 3: the fuel-flow and electrical-power log of one engine run (Appendix A numbers: 44.4 ml/min, 40 W). 4-5. Any dimensioned build with a measured output.
4. Repeat Puharich's 30-minute run with a proper gas-volume reading and a power analyser.

6. Summary of verdicts

7. Corrections to earlier documents (for the orchestrator)

• claims.md claim 1: replace "with current minimised at resonance" by "with current deliberately restricted (Meyer's wording: 'without consuming amps')". Series resonance maximises current.
• deep/Birth (pp.1-56) "Observations": add that Memo 424 has no calculation (read in full by this reviewer); the "78.54 ohms" statements are in Memo 426 pp.142-143.
• facts.json / any copy of Appendix A: "3.3 amp/hr" is 3.3 A; the page prints ".740 ml/sec" [corrected 2026-10-09 after QE: was "740 ml/sec" is 0.74 ml/s].
• Puharich entry: 114.9 % becomes about 77 % and 91.3 % becomes about 63 % when the gas volume per mole is corrected to 33,600 cc; mention that the patent's own "33,400" appears once.
• Electronics World entry: the "dielectric constant of about 5" is not the value at these frequencies (about 78).
• Any later text that repeats "Your theory works" should add Nagypal's numbers (20 mA, 0.5-1 cc/min = 2-4x the Faraday ceiling for 20 mA true DC, if that current is the true cell current) and his distributor offer.