Naudin-JL: Mathematician review (Step 2)

Reviewer: PhD mathematician. Date: 2026-10-09. Scope: derivations, units, notation, hidden assumptions, arithmetic and error budgets for the seven central claims in claims.md. I read the Step 1 files (facts.json, claims.md, all deep/ reads), the Investigator's sites.md leads and research/ notes, the extracted source pages for the Naudin pages I rely on (_text/), and the saved Bishop, EarthTech and JLN pages. My own arithmetic was run with numpy (script in the session scratchpad, chk.py); every figure marked [calc] below was recomputed there.

Tags: [read] from a document in the folder (page or section given); [web] from the web (URL given); [memory] recalled, with confidence; [calc] my own calculation from [read] inputs.

Source-gap reminder (from claims.md): almost all of Naudin's own data pages are saved as text only; scope screens, graphs and run tables are images that were not retrieved. Where a conclusion below rests on a description of a result rather than the result itself, I say so.

Stance on stakes: Naudin, Bearden's company (Magnetic Energy Ltd), Moller/Frolov (Faraday Lab), Bedini, Gravitec and the patent applicant (Advanced Electromagnetic Systems) are interested parties for their own numbers. Bishop and the Sisyfos authors are sceptics with a stated aim (Jelinek and Pekarek: stop "pseudoscience" in schools) and Bishop's text is polemical. I check their mathematics, not their tone.

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0. Corrections to Step 1 (and to the Investigator)

1. claims.md, claim 3 / facts.json (MEG). Step 1 pairs "the paper's own scope readings are 'M RMS' values" with Naudin's data as if the same flaw applied to both. It does not apply equally. Bearden's p.67 readings are labelled "M RMS" (RMS of the power waveform), which the Tektronix note calls meaningless [read: deep/MEG-Bearden s.4; _text/2002-MEG-THS720P]. Naudin's v3.2 screen, as transcribed by Horky, is labelled "PWR OUT M Mean 6.764 W" and "PWR INP cMean 3.179 W" [read: deep/Horky s.2, table]. The same Tektronix note says the correct method is "instantaneous multiplication ... then take the mean value of the power waveform" ("Mean (CH1CH2)"). So Naudin's number is the right kind of quantity; whether it is right in value* depends on probe phase and deskew (section 3 below). Do not describe Naudin's readings as "RMS watts".
2. claims.md, claim 3: "Smith replies that Bishop's critique used a wrong power formula." Confirmed, and I can be specific: Bishop's eq. (3), P_ave = V·I0/sqrt(2) for constant V and sinusoidal I, is wrong. A constant voltage times a zero-mean sinusoidal current has mean power zero [read: Bishop p.3 vs Smith s.2; calc: mean(12 sin) = 0]. Smith is right on this. But Smith's other reply, that the "conditioned" 100 kohm resistor "is no longer 100K" because "Naudin's own voltage/current measurements show this" [read: Smith s.3], is circular: it uses the measurement under dispute to justify the measurement. See section 3.
3. claims.md, claim 2: "Ianconescu et al. matched four measured lift points ... within about 6.5%." True as stated, but incomplete. The match is at equal lifter voltage. At those voltages the paper's calculated currents exceed the measured currents by roughly 25 to 65% (e.g. 18.9 kV: 0.46 mA calculated, 0.277 mA measured; 22.8 kV: 0.76 against 0.606) [read: deep/Ianconescu, Tables 1 and 2]. Because the model's thrust is F = I·(1.284 b)/mu, thrust per mA is then not confirmed: measured thrust per mA is 21 to 27 g/mA, the model's is 18.4 g/mA [calc from Tables 1-2]. The paper says current agrees "less well, especially at low current" [read: p.25]. The "lifted mass" column is also total gram-force including the 7 g lifter, measured only where it exceeded 7 g.
4. Investigator's CFR calibration note (research/2026-10-09-jlnlabs.md). Agree with the Investigator that the page writes "56525 / 55700 = 0.985" and that this is input/output. I checked: 56525/55700 = 1.0148; output/input = 0.9854 [calc]. Harmless, but the printed fraction is upside down.
5. Investigator's MAHG "RMS x RMS" concern. I checked the arithmetic: for a pulse train in which V and I have the same shape, RMS(V) x RMS(I) equals the true mean power exactly (square pulse: 36.0 W against 36.0 W; half-sine: 25 000 against 25 000 [calc]). By the Cauchy-Schwarz inequality RMS x RMS is never below the true mean power, so the RMS-RMS definition cannot by itself inflate COP. The dangerous definition is the other one on the page, "average voltage and current" (section 5).
6. claims.md, claim 1: "Losonc's calculation gives zero net electrostatic force in vacuum". Correct, but the zero is not a finding about lifters; it is a theorem (section 1.3). Losonc also contains an inconsistent sentence (F2 of about 20 mN is called "an order of magnitude smaller" than 3.65 mN, which is about 5 times larger; 2.3 x 5 x 0.31 = 3.57, not 3.65) [read: deep/Losonc s.6].
7. Confirmations of earlier corrections. ARL eq. 6 (copper ions) recomputes to 0.0230 g, not 0.002 g [calc, agrees with claims.md]; nitrogen ions give 0.0153 g [calc]. Electrons give 6.7e-5 g, matching eq. 5. Patent US 2005/0057116 beta: 2 + (300-4)·4/2 = 594 (patent rounds to 590) [calc]. I could not reproduce the patent's "136 Torr" (deep read gets about 34 Torr from the printed inputs); I did not redo it.

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1. Claim 1: "Lifter thrust is not simply ion wind" (electrokinetic / electrogravitic part, including in vacuum)

a. Is the mathematics internally consistent?

• Naudin's own argument is a qualitative chain, not an equation. On the vacuum-tube pages he reasons: no corona in the tube, therefore no ion wind from the wire, therefore any force is "electrokinetic / asymmetric attraction by the dielectric medium (the air)" [read: _text/2003-Lifter-unlinked-wire..., ...true-lifter...]. There is no force law, no estimate of the electrostatic force that would be present anyway.
• The missing estimate is easy and removes the puzzle. His foil is 200 x 20 mm, 12 micrometre thick: mass = 2700 kg/m3 x (0.2 x 0.02 x 12e-6) = 0.13 g, weight 1.27 mN [calc]. An ordinary conductor-to-conductor electrostatic pull is F = (1/2) eps0 E^2 A. To lift the foil it needs only E = 2.7e5 V/m averaged over its 4e-3 m2 area (270 V/mm). A field of 1e6 V/m (1 kV/mm, i.e. 25 kV over 2.5 cm) would give 17.7 mN, fourteen times the weight [calc]. A 25 kV conductor a few centimetres from a 0.13 g grounded foil attracts it with ordinary electrostatics. The "25 mW" figure is simply 25 kV x 1 microampere [calc: 0.025 W] and says nothing about the force.
• "Linked" test (910 g on a torsion arm). If wire tube and plate are rigidly joined, the plate-wire force is an internal force pair and sums to zero (Newton's third law for the Coulomb force). A motion toward the wire side therefore needs an external force on the charged assembly: a net-charged body at +25 kV sitting in the room's non-uniform field feels a force from induced charge on walls, benches and the experimenter, and any leakage or corona at the tube ends, leads or glass surface in air supplies ion wind. Naudin states "no hissing sound" but gives no force, displacement, torque, or control (e.g. the assembly with the plate removed, or with the tube leads shielded) [read]. I cannot evaluate videos (not in the folder).
• Losonc's computation is consistent but cannot say what is claimed. His 2-D boundary-element model gives net x-force of about 1e-15 N from the Coulomb-law sum and -2.4e-4 to -6.2e-4 N from the pressure method, falling about 2.5 times when the mesh is refined from n = 1000 to 3000 (so it is discretisation error) [read: deep/Losonc, Tables 4-5]. The Coulomb-sum zero is guaranteed by construction: a symmetric pairwise interaction matrix sums to zero net self-force (Newton's third law), so a "zero" here is a check on the code, not new physics. The physical conclusion "no reactionless electrostatic force" follows from the same theorem. His further step ("Stein measured at least 0.31 mN in high vacuum, therefore an unknown electro-gravity force") is an argument by elimination. It is only as good as the vacuum measurement it leans on (Stein's paper was not obtained) and it ignores field-emission and leakage currents, charging of insulators and lead-wire forces in the 40 kV vacuum case, which his model omits by construction [read: deep/Losonc s.8].
• Ion-wind arithmetic in the literature (what "too small" means). ARL's ballistic estimate F = (2mV/q)^(1/2) I (eq. 3) with copper ions at 40 kV and 1 mA gives M = 0.023 g, about 200 times too small for a 5 g lifter [calc]. That kills the collisionless ion-recoil model only. The collisional (drift) form F = I·l/mu (ARL eq. 14) with N2+ mobility mu = 2.5 cm2/Vs and l = 0.04 m gives 0.16 N (16 g) [read: deep/ARL s.6; calc: 1e-3 x 0.04 / 2.5e-4 = 0.16 N]. That formula is the standard electrohydrodynamic (EHD) corona-thruster formula [memory, high], the same one Tajmar evaluates (his eq. 10 gives 163 mN at 22.8 W; I reproduce 164 mN [calc]). So "ion wind is 3 orders of magnitude too small" is wrong as a statement about ion wind in general; ion wind in air, done in the collisional form, is the right size. Naudin's page states the opposite ("ionic wind ... is not responsible of the main upwards thrust") but gives no calculation.

b. Consistent with established experiments?

• My check of Naudin's own lift data against the drift formula. Using F = I·l/mu with gap l = 0.03 m (Naudin's stated wire-to-plate distance) and mu = 2e-4 m2/Vs (the value Ianconescu uses) gives l/mu = 150 N/A [calc]. Naudin's numbers [read: Lifter1 and v4 pages]:

The v4 hover point sits within 4% of the ion-drift scaling; the Lifter1 points are about a third of it. Hovering gives the force only at the weight, and Naudin's quoted voltages (40 to 44 kV) may be supply voltages, not voltage at the lifter after any series resistor (Ianconescu's source reads 25 kV against 11 to 23 kV at the lifter) [inference; unknown for Naudin]. This does not prove that the thrust is ion drift, but it shows the observed thrust per ampere is of the drift order and not anomalously large. - Thrust per watt: Lifter1 1.35 mN/W; v4 3.86 mN/W [calc]. Mainstream EHD thrusters at atmospheric pressure are in this range [memory, medium]. I do not rely on that point. - Vacuum. The experiments are, in order: Brown's reported vacuum work (letter via Naudin in ARL Appendix B; the lab notes were "never published" [read]); Talley (Air Force, late 1980s), who found "no detectable propulsive force" under high vacuum for static DC, quoted in the NASA/ISR report [read: deep/NASA s.2]; NASA/ISR 2004 (Canning et al.), whose apparatus could not resolve small forces (rotation of less than a sixth of a turn was not detected) [read: deep/NASA s.3]; Tajmar's sealed-box air test, which measured no net thrust to about 10 micronewtons, but which by construction cannot detect a force that is internal to the box (an ion wind also gives zero), so it tests only a reactionless force [read: deep/Tajmar s.1]; the Gravitec/NSSTC video of 2003 (Naudin's page of 2007), where the effect "is weaker" at 1.72e-6 Torr and the arm "retrieves its initial position" when the voltage returns to zero [read: _text/Related-Research-2007-Gravitec]. The video has no force numbers in the text I read, and the 45 kV is applied through a torsion-wire arm, so lead-wire and chamber-wall forces are not excluded by anything stated. The page is from an interested party (Gravitec Inc, patent holder, supplier of the video); I record the claim as theirs. - Honda/Musha (the electrogravitic side). Musha's measured weight loss is 0.9 +/- 0.63 g (about 3% of 62 g) with a scatter of about 70% [read: deep/Musha s.2]. His own model has arithmetic I could partly reproduce (Eq. 14 gives 1.28 g with inputs R = 1 mm, N = 1e24, omega_e = 6e13) but the inputs are chosen: omega_e is two orders from the 1e15-1e16 he quotes earlier, N is a hot-plasma density used for glass, the model scales as N^2/omega_e, and the deep read could not reproduce the constant 3.23e-13 from Eq. 13 [read: deep/Musha s.5]. His competing "electrogravitic" estimate (Eq. 3) also lacks the stated Z.

c. Tested? By whom? Replicated?

• Air lift: tested by ARL (3 lifters + wire, 30-37 kV, no force measurement, lift only [read]), Ianconescu et al. (balance, 4 points), NASA/ISR (rotation), Martins and Pinheiro (simulation only, no experiment [read]). Replications in air are numerous (Naudin's self-registered logbook says 351 by October 2006: one source, his own page; I did not see the entries beyond the first).
• Vacuum: see (b). No neutral, calibrated, controlled vacuum test with a sensitive thrust stand and shielded leads is on record in this folder. Dismissed without testing? Not exactly: Talley and NASA/ISR did test, with stated sensitivity limits. Brown's and Gravitec's positive claims are not reproducible from the records available (notes unpublished; video).

d. If true, what would have to change?

A static electric field acting between two bodies in vacuum producing net momentum change without any exhaust would require a force not equal and opposite between the bodies (violating momentum conservation in Maxwell electrodynamics) unless the field carries momentum to something else (the room, the chamber, charged leads). Mainstream electrodynamics would need an extra coupling term (a "gravitational" or vacuum-medium coupling) with no known Lagrangian. None of the sources gives one in testable form: Musha's relies on a minority inertia theory and an unreproduced constant.

Verdict claim 1 (split)

• Strong form, "air thrust is not ion wind (collisional momentum transfer)": Tested, not supported. The ion-drift calculation gives the correct order and, for v4, the right number (F/I within 4%); Ianconescu fits within 6.5% (with the caveat in section 0 item 3).
• Naudin's vacuum-tube tests as evidence for an electrokinetic effect: Refuted by calculation (as evidence): ordinary electrostatic attraction of a 0.13 g foil by a 25 kV conductor is about 14 times the weight at 1 kV/mm; the linked version has uncontrolled external forces.
• Residual high-vacuum thrust (Brown, Gravitec): Never properly tested by a neutral controlled test, not dismissed untested (Talley, NASA/ISR, Tajmar's air-box limit). Both positive sources are interested parties and no force record is in the folder.
• "Electro-gravity by elimination" (Losonc): Not testable as stated.

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2. Claim 2: "Lifters are real, reproducible and scale"

a. Mathematics

Naudin's numbers are arithmetically sound: 41.9 kV x 570 microampere = 23.9 W; 40.5 kV x 2.01 mA = 81.4 W; 44 kV x 3.02 mA = 132.9 W [calc]. Hover thrust equals weight, so 2.3 g needs 22.6 mN. The apparent efficiency jump from Lifter1 (0.128 g/W) to v4 (0.39 g/W) is a factor of three, which the page does not explain (see section 1 table: the ion-drift scaling predicts roughly constant F/I for a fixed 30 mm gap, and v4 matches it while Lifter1 is three times worse). Possible causes (corona onset current wasted on edges, a series ballast resistor in the power measurement, wire radius) are guesses; no data decide.

b. Consistent with experiment

Yes: lift in air at 30 to 45 kV is confirmed by ARL (square lifter "hovered vigorously", 30 kV, 1.5 mA) and Ianconescu (7 g lifter lifting 13 g gram-force total at 22.8 kV) [read]. ARL notes arcing destroys lift, polarity and orientation do not matter, a ground plane is not needed [read: deep/ARL s.4].

c. Tested / replicated

Independent builds in air: ARL (Naudin's design), Ianconescu (own build), NASA/ISR (disc-and-cylinder, not a Lifter). The "351 registered replications" is Naudin's own log, an unverified count (single source: his page; entries are submitted by experimenters). I record it as documented in one published source with no independent count.

d. If true

Nothing in mainstream physics changes: air-propelled EHD craft are known (de Seversky, Christenson and Moller 1967) [read: deep/Tajmar s.2].

Verdict claim 2

Established for lift in air at about 30 to 45 kV (the lifters fly; the thrust is of the ion-drift magnitude). Plausible, untested for the scaling claim as an engineering statement (efficiency and size scaling rest on Naudin's two data points, one matching the drift scaling and one at a third of it). The 351-replication count: not independently verified (single source).

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3. Claim 3: MEG replication gives "apparent" COP above 1, open loop

a. Is the mathematics internally consistent?

Bearden et al. (interested party; every number is the inventors' own). - Fig. 19: output 1.96 kV peak-to-peak, 15.44 mA RMS, "M RMS 12.7 W". The RMS of a power waveform p(t) = P(1 - cos 2wt) is sqrt(1.5) P = 1.225 P, so a mean of 12.7/1.225 = 10.4 W; direct check 693 V x 15.44 mA = 10.7 W [calc]. So the output side is roughly self-consistent once corrected, with an effective load of 45 kohm. - Fig. 18 input: "High 51 V" x "RMS 117.5 mA" = 5.99 W, but the displayed "M RMS" is 3.588 W [calc]. The "High" level is not the mean, so the product is not expected to match, but the paper does not say what the 3.588 W represents. The ratio 12.7/3.588 = 3.54; after RMS correction about 2.9; Fig. 21 at the same input gives about 2.2 [read: deep/Bearden s.4-5]. Three different "COP" figures for the same operating point: 3.54, about 2.9, about 2.2. - 3.588 W at 100 W per division is 0.036 of a division above zero; the number depends entirely on the instrument's internal arithmetic and zero offset [read: deep/Bearden s.4]. - Fig. 21 (COP per coil 1.7 to 2.7) uses "input potential" that is never defined; the "net unit COP is double" (about 5.4) simply doubles the single-coil COP, but the input is the same for both coils, so doubling the output and keeping the input gives a COP of 2 x 2.7 = 5.4, which is only legitimate if the single-coil COP used the full input. The text says "single output coil's power divided by the input power", so yes, 5.4 is the arithmetic consequence [read: p.36]. The doubling is correct as arithmetic; the open question is whether the input power is right. - Projections to 550 V / COP 43 (Figs 22-23) have no stated model; extrapolation of a curve fitted to eight points.

Naudin (interested party; his own data). - v2.1 page: DC input at the control board 3.25 W with the 9 W lamp load; 1.75 W without load; output "6.76 W". He subtracts 1.75 W and reports a "real" input of 1.5 W. Ratios: 6.76/3.25 = 2.08 (total input) and 6.76/1.5 = 4.5 [calc]. Subtracting the controller's own draw as though it were not an input is generous: the gate drive and LED are part of what must be paid to run the device. The honest ratio is 2.08. Naudin himself writes "unfortunately measurement artifacts remain possible" [read: _text/2000-MEG-v2-1]. - V x I check on the screen figures transcribed by Horky: 255.3 V RMS x 27.23 mA RMS = 6.95 VA against 6.764 W real power, a power factor of 0.973 (phase angle 13 degrees) [calc]. The three numbers are mutually consistent as measured. The question is therefore not arithmetic but whether the voltage and current channels are correct in phase. - Phase sensitivity (my calculation). Mean power = V_rms I_rms cos(phi). To turn a true 3.25 W (equal to the DC input, i.e. COP = 1) into the measured 6.76 W at 6.95 VA requires an error in phase of 49 degrees, i.e. a time skew of about 5.7 microseconds between voltage and current channels at 23.8 kHz [calc]. For a typical probe or current-sensor mismatch of tens of nanoseconds, this cannot happen. A 1 microsecond skew is 7.2 degrees at 20 kHz and would multiply the apparent power by 1.2 (true phase 60 degrees), 1.34 (70 degrees) or 1.70 (80 degrees) [calc]. So if the circuit were strongly reactive (a high-Q winding with 5.7 H secondary inductance and stray capacitance) a skew of a microsecond or two could matter a great deal. Naudin's screens show the voltage and current "in phase" and he checked the phase with an analogue PM3215 scope [read: _text/2000-MEG-v2-1]. I therefore cannot show that phase error alone explains his factor of 2.08; it is a candidate, not a demonstration. - The honest statement of the mathematics: Naudin's measured numbers do not contradict each other; the whole claim stands or falls on a power measurement of a pulsed, resonant, high-voltage circuit made with one handheld isolated-input oscilloscope [memory, medium; THS720P is a handheld scope, from Flickinger's message naming it], current taken from a 10 ohm resistor and a 1/10 probe [read].

Naudin's own energy audit fails by his own numbers. Naudin offers that "most of the power is radiated in EM form" because the load resistor warms less than the apparent power. He reports 2.8 mT near the load at 16 kHz and 1250 V/m at 50 cm [read: _text/2000-MEG-v2-1]. At 20 kHz the wavelength is 15 km, so 0.5 m is deep in the reactive near field. Treat the 1250 V/m as a quasi-static dipole field: dipole moment p = 4 pi eps0 r^3 E = 1.7e-8 C m (equatorial). Radiated power of an electric dipole P = w^4 p^2 / (12 pi eps0 c^3) = 8e-12 W [calc]. For the magnetic side, a dipole giving 2.8 mT at 2 to 5 cm radiates 4e-15 to 9e-13 W [calc]. Radiation is eleven or more orders of magnitude below a watt. So the "missing heat" cannot be radiated; either the apparent power is wrong, or the heat measurement is not what he thinks. His observation that the load heats less than the apparent power is itself the strongest piece of evidence in his own page and supports the first reading.

Bishop (sceptic, polemical). - Eq. (3) is wrong (see section 0). His input power 28 V x 0.125 / sqrt(2) = 2.47 W rests on treating the supply current as zero-mean AC. A switched DC supply carries a unidirectional current; Smith's reading ("AC stood on a DC level") is right, and the input should be V x (mean current). If the 125 mA is the amplitude of a ripple about a 125 mA mean, the input is 28 x 0.125 = 3.5 W [calc], close to Naudin's 3.2 W. Bishop's input is a misread baseline. - His output check is the sounder half: 500 V amplitude and 44 mA amplitude imply 11.4 kohm, not the nominal 100 kohm; a 100 kohm resistor at 500 V amplitude carries 5 mA and dissipates 1.25 W [calc]. Bishop's "wrong by a factor of nine" is the right arithmetic (500/0.044 = 11.4 kohm; 100/11.4 = 8.8). Smith's defence (the resistor is "conditioned") is allowed in principle, since a carbon resistor can have a voltage-dependent resistance. But then V^2/(2R) with R = 11.4 kohm is 11 W in a 5 W resistor, which should heat strongly, whereas Naudin's own note says the heating is less than the apparent power [read]. A calorimetric measurement on the load would decide it, and Naudin says it "has not yet been done" and makes him "pessimistic".

Flickinger / Naudin on non-linear loads. COP above 1 appears only with non-linear loads (varistors, conditioned resistors, fluorescent tubes) [read: research/2026-10-09-jlnlabs.md, megnot01.htm; Horky p.14]. The Jelinek-Pekarek reply is correct in principle: the load is outside the energy-balance surface, so a non-linear load cannot change the device's energy balance. It can change the measurement, because non-sinusoidal currents with a changing waveform make RMS-based or cos-phi based power wrong. A result that appears only when the measurement is hard is a warning, not evidence.

Jelinek and Pekarek: checked derivation (Poynting argument)

• Eq. (5): the printed sign of the two field terms is wrong; correct is dU/dt with a minus sign (Poynting: outward flux = -J.E - d(field energy)/dt) [read: deep/Jelinek s.5.1; I agree and have checked it against the standard form, memory high]. Harmless because both terms average to zero over a period.
• Eq. (10) drops the cross terms H_PM . dB_C/dt; the missing term averages to zero in periodic steady state because H_PM is constant. Eq. (13) needs a lossless single-valued constitutive law; with that reading linearity is not needed. I accept the deep reader's re-derivation: for a lossless, non-hysteretic core in periodic steady state, mean power in equals mean power out, whatever the load and whether or not a magnet is present. For a hysteretic core, output is less than input by the loop area times frequency (the deep reader's numerical check: about 3.2 kJ/m3 per cycle absorbed). Appendix 1 ("the circuit does not depend on the magnet") is true only for a linear core and is the weak part; a biased saturable core does change the waveforms, which is the patent's flux-switching mechanism. The energy conclusion does not need Appendix 1.
• The unavoidable hidden assumption: all energy enters or leaves through the four electrical ports. Bearden's explanation (extra energy from the "active vacuum" through the magnet) is outside the proof by assumption, and the critique does not engage it. That is a limit on the proof, not a flaw.
• The Horky numbers were not analysed by the critique (it quotes none) [read: deep/Jelinek s.6]; its "wrong power formula" diagnosis is a hypothesis for Horky, not a finding. In Horky the table row labelled I1-I2 is really I1-I0, an undefined no-load current, so the "input power" there is not supply power [read: claims.md Corrections; deep/Horky].

b. Consistent with established experiments?

Faraday's law, transformer theory and magnetic-amplifier practice (a DC bias shifts a core's operating point; this is ordinary engineering [memory, high]) account for waveforms that depend on the magnet. Nothing established gives a net energy gain from a passive core with copper windings. Naudin's own magnetic amplifier test (magnet raised output 120% for 0.35% more input: 13.78 to 30.39 mW out, 853.2 to 856.2 mW in) comes with his words "There is NO Overunity here" [read: research/2026-10-09-jlnlabs.md; ratio 30.39/853.2 is 3.6% of input]. That is the principle (magnet changes coupling) without any energy claim.

c. Tested? Replicated?

• Bearden's group: the authors' own data, open loop, no calorimetry, no independent witness; an independent test was "underway by the authors" [read: deep/Bearden s.2]. Bearden said (via the Investigator's ZPE note) that Naudin reached COP 7.3 in a third build and that a DoD-linked university replication and certified laboratory test were announced in Dec 2000; neither is found [read: research/2026-10-09-zpenergy.md; Investigator: not found]. That is an absence to be noted, not evidence either way.
• Naudin: apparent COP 1.75 (7 Nov 2000), 2.08 or 4.5 (12-Dec), v3.0 run 2: 10.28 W / 3.179 W = 3.23 [calc, from Horky transcription]. The loop was never closed; Naudin wrote "I am trying to close the loop ... have not yet succeed" (13 Nov 2000) and his secondary coils broke from internal sparking (16 Nov) [read]. A device claimed to give COP greater than 1.75, 2 or 3 could be closed with a start battery; no one has reported it.
• Horky 2009: a student build, COP 1.57 to 2.89, "apparent power", undefined I0, no heat measurement; written as advocacy [read: claims.md]. A detail in my reading of Horky's transcription of Naudin's v3.0 run #2: the output current on the screen is listed as "Pk-Pk 111.2 mA", the same number as the input mean current; this could be a transcription duplicate [read: deep/Horky s.2; unknown].
• No calorimetry on the MEG load by anyone; no closed loop.

d. If true

A passive magnetic core with a static magnet would have to deliver net energy per cycle: either a violation of energy conservation, or an energy source outside the electrical ports (Bearden's "active vacuum"), for which the paper provides no coupling and no measured amount. Classical electrodynamics (Poynting's theorem) would need an extra source term in the energy balance.

Verdict claim 3 (split)

• Strong form (true net energy gain, COP > 1 in a closed energy balance of a passive core and coils): Refuted by calculation, subject to the stated assumption (all energy enters through the four ports; core lossless-or-lossy but single-valued). The calculation is Poynting's theorem for a periodic steady state, with the Jelinek-Pekarek signs and cross terms corrected.
• Weak form (an "apparent" measured COP of 1.75 to 3.5 on scope power readings): Never properly tested. No calorimetry, no closed loop, no phase or deskew verification published; the one heat observation Naudin made points to a lower output than the apparent power; the Bearden "M RMS" readings are invalid quantities (Tektronix) while Naudin's "Mean" readings are valid in kind and unverified in value.
• Bearden's vacuum-energy explanation: Not testable as stated (no coupling or equation given).
• Projections to COP 30 to 43: Not testable as stated (no model).

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4. Claim 4: Mizuno-Ohmori plasma electrolysis ("CFR") gives reproducible excess heat

a. Mathematics

• Naudin's arithmetic is consistent. Calibration: 8 mL x 2.26 kJ/g + 600 g x 15 K x 4.18 J/gK = 55 700 J against 56 525 J input (ratio 0.985) [calc]. Low-power run: 26 mL + 150 g x 23 K gives 73 181 J against 148.4 W x 499.2 s = 74 081 J (0.988) [calc]. Medium-power run: 10 g x 2.26 kJ/g + 150 g x 21 K x 4.18 = 35 767 J against 289.2 W x 82 s = 23 714 J, ratio 1.51 [calc].
• Hidden assumption 1: every gram of lost mass was vaporised. The latent term assumes 2260 J per gram of mass lost. If liquid droplets, foam or splashed electrolyte carry mass off, the weighing counts mass but no latent heat. The latent-heat bound makes this concrete: 289.2 W for 82 s can vaporise at most 10.5 g [calc]; Naudin lost 10 g in the medium run, i.e. essentially all of the input would be needed for vaporisation alone, and then the heating of the water (13 kJ, 56% of the input) is on top. For the run Kowalski quotes (run 28: 170 g evaporated, 1200 W in, 3093 W out): 170 g x 2.26 kJ/g = 384 kJ is delivered at 3093 W in 124 s; in 124 s at 1200 W the input can vaporise at most 66 g [calc]. So "170 g" requires either 2.6 times the input or non-evaporative mass loss. I rely on Kowalski's description of run 28 (one source: a web commentary, run table not read).
• Hidden assumption 2: the calibration transfers. The calibration is with a resistive heater in the same beaker and quiet boiling; it has no plasma, no splashing and no foam. A calibration that cannot produce the suspected artifact cannot exclude it [inference from read: research/2026-10-09-jlnlabs.md].
• Hidden assumption 3: the cooldown accounting. The EarthTech replication reports that Naudin adds the evaporation energy during the cooldown after power-off, which they call double counting because the sensible heat that drives that evaporation is already in the heating term [read: research/files/EarthTech page, "Cooldown"]. The energy-balance reasoning is correct: E_out = m c dT (at power-off) + evaporation until power-off; evaporation afterwards is paid from the first term. Their Table 2 shows the effect numerically: in runs DEW1 to DEW3 COP = 0.97-0.99 and COP2 (with loss corrections) = 0.99-1.01, while "COP with cooldown" (Naudin's method applied to their data) = 1.57-1.62, and their cooldown energies (e.g. 36 416 J) are close to their heating terms (39 647 J) [read]. So Naudin's method turns a COP of about 1.0 into about 1.6, matching the "typically around 1.6" EarthTech quotes for Naudin's results [read: EarthTech intro]. I did not find in the Naudin pages I read whether this addition was used in the medium-power run (single source for his use of it: EarthTech via private communication with Naudin).
• Naudin states his own condition for excess heat ("only at this moment, the heat produced is greater than the electrical power input" when the cathode is incandescent) [read: research/2026-10-09-jlnlabs.md]; the 33-run table is an image not retrieved.

b. Consistent with experiments

Mizuno 2004 himself says "there have been few claimed replications ... In most cases, no excess heat or hydrogen is observed" [read: research/2026-10-09-lenr-canr.md], which sits uneasily with Naudin's "fully replicable". Kowalski, Little and Luce (ICCF-12, 2005): mean COP 1.00, standard deviation 0.02, at 350 V 1.03, with splashing and foam droplets named as error sources [read: same note]; Mizuno's own earlier report of heat above input in some runs (up to 200% in the 2000 JJAP abstract quoted on Naudin's page) is an interested-party claim by the originator [read: _text/2003-CFR-test-data-results].

c. Tested? Replicated?

Replicated attempts: EarthTech (Austin, Texas) in 2003 on Naudin's own apparatus design with a Clarke-Hess meter and a 10 mg balance: COP2 average 0.98 [read]. EarthTech notes that their earlier 1998-2000 attempts on Mizuno's original also failed "despite the full cooperation of Dr. Mizuno" [read]. Naudin lists replications at CNAM Paris, South Africa and Boulder (index page; not read in detail). No second positive independent quantitative replication is in the record I have.

d. If true

Net energy from a tungsten cathode in K2CO3 would need an unknown reaction (Mizuno proposes a nuclear one; Naudin "atomic hydrogen trapped and recombining", which is chemistry and bounded by dissociation enthalpy). Standard electrochemistry and nuclear physics would need a new low-energy channel with no radiation or products documented in the folder.

Verdict claim 4

Tested, not supported for Naudin's excess-heat figures (independent instrumented replication gives COP 0.98 to 1.00; Naudin's 1.5 to 1.6 is reproduced numerically by a cooldown double count applied to EarthTech's own data). Note the unresolved exceptions: Mizuno's original reports are by an interested originator and the Naudin run table was not retrieved.

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5. Claim 5: Moller's Atomic Hydrogen Generator (MAHG), COP 5 to 21

a. Mathematics

• Energy argument (calculation, no experiment needed). The cycle H2 -> 2H -> H2 returns the gas to its starting state. Enthalpy is a state function: the energy absorbed in dissociation equals the energy released on recombination, so the net gain from the cycle is zero. Dissociation enthalpy is about 436 kJ/mol H2 [memory, high]. What Langmuir's hot filament does in practice is carry heat from the filament to the wall by the dissociation-recombination route (atomic hydrogen is a good heat carrier); this changes where the heat goes, not the energy total. Kowalski makes the same point: "any chemist would say that this is not possible, unless the excess energy comes from another source" [read: _text/...Kowalski-item289, p.1, point 2]. Frolov, quoted on Naudin's page, said the 250% half-wave result "gave reason to think that a possible mistake had been made" [read: research/2026-10-09-jlnlabs.md].
• Input-power definitions (the arithmetic that can create a COP). The data sheet says "Input (V), Input (A): Rms Voltage and Rms Current" and, separately, "The average voltage and current are also measured on the digital oscilloscope" [read: research/pages/jln_mahg_tests_pultests.htm.txt]. For a pulse train of duty D with amplitude Vp, Ip:

At D = 5% the third definition understates the input by a factor of 20 [calc: 36 W true against 1.8 W]. The reported COP of 21 (51 Hz, 5% duty, "RUN 76") divided by 20 is 1.05, and the 1153% run at 5% duty becomes 0.58 [calc]; the pure-DC blank test gave 64%. This does not show that mean x mean was used; the page does not say, and the voltage across a switched filament and the voltage at the battery terminals differ (at the battery the voltage is nearly constant and mean x mean would be correct). It identifies the one measurement detail the duty-cycle dependence of the COP would be explained by, and it is checkable from the scope files Naudin holds. - Internal inconsistency to resolve. Pure DC blank (runs 38 to 40): 64% efficiency. Pulsed runs with the same calorimeter: 224% (runs 11 to 37) and about 240% (long runs) [read]. If the calorimeter under DC loses 36% as Naudin says, the same loss applies under pulses, so the pulsed input is understated by at least a factor of 3.5 (224/64) or the pulsed output is not heat from the input. The 36% loss explanation applies to both modes equally. - Filament temperature formula. Naudin writes T = (P/(kS))^(1/4) with S = 1e-3 m2 and k = 5.67e-8 [read]. For a 0.25 mm wire, S = pi d L means L = 1.27 m of wire [calc: 1e-3/(pi x 0.25e-3)]; the filament length is not in the text I read. With his formula, 774 K corresponds to 20 W (5.67e-8 x 1e-3 x 774^4 = 20.4 W [calc]), and 365 W (875 W/2.4) gives 1590 K, which is below the 2000 K he gives as the minimum for dissociation; the formula assumes only radiation (no conduction to the hydrogen and walls) and unit emissivity. His own temperatures therefore do not show dissociation at the claimed levels, and "1% to 7% atomic hydrogen for 25 ms of each 100 ms" is not backed by an equation on the page. - Units: output = flow (m3/h) x dT (K) x 1161.11 W [calc check: 4.18e6 J/(m3 K)/3600 = 1161.1 W per (m3/h K)]. Correct. At 875 W, flow x dT = 0.754 m3/h K.

b. Consistent with experiment

Langmuir's atomic hydrogen torch is established; it is used for welding [memory, high]. No established experiment gives more heat than electrical input from it. Frolov's own smoothed-DC result was 82% against 124 to 130% with pulses and 250% with half-wave pulses [read: research/2026-10-09-jlnlabs.md], the same pulsed-versus-DC pattern as Naudin's, which is what an input-measurement artifact would give and also what a real pulsed effect would give; the data cannot separate them.

c. Tested? Replicated?

Naudin says his results "confirm" Frolov's, using different electronics (the page's own words). Both are on the same side of the fence: the originator's contractor (Faraday Lab, paid by Moller, 50-50 contract per Frolov in Kowalski) and the replicator who hosts Moller's page "with permission". No independent party measured it. A test in Australia was "planned" [read: Kowalski]; no result is in the folder.

d. If true

A net energy source in a H2 cycle would contradict the first law or require an unidentified energy input. Moller proposes none beyond "free energy".

Verdict claim 5

Refuted by calculation for the strong form (net energy from the dissociation-recombination cycle: enthalpy is a state function). Never properly tested for the measured COP: no independent test; the measured numbers contain an internal inconsistency (64% blank against 224% pulsed on the same calorimeter) and an input definition that would produce a COP rising as duty falls.

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6. Claim 6: the two Cornille-Naudin patents

FR 2 789 818 A1 (1999), fast charger

a. Mathematics

• The patent states the textbook result correctly in substance: charging a capacitor from a fixed source through a resistor dissipates half the energy, independent of R (the patent writes "half the charge", loosely) [read: deep/FR s.3]. For N equal voltage steps the loss is (1/2) C V^2 / N, so charging efficiency is N/(N+1): 0.75 at N = 3, 0.90 at N = 9, 0.95 at N = 19 [calc]. This stepwise result is supported on the web by a 2020 paper (not the 1992 AJP article the patent cites, which I could not find) [web: https://staff.najah.edu/en/publications/11442/]. A switched series inductor with a freewheel diode (the Fig. 1 topology) is a step-down converter [memory, high], whose efficiency can exceed 90%, so ">90%" is within what the topology can do.
• The numbers 83 s against 30 s are 2.77 times, not "2.5 times" or "divided by 3", the patent uses both [read: p.8; calc 83/30 = 2.77].
• No energy accounting: no input energy, final stored energy (1/2 C V^2 with C = 1.3 F, V unstated), loss definition, instrument or source. "Entropy" is invoked as the explanation without an equation. The patent claims shorter charging time and lower loss, not overunity.

b-d. Experiment / tested / if true

No independent test. If true, nothing would have to change (this is ordinary power electronics); the examiner's search report cited prior art against claims 1, 2, 4 and 5 [read: p.17]. Applicant is the patentees' company (interested party).

Verdict (FR 2 789 818)

Plausible, untested (consistent with known physics; the figures are the patentees' own; no data). Not an overunity claim.

US 2005/0057116 A1 (priority 2001), "Electrical Power Source"

a. Is the mathematics internally consistent? No, in three places.

1. The energy ledger omits the work. The mechanism is a constant-charge change of capacitance from C1 (plasma on, two glass walls in series) to C2 (plasma off, gap filled with dielectric layers), with beta = C1/C2. At constant charge Q, stored energy goes from E1 = Q^2/(2 C1) to E2 = beta E1 (formula 10). Their efficiency (formula 20) is alpha1 = E2 / (2 E1 + Es), where 2 E1 is the charging input at best and Es is the plasma drive energy. The rise from E1 to beta E1 is booked as "almost free" ([0031]) and left out of the input. For any beta above 2 the formula gives alpha1 above 1 as Es goes to zero (formula 11: gamma = beta/2) [read: deep/US s.5]. That is the mark of a missing term: raising the stored energy at constant charge needs an equal amount of work. In the patent's own mechanical analogue (Fig. 1, [0004]) that work is paid by the person pulling the plates apart and efficiency "cannot exceed 100%". In the plasma version the same work has to be done by something: the screening charge sitting on the plasma sides of the glass (charge equal to Q at each wall) has to be removed against the attraction of the outer-plate charges. That costs (beta - 1) E1, and it can only come from the plasma excitation energy Es, the switch, or an external source. With the work counted, alpha is at most 1.
2. Multi-cycle formulas violate charge conservation. Formula 7 conserves charge, Q = C1 V1 = C2 V2. Formula 22 then sets Q0 = C1 V2, which is beta times the existing charge. If plasma is relit with the supply disconnected ([0065]), charge on the plates is conserved, so the voltage falls back to V1 (C2 V2 / C1 = V1) and the cycle returns to E1: a closed cycle at constant Q exchanges no electrical energy with the circuit (the integral of V dQ is zero). The beta^3 and beta^(2n-1) growth in formulas 25 to 28 needs charge (beta - 1)Q to arrive from nowhere [read: deep/US s.9; checked: agree]. Internal inconsistency.
3. The headline number is an assumption. 338% = 0.175 J / (0.00175 J + 0.050 J) with E1 = 1.75 nF x (1 kV)^2 / 2 = 8.75e-4 J, beta = 200 ("reasonably taken") and a plasma energy Es = 50 W x 1 ms = 0.05 J [calc: 3.38]. Break-even for alpha1 = 1 needs beta = 2 + Es/E1 = 59 [calc]. The patent's own caveat in [0064]: with beta = 10, "the total efficiency may become smaller than one" [calc: 0.17]. And the only measurement (Fig. 8) shows a voltage rise from 500 V to 1750 V, i.e. beta = 3.5 [calc: 1750/500], which is 57 times below the assumed 200 and 17 times below the break-even 59, with no input energy recorded. Using the patent's own formula 20 with beta = 3.5 and Es = 50 mJ: alpha1 = 3.5 x 8.75e-4 / (1.75e-3 + 0.05) = 0.059 [calc]. Even the 500 V figure is not tied to a defined state (the deep read also notes a faster-than-expected leakage before K1 opens). - Three unreconciled accounts of the source of the extra energy: Coulomb work over a few Debye lengths ([0031]), "the surrounding magnetic ether" ([0064]), Earth's potential energy (formula 32: Cp = 700 microfarad and Vp "several millions of volts") [read]. The Earth-ionosphere potential difference is usually given as about 250-300 kV [memory, medium] and not millions. Only one of the three could be right, and none appears in the claims. - Formula 19's 136 Torr was not reproduced by the deep reader (about 34 Torr); I did not redo it and call it unverified.

b. Consistent with experiment?

The Fig. 8 trace (500 to 1750 V on opening K1) is consistent with ordinary variable-capacitor behaviour at constant charge, in which the voltage rises when the capacitance falls and the energy comes from the agent that changed the capacitance. Tests of plasma-switched capacitors as net sources: none in the folder.

c. Tested?

One unpublished trace, no input measurement, no repeats, no dates or names [read: deep/US s.8]. Legal status [read: research/2026-10-09-espacenet-epo-register.md]: assigned to AES, abandoned in 2006 after an unanswered Office action; EP deemed withdrawn in 2008; FR2822590 granted; the company was struck off in 2021. This is an absence to analyse: competing explanations are commercial failure, loss of the applicant's interest after the Office action, or the applicants did not obtain a result they could show. The record I have cannot decide among them; the Office action itself (INPI/USPTO file) would add the examiner's reasoning.

d. If true

Charge conservation and the first law would both have to fail, or the plasma would have to be tapping an energy source for which the patent gives no coupling.

Verdict (US 2005/0057116)

Internally inconsistent (multi-cycle formulas break charge conservation; the single-cycle ledger omits the work of changing the capacitance, giving alpha above 1 for any beta above 2) and Refuted by calculation for the "efficiency above one" claim once the work is included. The one measurement reports no input energy: Never properly tested.

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7. Claim 7: other devices Naudin hosts or replicates

I checked far less here: these are digest-only (no deep read, no page images), and the folder holds Naudin's own pages, so I limit myself to what can be reasoned from the transcribed numbers.

• Steorn Orbo (Naudin's replication). Naudin reports that loading leaves the 400 mA input unchanged and says Larsko's "4.75" is not a COP [digest, facts.json]. The Steorn CEO (Jan 2010) called Naudin's version "in no way a valid replication ... almost certainly not OU" [read: research/2026-10-09-zpenergy.md]. Both are interested parties. Mathematically, an unchanged input current under load is not a statement about power unless voltage and phase are also unchanged. I cannot check more.
• Bedini G-field generator ("120% or better"), Mini-Romag (24 W self-sustaining, no data), 2SGen, KAPAGEN (up to 2100 W, input not given), GEGENE ("great efficiency"), Meyer-type water fuel cells, Hendershot (Epps). Each is a claim with either no data in the folder or no input measurement. KAPAGEN: a claim of 2100 W of lamp light with the input not given cannot be evaluated at all [read: digest]. Naudin's own 1999 note says the Bedini Magnetic Gate shows no overunity in a closed loop [read: facts.json]; that statement from the host is a counter-example to the general claim and I keep it. "Regauging" and "taking electrons from the Earth" are interpretations without equations in the pages I saw.
• Epps on Hendershot. Epps's "non-reciprocal" argument did not hold at higher voltage in a test with Naudin [read: digest]. Reported, not verified.

Verdict claim 7

Never properly tested for the measured claims (no input measurement, no neutral test, closed-loop failures reported by Naudin himself for the Bedini gate); Not testable as stated for the "regauging"/"Earth electrons" explanations. A hosting page is not a replication: the individual verdicts depend on documents not read in depth.

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8. Summary table

9. What would settle the open items

• MEG: calorimetry of the load against measured mean input power with a calibrated power analyser (or sample-by-sample mean(v i) with deskew), then a closed loop with a start battery. A resistive-load run (linear, no "conditioning") is the control.
• MAHG: the scope files for the 5% duty runs, with a true v(t) x i(t) mean on the same record, and the pure-DC blank at the same average power.
• CFR: repeat EarthTech's accounting with an enclosed vessel capturing steam and droplets (condensing the vapour and weighing it), and a plasma-mode calibration.
• Lifter vacuum: a thrust stand with shielded leads, run with the electrodes swapped and the test body replaced by a dummy of the same capacitance; the Gravitec/NSSTC raw data and the Brown laboratory notes (Paris, Bahnson, GE) are the records named but not obtained.
• Patent US 2005/0057116: the Office action text and the measured input energy for a Fig. 8-type run.

10. Investigator's findings I kept and how they weighed in

CFR calibration, low/medium run numbers and Naudin's incandescence condition (used in section 4); MAHG run conditions, blank and supply change (section 5); magnetic amplifier test with "NO Overunity" (section 3); patent legal history (section 6); EarthTech replication (section 4, central); Kowalski/Little/Luce ICCF-12 (section 4); Mizuno 2004 on rarity of replication (section 4); NASA/ISR, MSFC, Tajmar and Schreiber 2020 (+/-0.3 mg to 10 kV, not read by me beyond the Investigator's note), Exodus Propulsion patent (interested-party vacuum claims; not read by me), Porcelli and dos Santos Filho IET 2016 (dipole account; not read by me); Bishop and Smith (section 3); Flickinger's varistor remark (section 3); Bearden's later claims of COP 7.3 and a DoD-linked replication (section 3, not found); AES company record (struck off 2021; section 6). Items marked "not read by me" were kept in the record and not weighed beyond the Investigator's description.

Web checks this pass: one search (stepwise capacitor charging; the 1992 AJP article could not be found, a 2020 paper confirms the N-step result). The other medium-confidence [memory] items (Earth-ionosphere potential, EHD thrust formula being standard, THS720P being a handheld) I left tagged [memory]; none of the verdicts turns on them.