Gunderson: Mathematician's review (Step 2)

Reviewer: PhD mathematician role. Scope: derivations, notation, units, hidden assumptions, energy bookkeeping. Sources read myself [read]: US 2006/0163971 A1 paras 0036-0044 (extracted text); US 8,093,869 B1 text of the "mechanism" passages: mutual opposition (lines ~735-755), harmonic power (~975-985), the 90+180+90 phase argument (~2005-2100), the transformer analogy (~2330-2365). Also facts.json, claims.md, both deep reads, sites.md "Leads for review" and the research notes (energeticforum, google-patents). I did not re-render the patent figures; geometry statements below rest on the deep reads of the text. Own calculations: a short NumPy script run during this review (lumped electromechanical model, Fourier check, sensitivity estimates). Numbers are reproduced inline so they can be rerun by hand.

Source note: both patents are the applicants' (Magnetic Power Inc., then Chava) own characterisation. Neither contains a measurement, a prototype description, or a power-in versus power-out budget [read]. Everything quantitative below about the devices' performance comes from the Investigator's web finds (forum posts), which I weigh in the sections that follow.

Ideas you need first (short, for the reader)

• Lenz's law: an induced current makes a magnetic field that opposes the change that caused it. Energy reading: the electrical power taken out is paid for by extra opposition (drag) felt by whatever drives the change.
• Impedance (Z): for a sinusoidal signal, Z = voltage/current as a complex number. Its real part is a "resistance" that dissipates or transfers power; its imaginary part is "reactance" that stores and returns it. Average power is (1/2) Re(Z) |I|^2.
• Two-port, reciprocal: a box with an input pair and an output pair of terminals, built only from passive reciprocal parts (coupled coils, resistors, ordinary magnetostrictive or piezoelectric transducers). Such a box can never deliver more average power at its output than it receives at its input.
• Parseval's theorem: for a sum of sinusoids of different frequencies, the average of the square equals the sum of the squares of the individual amplitudes (halved). Cross terms average to zero.

Verdict summary

Claim 1: "Virtual motion" of magnet flux (US 2006/0163971, paras 0014-0034)

a. Internal consistency. The document has no equations [read: deep read pp.1-10]. In circuit terms the claim says: the flux Phi linking each loop of the output wire changes with time because a coil modulates the magnetisation (and therefore the permeability) of a soft core while a permanent magnet supplies a bias flux. Faraday's law, EMF = -dPhi/dt, then gives an output voltage. That is self-consistent and is the principle of the fluxgate and the variable-reluctance (parametric) generator. The phrase "virtual motion" (flux appearing to move like the sun seen through agitated water) is a metaphor for a time-varying flux pattern; it adds no testable content beyond Faraday. Nothing is wrong, nothing is quantified. Unit issues: none, because no quantities appear.

b. Consistency with experiment. Modulating a bias flux to induce EMF with no moving parts is well established (magnetic amplifiers, fluxgates, variable-permeability devices) [memory, high]. The patent examiner cited relevant prior art (Sony US4103197, Magnetics Research US4639626, and others) [web: https://patents.google.com/patent/US7830065B2/en, via Investigator]. Whether the specific holed-core geometry gives a useful output is not shown.

c. Tested? No data in either the 2006 publication or the grant. The only experimental sentence is [0040]. Investigator: the 2006 text became US 7,830,065 B2 (granted 9 Nov 2010) with a resonant circuit and square-wave source added to claim 1, and an 11th claim reciting the geometry "improves the efficiency"; it lapsed for non-payment of the 12th-year fee in 2022 [web]. So the geometry was claimed with a resonant drive and was patented, which says the office accepted it as a structure, not that it was shown to work.

d. If true. Nothing in mainstream physics changes for the weak form.

Verdict. Weak form: Established in principle. Strong form (a specific output level from this device): Never properly tested; no neutral test on record and no claim of one in the documents.

Claim 2: Lenz "aiding", falling input, magnets as the energy source (paras 0036-0044)

Key text [read]: [0039] the induced flux "is directed to oppose the permanent magnets ... not the input flux source"; [0040] magnets are "the source of motive pressure ... 'pushed against' ... for very long periods of time, before becoming demagnetized or 'spent'"; [0043] on the non-magnet side of each hole "induced magnetic flux (c) aids the input flux (a). This is the reverse of typical generator action"; [0044] the device "will display an absence of electrical loading at the input and/or an overall amplification of the input signal. This ultimately causes less input energy to be required".

a. Internal consistency. Three problems.

1. Energy source stated inconsistently. [0036] says the device "does not require consumption of natural resources"; [0040] says the magnets are consumed ("spent", "demagnetized"). The grant deleted the "no consumption" and "persists until the magnets are no longer magnetized" wording but kept [0044] and [0040] [web: google-patents note]. In 2018 the inventor's own site names ambient energy as the source ("force ... taken from the ambient energy") [web, Investigator: Wayback grahamgunderson.com/ou]. Three different stated energy sources over twelve years (magnets, none, ambient) is a flag; the point to put to the reader is that the energy source has not been pinned down by the inventor.
2. Hole geometry. The field of a current in a wire passing through a hole circulates around the wire (Ampere's law). In the core material on the two sides of the hole the circulating flux points in opposite tangential directions. So if the reaction flux (c) adds to a unidirectional input flux (a) on one side of the hole, it subtracts from it on the other. The text assigns "aiding" to the non-magnet side and "cancelling" to the magnet side. I could not check this against the figures beyond the deep read; as written, the count of "aiding" versus "opposing" regions is not shown to net out to aiding, and no integral of the energy exchange is given.
3. Cancellation is not a free resource. Where reaction flux annihilates the magnet's flux ([0043]), a reduction of a static bias flux is a real change of stored magnetic energy that must be paid for by something (see b below).

Why the energy claim fails (calculation). Let the drive be any sinusoidal source and treat the device as a two-port made of passive, reciprocal parts: input coil, output coil, a core, and a resistive load R_L. The permanent magnet contributes a static bias (it sets the operating point on the B-H curve) but, in steady cycling, no net energy. For such a network, average input power >= average output power + losses, always. The standard result: the impedance seen at the input is Z_in = Z_11 - Z_12^2/(Z_22 + Z_L). Loading the output changes Z_in, so the current drawn and the phase change; in a resonant input circuit a load can move the operating point so that the drawn real power at the source changes. But real power into the box is still at least the real power into the load.

Parametric exception, stated fairly. If the core's permeability is varied in time (the "pump"), a time-varying inductor can amplify a signal. The Manley-Rowe relations (standard result for parametric devices [memory, high]) say the extra power comes from the pump source, not from the static bias. Here the input coil modulating the core is that pump. So "amplification of the input signal" can happen in the sense of signal gain, but the energy then comes from the pump coil's supply, and the pump power is part of the input. A static magnet is not a pump.

Magnet energy budget. The most energy a sintered NdFeB magnet can store per unit volume is of order (BH)max ~ 400 kJ/m^3 [memory, high; roughly 50 MGOe grade]. A 10 cm^3 magnet is 4 J at the very most, and only a fraction is recoverable without moving the magnet. A 10 W output would exhaust 4 J in 0.4 s. Over "very long periods" (para 0040) at watts, either the magnets are not the source or the output is tiny. The document gives no number to test this. This is a rough bound, not a precise result.

b. Consistency with experiment. No known device shows sustained net output with falling input at constant conditions. Strong form conflicts with energy conservation and the passive-network inequality above.

c. Tested? The Investigator found the following, which I keep in the record and weigh. - Interested-party claims: MPI's "POWERGENIE" report (24 Apr 2008) says "reaction-less behavior ... soundly demonstrated"; Chava's site, quoted on rexresearch, says an early prototype gave "more than 100 times the input" at "very low power level"; no data in either [web, Investigator]. - ESTC 2016 "Magnetic Implosion Transformer" (a later, different device: an H-bridge, step-up transformer, two dissimilar ferrite C-cores with about 20 manganese-ferrite magnets, around 50 kHz). Gunderson says a lamp drew "570% more energy than could be accounted for". One engineer-witness, Mark McKay PE, a friend of about 10 years, reports two power analyzers and a scope agreeing at 1.53 W in and 9.43 W out (COP 6.16), and that an hour later input read 0 W with output 9.5 W; Gunderson reportedly saw input go to about -0.25 W [web: energeticforum thread 13945]. A second attendee ("Reiyuki") reports the demo at about 3.5 W in and 8.5 W out, with COP strongly dependent on the phase of the output interruption, and a recalled table in which 140 degrees gave -1 W in and 3 W out [web, same thread]. He also quotes Gunderson: "he doesn't know why it works". The 2015 device was reported at COP ~1.02-1.03 [web]. - No independent replication was found as of the Oct 2016 posts the Investigator read (pages 1 and 5 of the thread; pages 2-4 not read).

This is documented eyewitness instrument reporting from one named engineer, supported in outline by a second attendee. It is evidence and I do not dismiss it. It is also second-hand, reports readings rather than raw waveforms, and concerns a different circuit from the 2006 patent (the patent itself has no data).

Mathematical caution about the measurement (not an accusation of error). Real power with a sinusoid is P = V I cos(phi). When the drive circuit is resonant, the apparent power S = V I can be hundreds of volt-amperes while P is a watt or two, because phi is near 90 degrees. The error in P from a phase error d (radians) is about S sin(phi) d. For illustration (I have no actual V and I; these are assumed values): at S = 500 VA, a phase error of only 0.18 degrees gives 1.53 W. At S = 100 VA the same error needs 0.88 degrees. Reported operating conditions (200-300 V resonant bridge; 1-2 kV spikes on a synchronously-rectified output; 20-50 kHz) are the kind where probe and analyzer phase skew matters, and a COP that "depends on the phase" is what a phase artefact would also produce. A negative input power on a battery-fed bridge, if real and averaged correctly, means the battery is being charged. That is directly checkable with a coulomb counter (integrated amp-hours) without any phase measurement. A 12.7 Ah, 12 V battery stores about 550 kJ; a one-hour 9.4 W output is 34 kJ, 6% of that, so a battery-fed hour cannot by itself distinguish a free source from a stored one unless charge is counted. McKay himself says the system could be "looped" to run itself if the readings are right; that test was not done in the account.

d. If true. Energy conservation would need a new reservoir, or the passive-reciprocal bound would fail because some element is not passive. It would also contradict the usual sign convention in electromagnetism that induced currents oppose their cause.

Verdict. Strong form (output exceeds all inputs, magnets or ambient as source): Refuted by calculation (energy and passive-network bound; the numbers above). The instrument reports of COP above 1 with a different later device: Never properly tested (no neutral, controlled test; not dismissed, but no independent party has tested; one witness plus the inventor). Weak form (the input can show little real-power loading at some tuning): Plausible, untested; it is what a resonant, phase-tunable circuit does with reactive power.

Claim 3: 90 + 180 + 90 = 360 degrees (US 8,093,869, pp.13, 19-20)

Text [read, lines ~2020-2100]: the strain node is a quarter wavelength from the source, so the wave there lags 90 degrees; the coil's reaction wave is "180 degrees out of phase" (Lenz opposition), giving 270 degrees; it travels back a quarter wavelength (another 90 degrees), arriving at 360, "mathematically equal to ... 0 degrees". Hence "constructive wave interference", the source is "aided" and "may be maintained with less acceleration input ... since some of the accelerating activity is now self-produced".

a. Internal consistency. - Arithmetic: correct. 5000/125,000 = 4 cm wavelength, a quarter is 1 cm = 90 degrees; the 600 m EM comparison (c/f = 2398 m, quarter = 600 m) is also correct [read: p.11; deep read check]. - The 180 degree step is assumed. The patent itself concedes that the current phase depends on "inductance and tuning capacitor" (deep read). For a coil with resistive load, the current follows the EMF, which is the derivative of the flux, so it leads the flux by 90 degrees, not 180. With inductive reactance it lags that EMF. So the phase of the reaction relative to the incoming wave is a circuit-dependent number the patent does not compute, and it sets "aid" versus "oppose" by choice of tuning. The statement is not self-contained. - Phase is not the same as energy flow. "In phase with the acceleration" is used to mean "does positive work on the source". Energy flux in an elastic wave is force times velocity. A reaction wave arriving in phase with the source's force adds velocity in phase with force, and the source then does more work (P = F v), exactly as pushing a swing in time with it builds amplitude. Whether the returning wave gives energy back to the source requires its force to be in phase with the source's velocity, and this is not what the 360-degree argument establishes. The patent's step from "constructive interference" to "less input needed" is therefore a non sequitur as written. - Equivalent description. A wave sent into the load region that returns with reversed sign is an ordinary reflection with a negative reflection coefficient, of magnitude below 1. The returned energy is that fraction of what was sent minus what the coil took out. It cannot exceed the incident energy.

Calculation (lumped model, my own). To see the energy bookkeeping without a wave simulation, take one resonant mass-spring oscillator (m = 1 g, k = 10^6 N/m, resonance 5.03 kHz, mechanical loss c_m = 0.05 N s/m) driven by a force of amplitude 1 N, with a coil: EMF = Gamma v, coil current i = EMF/(R + j w L), back force on the mass = Gamma i opposing the motion (Lenz; Gamma = 2 V s/m, L = 1 mH). The load adds to the source's mechanical impedance the term Z_e = Gamma^2/(R + j w L), with real part Gamma^2 R/(R^2 + w^2 L^2), which is positive for every R and L. Results at resonance (W, average):

Two lessons. (i) At fixed force the input power falls as the load is added, from 10 W to 5.7 W, because the extra damping reduces the motion at resonance, and the load power is always less than the input. A statement like "less input is needed as more output is drawn" can be true in this limited sense without any gain: here the output (2.4 W) is below the input (5.7 W). Input drops, but efficiency (load/input) is only 42%. (ii) If instead the reaction sign is reversed ("Lenz aiding": Re Z_e negative, an unphysical sign for a passive coil), the same model at R = 100 gives 21.4 W in, 57.1 W into the load and 78.6 W lost mechanically: 135.7 W out for 21.4 W in. That is what aiding actually means mathematically: negative resistance, an active element that creates energy. A coil connected to a resistor is passive; the positive-real-part result is forced by the energy conservation of a lossless reciprocal transducer. The patent offers no mechanism for the sign change.

A distributed (wave) model was not computed; the energy bound (reflection coefficient magnitude below 1) already covers it.

b. Experiment. Magnetostrictive and piezoelectric transducers are standard and always show loading by the electrical side [memory, high]. The family of magnetostrictive harvesters that cite this patent (US DOE US9960341B1, Oscilla Power, Tokai Rubber, Mitsumi) [web, Investigator] use the transduction, not the "self-produced" energy claim.

c. Tested? No data in the patent. The Investigator found no tests or replications. Interested-party Chava statements about prototypes exist (claim 2 above) with no figures.

d. If true. A passive coil on a magnetostrictive rod would act as a net energy source; reciprocity or passivity of electromechanical transducers would fail.

Verdict. Split. The phase arithmetic: correct. The 180 degree step: Internally inconsistent (the patent itself makes the phase depend on the circuit). The conclusion "reaction aids the drive so less drive energy is needed" as an energy gain: Refuted by calculation. A limited, conventional version (loading changes the drive power needed at fixed force while output stays below input): Established.

Claim 4: Opposed currents in neighbouring coils (pp.12, 21)

Text [read]: at a second-harmonic resonance two neighbouring coils carry opposite currents; this "adds to the total amount of magnetic opposition ... Because electric power is generated via magnetic opposition, this additional magnetic opposition increases the total electrical energy delivered"; and, by analogy with a loaded transformer, "an electrical load drawing an increasing amount of electrical energy ... causes an automatic increase in the electrical power delivered simultaneously by conductive turn 502-503".

a. Internal consistency. Two separate statements. - Reactance cancellation. If two coils on the same core carry opposing currents, their mutual inductance enters with the opposite sign: L_total = L_1 + L_2 - 2M. A smaller inductive reactance means less of the EMF is dropped across the machine's own inductance, so more current and power reach the load for the same EMF. This is a correct, modest circuit effect (the same reason bifilar windings have low inductance). It does not create energy; it improves matching. - "More opposition means more energy." Power is EMF times current. The EMF is set by the strain amplitude in the rod. More electromagnetic opposition means more mechanical drag on the vibration, which the drive must overcome. In a conventional transformer the same thing happens: when the secondary is loaded, the primary draws more current, so the input rises with the output. The patent quotes that exact transformer behaviour as support, but a rise in primary current is a rise in input, the opposite of "less input". The text never says where the extra delivered energy comes from.

b. Experiment. Opposing-sense coil pairs and mutual-inductance effects are standard [memory, high]; no experiment on this device is given.

c. Tested? No.

d. If true. As a net-gain statement, again a violation of passivity; as written it does not claim input falls here, so it can be read conventionally.

Verdict. Reactance cancellation: Plausible, untested (no measured improvement given; effect is mathematically sound and small). "More energy delivered through added opposition" as a net gain: Refuted by calculation. As the bare sentence stands, with no input-versus-output accounting: Not testable as stated.

Claim 5: Square wave, "power is the square of the sum" (pp.13, 21-22)

Text [read]: "The instantaneous electrical power developed in this manner is the square of the sum of the energy induced by each acoustic frequency", with the peaks of odd harmonics coinciding at the central node.

a. Internal consistency. Instantaneous power in a resistor is i(t)^2 R, and with i(t) a sum of harmonics, i^2 is the square of the sum at each instant: true. The error is in what is concluded from it. Power that matters for energy is the average over a cycle. For harmonics of different frequencies the cross terms average to zero (Parseval), so the average is the sum of the squares, not the square of the sum.

Check with an ideal square wave of unit amplitude: its fundamental has amplitude 4/pi = 1.273, with mean square 0.8106; adding odd harmonics (amplitudes 4/(pi n)) raises the mean square to 0.9006 (up to n = 3), 0.9496 (n = 7), 0.9798 (n = 19), 0.998 (n = 199), tending to exactly 1, the mean square of the square wave itself. The harmonics therefore add about 23% to the average power relative to the fundamental alone. The peak of the instantaneous square (the sum of the series) reaches 1.39 (Gibbs overshoot of about 18% in amplitude, squared) while the mean stays at 1. Peaks that coincide give a spiky waveform but not more energy.

Also, that 23% is paid for in the drive: a square-wave source of the same peak voltage delivers that same additional power. No comparison against the input is made.

b. Experiment. Harmonic content of a square wave and the properties of the odd modes of a free-free bar (strain maximum at the centre for odd modes, zero for even ones) are standard [memory, high], and the patent's central-node geometry is consistent with that.

c. Tested? No data.

d. If true. Parseval's theorem would fail; not credible.

Verdict. Instantaneous-peak statement: true but not about energy. Average-power gain "substantially increased" beyond the input: Refuted by calculation. Conventional version (a square drive carries more power than a sine of the same fundamental, and a resonator responds at its harmonics): Established.

Claim 6: Source-to-pickup spacing of at least 1/8 (preferably 1/4) wavelength (claim 1; pp.10-14)

a. Internal consistency. Consistent. 1/8 wavelength is 45 degrees, 1/4 is 90 degrees; the coil sits at a strain maximum of the standing wave. Claim 1 ends with a load of "nonlinear time-changing resistance" using semiconductor switches, which the description does not define (deep read). A resistance that changes in time and with current is not a single quantity and cannot be assessed mathematically from the text; it is also not linked to any gain. OCR confusion over "1/8" and "1/4" was resolved from page images in the deep read [read: page images pp.12, 13, 14]; I accept those readings.

b. Experiment. Magnetostrictive rods driven at one end with a coil placed away from the end are standard in sonar and harvester work; the 12 prior citations go back to the 1930s-50s [web, Investigator]. The distinction from "vibration harvesters" (which are driven by environmental vibration) is a statement about structure and priority, not physics.

c. Tested? No data. Cited by later harvesters [web].

d. If true. Nothing changes.

Verdict. Power transduction by such a structure: Established. The claim that this spacing or separation yields extra energy (as opposed to being just geometry): Plausible, untested. The granted claims recite no over-unity result [read; Investigator confirms for the sibling patent].

Investigator's findings: how they bear, retained in the record

• Grant of the 2006 application as US 7,830,065 B2 (9 Nov 2010), later lapsed (12th-year fee unpaid, effective 9 Nov 2022); the office classed it under H02K53/00 "Alleged dynamo-electric perpetua mobilia" (the classification label is the office's characterisation) yet granted structural claims [web: https://patents.google.com/patent/US7830065B2/en]. The grant softened "does not require consumption of natural resources" to "believed to" and removed "persists until the magnets are no longer magnetized" and "reduction of required input power as loads are applied", while keeping [0040] and [0044]. This bears on claim 2: the applicants' own wording of the energy claim was narrowed during prosecution, though the central sentence stayed.
• US 8,093,869 is active, with fees paid late in 2019; adjusted expiry 2029 [web]. Cited by mainstream magnetostrictive harvesting work [web].
• Later inventor material: ESTC 2015 "Overunity Disclosure" (reported COP ~1.02-1.03), ESTC 2016 "Magnetic Implosion Transformer", 2018 grahamgunderson.com/ou, which names Floyd Sweet's Vacuum Triode Amplifier (VTA) and conditioned barium ferrite as roots [web]. These are the inventor's own description of later, different devices; I treat them as such.
• Witness accounts (McKay, Reiyuki): weighed under claim 2, with a testable closing experiment below.
• Related work (MEG US 6,362,718, E.V. Gray, TK/Kapanadze circuits, Tae Chang N.E.T. sound-wave resonance generator, filed 3 Dec 2008, the day of Gunderson's non-provisional): noted. The mathematics above applies equally to each in its own terms; I have not analysed them.
• Absence of evidence. Chava announced further prototypes, a "very broad" patent application and 30 patents in 3 years; none appear (no later family under Gunderson or Chava; provisional of July 2016 reportedly filed; no published follow-up) [web, Investigator]. A mathematician cannot decide between the Investigator's competing explanations (failed validation, lapsed filings for cost, trade secrecy, funding loss, suppression). One mathematical observation only: the reported later claims have precisely the measurement structure (reactive power, phase-sensitive) in which a real effect and an instrument artefact are hard to tell apart, so the absence of a follow-up with calorimetry or charge counting leaves the question open rather than answered. USPTO file wrappers and Chava corporate filings would help decide.
• An anonymous critic ("Physics Review Board") calls Chava's MagGen solicitations fraud [web via Investigator]. That is a critic's characterisation; no court finding found. I do not rely on it.

What would settle the main disagreement

1. Energy accounting on one device. Run the device from a battery. Count charge with an integrating coulomb counter (not instantaneous power) and the load heat with calorimetry, for hours, then do the same with the magnets removed or replaced by non-magnetic spacers. If net battery charge is gained, or the load heat exceeds the integrated input by more than the measurement uncertainty, the passive-network bound is violated and the claim is supported.
2. Closed loop. Feed the output back to the input source and remove the battery (the "loop" McKay mentions). Sustained operation is a decisive signal.
3. Phase artefact check. Measure the same quantities with a method independent of phase: a DC input with a charge counter, and a shunt-based, bandwidth-checked output measurement.
4. For the acoustic patent: measure acoustic power into the rod and electrical power out with a calibrated force sensor (or a second identical transducer as a load), at several load resistances.

Corrections to Step 1

1. facts.json says it is not stated whether the 2006 application was granted. Investigator found it was granted as US 7,830,065 B2 (9 Nov 2010) with 11 claims (not 10), claim 1 amended to require a resonant circuit with a square-wave source, and a new claim 11 that recites "improves the efficiency"; lapsed 2022 [web]. facts.json also says no claim recites a gain; that holds for the published 10 claims and for 8,093,869 [read], but the granted 7,830,065 claim 11 uses "improves the efficiency" (an efficiency claim, not a stated over-unity result).
2. facts.json (key claim 3 and mainstream_conflict) correctly says the 180 degree step is asserted; I add that the patent itself ties the current phase to inductance and tuning capacitance, so the step is circuit dependent and not a fixed 180 degrees.
3. claims.md claim 5 reads as if the "square of the sum" were the power result; the patent's sentence is about instantaneous power. Averaged power obeys Parseval, so the claim is not a power result as written.
4. claims.md claim 2 says the input shows "no loading or an amplified signal" without noting the contradiction between [0036] ("no consumption of natural resources") and [0040] (magnets "spent"); worth stating.
5. The arithmetic in the deep read (5000/c = 0.00167%, quarter wavelength 1 cm and 599.6 m) is correct; the percentage in facts is rounded to 0.0016%. No change needed.
6. The deep read does not count the intermediate 270 degrees; the patent does (node lag 90 + Lenz 180). Not an error in Step 1, only for clarity.

Source and confidence notes

• [read]: all quotations from the two patents above, from extracted text; page images were not re-rendered by me.
• [web]: Investigator items, with their URLs as given in sites.md and the research notes; I did not independently re-fetch them (web-check budget not used). The facts I rely on from [memory] (Faraday/Lenz phase relations, Parseval, Manley-Rowe, bias magnet energy product ~400 kJ/m^3, free-free bar mode shapes) are all textbook and high confidence, so no verdict depends on a medium/low [memory] fact.
• Illustrative numbers (S = 500 VA, lumped model parameters) are my assumptions, labelled as such; they show sensitivity, not what was measured.