TernionAG: Mathematician review (Step 2)

Role: PhD mathematician. I check derivations, notation, units and hidden assumptions. Inputs: claims.md, facts.json, all of deep/, selected digests. Tags: [read] from a document (via the deep reads, which cite pages), [calc] my own arithmetic (Python/numpy/mpmath in the project venv, this session), [memory] recalled with confidence, [web] none (see "Web verification").

Source gap (repeated from claims.md): every Kassner/Ternion scientific claim rests on the patentee's own text. No lab notebook, test report, replication or independent record exists in the folders. The mathematics I can check is therefore the patentee's own theory and numbers, plus the essay's and Morray-TH's thermodynamic arguments. Conclusions about biology, preservation and colloids rest on the patents' assertions and on [memory].

Web verification: the web search budget for this session was exhausted, so every web check failed (two attempts, no results). No verdict below depends on a medium- or low-confidence [memory] item except where stated; the load-bearing facts are textbook values (DeltaG, DeltaH, Bessel zeros, Debye form) that I recomputed or that are high-confidence. Retry later: Debye tau for water (8.3 ps), the typical electret charge densities, Barkhausen-Kurz tuning law.

Preliminaries the reader needs (used throughout)

• Wavelength lambda and frequency f: f = c/lambda, c = 3.0e8 m/s. 18.6 cm = 1.61 GHz; 90 cm = 333 MHz.
• A disc resonator: two parallel round metal plates of radius R, gap d much smaller than R. The electric field between them, E(r,t) = A J0(kr) cos(wt), with J0 a Bessel function (the round-drum analogue of sine). The edge condition fixes allowed k: x = kR is a zero of J0 (edge "shorted") or of dJ0/dr = -J1 (edge "open"). Then lambda = 2 pi R sqrt(eps) / x, where eps = relative permittivity of the gap filling. Notice the gap d does not appear: that is the key fact used below.
• Zeros [calc, mpmath]: J0: 2.405, 5.520, 8.654; J1: 3.832, 7.016; first zeros of dJ_n/dx: n=1 1.841, n=2 3.054, n=3 4.201, n=4 5.318; second zero for n=2: 6.706.
• Debye relaxation: complex permittivity eps*(w) = eps_inf + (eps_s - eps_inf)/(1 + i w tau), tau = relaxation time. The loss part eps'' = d_eps * x/(1+x^2), x = w tau, peaks at x = 1. Its full width at half height spans x = 2-sqrt3 to 2+sqrt3, a frequency ratio of 13.9 [calc], so Q = f0/delta_f is about 0.29. Debye loss is one very broad hump, not a sharp line.
• Thermodynamic state functions: DeltaG = 237.1 kJ/mol and DeltaH = 285.8 kJ/mol for liquid water from H2 + 1/2 O2 at 25 C [memory, high]; DeltaG/(2F) = 1.229 V, DeltaH/(2F) = 1.481 V [calc, F = 96,485 C/mol]; T DeltaS = 48.7 kJ/mol [calc].

Claim-by-claim review (numbering follows claims.md)

Claim 1: dipolar substances have sharp natural frequencies (infra-red to metres) coinciding with anomalous dispersion bands; electrolyte bands ~2% wide, serum ~90 cm (<5%), water 1.28-1.5 cm

a. Internal consistency. The patents define two kinds of anomalous dispersion: "friction" (Debye) and "resonance" in electrolytes [read: US2089966 p.5, page image]. The numbers are self-consistent but the physics is mixed. Water's 1.5 cm is the Debye loss hump: tau = 8.3 ps gives f = 1/(2 pi tau) = 19.2 GHz, lambda = 1.56 cm [calc; tau value memory, high]. That agrees with Kassner's 1.5 cm. But a Debye hump has relative width delta_lambda/lambda of order 1-3 (Q ~ 0.3), whereas the patent's resonance band is delta_lambda/lambda = 2/100 (Q = 50): about 170 times narrower [calc]. So "water at 1.28-1.5 cm" and "bands 2% wide" cannot describe the same kind of feature, and the patent says as much (they are separate types). The step 1 observation that the patent gives no spectrum stands: there is no curve from which a width could be read. Also the notation: the 2/100 formula was OCR-garbled and was verified from a page image [read: US2089966 p.5], and "frequently scarcely wider than" is a hedge, not a fixed width. Serum "half-widths less than 5%" means Q > 20 [calc: 1/0.05]. b. Established results. Water's Debye relaxation near 20 GHz and tissue/serum dispersion (beta dispersion at tens of MHz, delta/gamma near GHz) are established [memory, high for water, medium for tissue]. A sharp (Q ~ 20-50) resonance in an ionic solution at 333 MHz is not known; electrolyte conductivity gives a smooth, broad dispersion [memory, medium]. Not checked on the web (budget gone). c. Tested. Detection reported only as "lightening of a beam in crossed Nicols" [read: US2089966 p.8]; no spectrum, no named lab, no replication in the folders. Never properly tested in the record I have. d. If true: a resonant (not relaxational) absorption mechanism in aqueous electrolytes at 10^8-10^9 Hz with Q of tens would have to exist, which dielectric spectroscopy of electrolytes and tissues would long since have shown.

Verdict: Never properly tested (the quantitative claim); the water 1.5 cm part is Established but it is the textbook Debye hump, not new. Split.

Claim 2: a field at the natural frequency alters "energy content" beyond heat by orienting molecules (double refraction); freezing in orientation gives an electret "richer in energy" that re-radiates on thawing (surface charge 0.5-2.0e-9 C/cm^2)

a. Consistency. Units: the charge density printed 10^-9 C/cm^2 (a "-8" in OCR was a misread; checked on page image [read: deep Process-...480e58 section 1b]). Scale [calc]: 2e-9 C/cm^2 = 2e-5 C/m^2; field at the surface sigma/(2 eps0) = 1.13e6 V/m; stored electrostatic energy per area for a 1 mm slab with eps_r = 2.5 is sigma^2 t/(2 eps0 eps_r) = 9.0e-3 J/m^2 = 0.9 microjoule per cm^2. So the "extra energy" that could be stored in the electret is of the order of a microjoule per cm^2: real, but small, and purely electrostatic. "Re-radiating at the same wavelength on thawing" has no quantity attached and no mechanism: an electret relaxes by charge and dipole decay, a thermally activated process that emits no narrow line. The definition "energy content change that is not merely a temperature change" is not a defined state function, so the claim is not stated precisely enough to check algebraically. Electrets were known (the patent concedes this). b. Consistency with experiment: electret formation by cooling in a field and measured surface charges are established [memory, high]; the magnitude is plausible (typical wax electrets 1e-9 to 1e-8 C/cm^2, memory, low; not web-checked). A resonant (frequency-selective) role in the orientation is the new part and is untested. c. No energy measurement, no control without field at the same temperature, no replication. d. Nothing in mainstream physics would need to change for the electret part; the resonant-orientation part would require a sharp dipolar resonance (Claim 1).

Verdict: electret formation Established; "energy content / re-radiation at the same wavelength" Not testable as stated (no defined quantity) and in any quantitative form Never properly tested.

Claim 3: practical effects: preservation (milk 28 days, veal 2 weeks, apple juice 4 months), colloid changes, catalyst-free vulcanisation/Bakelite/polymerisation, beans "twice as much", effects "in men and animals"

a. Consistency. Nothing to derive: there are no equations. The numbers (days of keeping, "twice") come without sample sizes, controls, temperatures during exposure, or spoilage criteria [read: deep US2089966]. Statistically a single trial per substance cannot support "twice". Powers 0.1-250 W are stated but not the energy absorbed per kilogram; the heating must be calculated before off-resonance controls mean anything: 250 W into 1 kg of water raises it 0.06 K/s [calc, c = 4186 J/(kg K)], i.e. 3.6 K per minute. Thermal pasteurisation, which is the null explanation, would therefore be expected at the high powers. A per-photon energy argument: an 18.6 cm photon carries 6.7e-6 eV, about 3,900 times below kT at 300 K (0.64 J/mol vs 463 kJ/mol for an O-H bond: ratio 7.2e5) [calc]. So a single photon cannot break or make any bond; any effect is collective (orientation, heating, field-driven chemistry). That does not rule out an effect; it rules out the "one photon, one bond" picture. b. Known results: microwave/RF sterilisation by heating, and microwave-assisted polymerisation and vulcanisation are established, and the 1945 Goodrich/Firestone purchase of electronic-vulcanisation patents fits that [read]. A non-thermal, frequency-specific effect is not established (the non-thermal microwave literature is contested; web check failed). c. Tested by the patentee only; no independent controlled test in the record. d. Non-thermal frequency-specific biological preservation at sub-watt-per-gram power would require a coupling mechanism that avoids thermal averaging.

Verdict: split. Heating-driven preservation/vulcanisation: Established. Frequency-specific non-thermal effects, and "men and animals" effects: Never properly tested (no control data in the record; I cannot say whether it was dismissed without testing, no source).

Claim 4: a plate pair is a tunable sharp resonator following Bessel-zero theory (10 cm radius disc at 26.2 cm); the 1932 tuning figures disagree with it

a. This is where my arithmetic is strongest. GB483062's theory is correct textbook radial-line cavity theory, and I confirm its numbers [calc]: - Worked example: R = 20 cm, T = 1.09 ns gives lambda = 32.67 cm, x = 2 pi R/lambda = 3.846, against 3.832 (first zero of J1) within 0.4%. J0(3.832) = -0.4028, J1 = ~0 [calc]. - Energy equation (12): U = (pi eps0/2) V0^2 (R^2/d) [J0^2 + J1^2] gives 9.02 microjoule for V0 = 1 kV, R = 20 cm, d = 1 cm [calc, matches the deep read]. delta = 0.3 means Q = pi/delta = 10.5; N = 2 delta U/T = 4.97 kW [calc]. The prefactor 1/(8 x 9e11) = 1.39e-13 equals pi eps0/2 per cm in his Gaussian-era units: correct. - Series formula (11): eps_res = d / sum(d_n/eps_n). Correct for a field normal to layers. Nomogram example: lambda = 10 cm, R = 8 cm, J0(x02) with x02 = 8.654 needs eps_res = (10 x 8.654/(2 pi 8))^2 = 2.96, "about 3" [calc]. Correct. - Fig. 4 table errors: derivative-zero entries 3.15, 4.3, 5.2, 6.8 should be 3.054, 4.201, 5.318, 6.706 [calc, mpmath]; 1.84 and 3.83 are right. - Edge conventions: the patent first says free edge gives J0 = 0 (x = 2.405) then (p.4) free edge gives J1 = 0 (x = 3.832); the worked example uses the second. That is a drafting inconsistency (a sign of two conventions, not an OCR slip) [read: deep]. For an open edge 3.832 is physically right for the axisymmetric mode, but the lowest mode overall is x = 1.841 (not axisymmetric), which the example does not use.

Now the 1932 figures (GB417501 / US2089966). For a disc with eps = 1, lambda = 2 pi R/x. Table [calc]:

All of the 1932 numbers satisfy lambda = 3D (ratios 3.00, 3.00, 2.97), a scaling rule that matches no Bessel root with eps = 1: x = 2 pi R/lambda = pi/3 = 1.05, below the lowest root 1.841. Reaching it needs eps_res of about 3 across the whole gap. Step 1 said a 1 mm water layer in a 1 cm gap gives only eps_res = 1.11; I confirm that (series, eps_water = 80: 10/(9 + 1/80) = 1.110, lambda 11.1 cm vs claimed 18.6 cm) [calc].

Correction to Step 1 (nuance): the inconsistency is not as total as "a factor of 3 unreconciled". The series formula of GB483062 does give gap-dependent tuning when the gap is substantially filled with dielectric: to get eps_res = 3.04 in a 1 cm gap the layer must fill 68% of the gap (6.8 mm of eps = 80), and for 11.6 in a 0.5 cm gap 92% (4.6 mm) [calc]. So the 116 cm agar figures could be reconciled if the "1 mm layer" is not the whole dielectric (thick glass trough walls of eps about 5-7 would also raise eps_res; the patent says glass walls appear in the trough design [read: deep d96c39]). But the stated geometry (1 mm layer in 0.5-1 cm gap) does not reproduce them, and the patents do not do this calculation. The statement in US2089966 p.5 that "closer spacing lengthens the wavelength" is consistent with eq. (11) only through the dielectric loading, whereas p.7 says closer spacing raises the natural frequency: a direct self-contradiction within US2089966 [read: deep ZZ-US2089966]. In the empty-gap theory (eqs 4-7) d does not enter the frequency at all. Hence: GB483062 theory correct; the 1932 numbers (esp. the gold sol 6.2 cm / 18.6 cm and the 10 cm / 30 cm cases) are inconsistent with it for the stated geometry; the agar case can be rescued only by unstated dielectric loading. b. Established results: radial-line and disc resonator theory is textbook microwave engineering [memory, high]. c. Never tested beyond the patentee's statements ("calculation and confirmed by experiment", no data). d. Nothing in physics changes: it is ordinary electromagnetism.

Verdict: the Bessel theory (GB417564, GB483062): Established (correct textbook mathematics, with the listed slips). The 1932 tuning rule and spacing statements: Internally inconsistent (with GB483062's equations and with each other, p.5 vs p.7 of US2089966), subject to the dielectric-loading rescue above, which is unstated.

Claim 5: special valves, coaxial-tube resonators, differential wavemeter, polarimeter; tuning tables 0.30-4.9 m; "about 40 percent" efficiency for a two-valve push-pull

a. Tables [read: page image p.9, p.11; calc]. Table 1: l = 19-62 cm gives lambda = 32.9-107.6 cm; lambda/l = 1.73, 1.61, 1.71, 1.89, 1.89, 1.49, 1.74; a straight-line fit lambda = 1.61 l + 4.3 cm has correlation 0.97. A simple quarter-wave line would give lambda = 4l and a half-wave line 2l, so ratio 1.5-1.9 shows the oscillation is not set by the line alone: consistent with Barkhausen-Kurz (retarding-field) operation where electron transit time is involved [memory, medium; not web-checked]. Table 3: l = 19, 37, 57 gives lambda = 245, 360, 450 cm, ratios 12.9, 9.7, 7.9 (lambda grows more slowly than l). The values of lambda^2 are 60,025, 129,600, 202,500: nearly linear in l (slope about 3,750 cm per cm) as for a lumped capacitance loaded line, but three points cannot test a law [calc]. Text and tables agree on ranges (Table 5: 205-290 cm matches "2.05-2.90 m"). The "about 40%" is one phrase for the Table 4 circuit: efficiency is undefined (DC-to-RF? radiated?), no powers or voltages, no measurement method [read: deep GB448419]. A single unqualified efficiency with no input and output power cannot be checked. Also GB448417: the polarimeter is item 7 on p.2 and item 2 on p.7: a drafting slip [read]. b. Consistent with 1930s ultra-short-wave tube technology (Barkhausen-Kurz, magnetron-type, push-pull) [memory, high on era; medium on details]. 40% for a decimetre-metre triode push-pull is high but not impossible at 3.5-4.9 m [memory, low]. c. No test in the record. d. Nothing changes.

Verdict: Plausible, untested (apparatus and tuning tables are ordinary engineering); the "about 40%" is Never properly tested as stated (no definition).

Claim 6: hand-held Tesla applicator radiating from 0.5 mm upward; lamps with narrow discharge path exciting ultra-short oscillations; infra-red plus 0.3 mm-50 cm waves

a. No quantitative derivation. Physical sanity [calc]: a wave of 0.5 mm is 600 GHz; a spark gap produces broadband noise rather than coherent radiation at such a wavelength, and a filament near 2,000-3,000 K emits a thermal spectrum whose Rayleigh-Jeans tail contains long wavelengths at a vanishing level. Claiming a lamp emits "0.3 mm to 50 cm waves" gives no power: unquantified [read: deep US2558568]. There is nothing to be consistent or inconsistent with. b. Hertz-style spark radiation of mm waves is historically known (Lebedev, Bose, spark mm waves, 1890s) [memory, medium]. Therapeutic efficacy: no data. c. None. d. None.

Verdict: Not testable as stated (no dose, spectrum, power or detection given); therapeutic effects Never properly tested.

Claim 7: significance: January 1945 Goodrich/Firestone purchase of electronic-vulcanisation patents based on Dufour, Le Duc, Kassner; Voss 1987: Kassner "foresaw the microwave oven"

a. Not mathematical. One check: the claim from Voss that US2089966 anticipated heating-applicators is consistent with the patent saying energy above about 2 m is largely converted to heat [read]; but the patent excludes pure heating from its definition, so Voss's compliment attributes to the patent something the patent itself disclaims in its key definition. Hedged ("foresaw") and not a technical claim. b. Dielectric heating of rubber is established [memory, high]. c. Historical; not a test. d. None.

Verdict: documentary claim, supported as a fact of the press record; Established that the purchase was reported (the source clippings are in the folder), significance Historically superseded but instructive for the heating applicators.

Claim 8: Ternion AG company record (founded 18 April 1932, CHF 100,000, 60/40, research account CHF 1.12 million, liquidation 20 Dec 1937, deleted 1952)

a. I recomputed all the arithmetic in the register copies [read: deep Ternion-AG-OCR-de-en; calc]: - Capital: 100 shares x Fr. 1,000 = Fr. 100,000; subscriptions 60 and 40 shares, cheques Fr. 60,000 and Fr. 40,000. - Voting cap (one fifth): 1932: 1/5 of 100 = 20 votes each, total 40, absolute majority 21: consistent. 1937: 54 shares represented, 1/5 x 54 = 10.8, Stoffel's 48 cut to 10, Hoffmann's 6 stay, total 16, absolute majority 9: consistent with the statutes if the cap is computed on the shares represented and rounded down. (The statute text says "of all votes present", ambiguous between shares and votes; the minutes follow the shares reading.) - Dissolution needs a 3/4 majority with half the capital represented (statutes section 15) [read]. 54 of 100 shares represented clears the quorum; 3/4 of the 16 votes is 12; the vote was unanimous (16 of 16) so satisfied. The minutes quote only the absolute majority of 9, but this does not change the outcome. - Balance sheet 31 Dec 1936: assets 51,154.90 + 25,000 + 1,120,380.15 = 1,196,535.05; research account 1,026,064.80 + 94,315.35 = 1,120,380.15; liabilities 100,000 + 1,016,535.05 + 80,000 = 1,196,535.05. All balance. Research account is 93.6% of assets. If the research account were written off, assets are 76,154.90 against loans 1,096,535.05: net deficit 1,020,380.15, 10.2 times the share capital [calc]. That is a straightforward insolvency calculation and supports the minutes' own explanation (liquidation to forestall bankruptcy), i.e. no mystery is needed for the closure. b. Nothing to compare except the Swiss register, which the copies are. c. Documentary. d. None.

Verdict: Established (documented; the arithmetic of the record is internally consistent). Kassner is not named in any of it (claims.md already says so).

Claim 9: F. W. O. Bauch did a Ternion project on UHF and decimetre technique during a 1934 GEC secondment

Documentary, no mathematics. I only note that the dates fit: 1934-end 1935 (about 1.5 years) per IWM and Swiss Sound; the Ternion link rests on one sentence in a 1996 memoriam [read]. Never properly tested in the sense that no independent record has been found (no records of Ternion in his interviews); the GEC secondment itself is Established. Split.

Claim 10 (essay): natural-frequency fields can raise or lower covalent and ionic bond strength

a. Mathematically undefined: "bond strength" is not a quantity in any Ternion text (their terms are "energy content" and orientation). Photon energy check [calc]: lambda 18.6 cm 6.67e-6 eV (kT/E = 3,879); 40 cm 3.1e-6 eV (8,342); 90 cm 1.4e-6 eV (18,770); 116 cm 1.07e-6 eV (24,193); water at 1.28 cm 9.7e-5 eV (kT/E = 267). Against 463 kJ/mol per O-H bond that is 7.2e5 photons per bond for 18.6 cm [calc]. Collective effects (field-induced reaction rate change, polarisation of a transition state) can modify reaction rates in principle, but a binding energy is a property of the electronic structure; a field of 1e6 V/m changes an atomic energy by roughly e E a0 = 1.6e-19 x 1e6 x 5.3e-11 = 8.5e-24 J = 5.3e-5 eV [calc], 1e-5 of a bond energy. In strong static fields the effect is the Stark shift and is tiny at ordinary field strengths. b. Consistent with measured Stark and field-assisted chemistry only at small magnitudes [memory, high]. c. No test. d. Would require a new interaction mechanism between sub-meV photons and valence electrons.

Verdict: Not testable as stated (no definition of the altered quantity) and, as a literal bond-energy change, Refuted by calculation in magnitude (shift of order 1e-5 relative at 1e6 V/m; per-photon energy 1e-6 relative).

Claim 11 (essay / Morray note 12): a closed water electrolysis-and-burning cycle, or chemical heat pump, could yield net energy

a. Algebra check of the Morray note (derived-correct): DeltaG/2F = 1.229 V; DeltaH/2F = 1.481 V; T DeltaS = 48.7 kJ/mol (17% of DeltaH) [calc]; practical 1.6-2.0 V gives 308.8-385.9 kJ/mol [calc]. Wrong or inconsistent: - Minimum total work to make H2 + 1/2 O2 from liquid water at 298 K is DeltaG, whatever route, including any resonance drive. COP defined by the note as 286/(W_elec + W_res) is bounded by 285.8/237.1 = 1.205 [calc]. That bound is reached by an ordinary 1.23 V reversible electrolyser which already draws 49 kJ/mol of ambient heat. Therefore "realistic COP 1.2-1.4" has its lower end equal to the textbook limit and its upper end beyond the second-law limit. COP much greater than 1.2 would let you run a fuel cell (returns up to DeltaG as work) off the product and gain work from one heat bath: a perpetual motion machine of the second kind. - Closed cycle: water to water is a closed path in state space; net DeltaH = DeltaG = 0 over the loop. Any asymmetry (cheap synthesis, standard burn) must be paid for when the field-modified water state is restored. - The note's bench diagnostic (COP_B > 1.0 signals new physics) is wrong: any cell at 1.23-1.48 V has COP > 1 in its definition with no new physics. The right test is total work in versus DeltaG with isothermal calorimetry of the cell. - Landauer misapplied: kT ln 2 = 1.73 kJ/mol [calc] is a cost for erasure that ensures a Maxwell demon cannot gain net work from a single bath; it is not a loose bound that leaves room. - Cold products: making products colder than ambient takes work inside the machine; reabsorbing ambient heat afterwards just returns it. - Spectroscopy: 600 GHz is lambda 0.50 mm and 5 THz is 0.060 mm [calc], 25-200 times shorter than Kassner's water bands (1.28-1.5 cm); 600 GHz is 20 cm^-1 (note says 22) and 5 THz 167 cm^-1 [calc]. Librations of liquid water are near 400-800 cm^-1, not 22 cm^-1 [memory, medium; web check failed]. b. Consistent with: all thermodynamic data of electrolysis (DeltaG 237.1, DeltaH 285.8) [memory, high]. The "mode-selective chemistry 10-30%", "THz electrolysis 20-40%" and the Bechinger engine claims are uncited; Bechinger's engine runs between two temperatures [memory, medium]. c. The proposed 3-cell experiment was not run. The patents never mention electrolysis or hydrogen (grep) [read]. d. Would overturn the second law of thermodynamics (Kelvin-Planck) for COP above 1.205.

Verdict: strong form (COP above DeltaH/DeltaG; net energy from the closed cycle): Refuted by calculation (second law). Weak form (RF fields assist electrolysis): ordinary energy accounting with RF counted as input, no gain: Plausible, untested as a rate effect, but no net energy. The note's COP "ceiling" and diagnostic: Internally inconsistent. Split.

Claim 12 (essay): engineered binding energies could be weaponised; defence interests may have suppressed Ternion

a. No mathematics. The reasoning is from absence, which has the usual defect that absence of a record is predicted equally by "never existed" and "suppressed". The documented liquidation (Fr. 1.12 million research account unrecoverable, loans Fr. 1.1 million) supplies an ordinary financial explanation [calc, see Claim 8]. The statement that American General Electric owns BAE Systems is wrong by the essay's own source [read: deep essay]. b. No evidence offered. c. No test possible on current evidence. d. N/A.

Verdict: Not testable as stated; the evidence is absence. The weaponisation premise inherits Claim 10 and is Refuted by calculation to the extent it needs bond-energy changes.

Claim 13 (essay): effects are hard to replicate because natural frequencies shift with temperature and pressure

a. Logic: an explanation that accounts for every failure without a stated protocol is unfalsifiable. It becomes testable only if one gives: the frequency as a function of T and P, the required control tolerance, and the width. With Q = 50 (delta_lambda/lambda = 2%) the allowed drift is 2% in lambda, e.g. 1.8 cm at 90 cm; a drift of the dielectric constant of 4% would exceed it (lambda scales as sqrt(eps)), and water eps changes about 0.36% per K near 25 C [memory, medium], so 5 K shifts lambda by roughly 0.9%, about 45% of the band [calc: 0.5 x 0.36% x 5 = 0.9%]. So a temperature tolerance of order a kelvin is needed; that is attainable in a thermostat bath, so "most experimenters do not control" is a weak excuse. The patent names temperature and pressure as tuning handles [read]. b. N/A. c. No replication attempt in the record. d. N/A.

Verdict: Not testable as stated (no protocol); becomes testable with the numbers above, then Never properly tested.

Corrections to Step 1

1. claims.md Claim 4 says the 1932 tuning figures disagree with GB483062 "by a factor of about 3 ... never reconciled". Confirmed for the 10 cm / 30 cm and 6.2 cm / 18.6 cm cases with the stated 1 mm layer (series eps_res = 1.11, predicted 11 cm vs claimed 18.6 cm). For the agar 116 cm cases, the discrepancy can be closed with a dielectric filling 68% (d = 1 cm) or 92% (d = 0.5 cm) of the gap, or thick glass walls; the patents do not say so, so "never reconciled" is right but "contradicts" is too strong for the agar case. Replace "contradicts" with "does not follow from the stated geometry".
2. Claim 4 says the 40 cm disc (R = 20 cm) at 32.7 cm in GB483062 and the 39 cm disc at 116 cm differ by "a factor 3.5". True for the empty-gap example; GB483062's own worked example is eps = 1 and a different (axisymmetric, open-edge) mode, so the comparison is only meaningful for the same filling.
3. claims.md Claim 1 puts water at 1.28 to 1.5 cm in the same sentence as "sharp natural frequencies" and 2% bands. Water at 1.5 cm is the broad Debye hump (Q about 0.3, full width ratio 13.9), not a 2% band. The patents themselves say so; Claim 1 should be split.
4. Claim 5 "about 40 percent" is for the two-valve push-pull Table 4 circuit (3.5-4.9 m) only, not for the whole apparatus, and has no defined input/output.
5. Claim 8: the dissolution resolution required a 3/4 majority (statutes section 15); the minutes quote only the absolute majority of 9. The vote was unanimous so it was satisfied: not a defect, but worth the primer's note. The vote-reduction arithmetic (1/5 of 54 = 10.8 rounded to 10) checks.
6. The deep read of the Morray note says "COP 1.4 exceeds the second-law limit"; I confirm: DeltaH/DeltaG = 1.205 [calc]. The deep read's Landauer figure 1.7 kJ/mol also confirmed (1.73).
7. The deep read says the surface field for the electret example is 5.6e5 V/m (for 1e-9 C/cm^2); for the quoted upper end 2e-9 C/cm^2 it is 1.13e6 V/m [calc]. Both are right for their stated charge.
8. Unresolved: whether the OCR "Fig. 4" Bessel table errors (3.15, 4.3, 5.2, 6.8) are the patentee's or OCR/printing; they are in a page-image reading, so I treat them as the patentee's.

Summary of verdicts

Investigator findings (2026-10-04)

Scope. I read sites.md "Leads for review" (leads 1-29), the research notes of 2026-10-03 and 2026-10-04 (Internet Archive, Google Patents, DEPATISnet, Arnold, Heller/Navy survey, related work, records) and the files in research/files/ that bear on the mathematics (DE1128930B description, US3095359A, US2495429 OCR). My first pass (above) was written before any of these existed; none of them was weighed in it. Every pertinent finding is kept below, whatever my judgement of it. Tags: [read] from the project files, [web] as recorded by the Investigator in the cited research note (I did not re-fetch the sites), [calc] my arithmetic this pass (project venv), [memory] with confidence. Web verification this pass: none done (no verdict below turns on a medium/low [memory] item except where marked "not web-checked"; the two I used, the temperature coefficient of the water relaxation time and serum conductivity, are flagged). Source gap unchanged: no lab notebook, test report or replication of Kassner's own examples has turned up; the new material is other people's related claims, patent-office and court treatment, and company/biography records.

1. The inventor's own work (priority 1)

1a. Kassner's own 1934 French texts call his first "natural frequency" a Debye relaxation frequency (lead 21; claim 1). [web: research/2026-10-04-depatisnet.md, FR 786,294 p.1, FR 788,428 p.1, quoted there in French]. FR 786,294: the natural frequencies "respectivement les fréquences de relaxation dites 'bandes de dispersion anomales'" lie in the quasi-optical range, "in conformity with Debye's dipole theory". FR 788,428: "the first of the natural frequencies is the one given by the relaxation time for the orientation of the dipoles". Only pp.1 and 6 of FR 788,428 and pp.1-2, 15, 17-20 of FR 786,294 were read by the Investigator; I have not seen the rest. Weighing against my claim-1 analysis: this supports my reading and sharpens it. My first pass said the water 1.5 cm figure is the Debye hump (tau = 8.3 ps, f = 19.2 GHz, lambda 1.56 cm [calc, re-run: 19.24 GHz]), that its Q is about 0.3, and that "2% wide" bands are about 170 times narrower [calc above]. Kassner's own text now confirms that at least the first natural frequency is the relaxation frequency, so for that type the 2% width cannot hold: relaxation is one smooth hump spanning a frequency ratio of 13.9 between half-height points. The GB 417,501 "hitherto unknown" sharp resonance dispersion is then a second, separate assertion (the patents list several types; the French text, as far as read, does not say the sharp type is also a relaxation). So within the patent family the two kinds of band are internally distinguished, not contradictory; the inconsistency is only if a reader applies "2%" to the relaxation type. Verdict effect: none to the label; the split is made explicit below.

A further observation I can add by arithmetic [calc; sigma about 1.5 S/m for serum and eps about 75-80 are [memory, medium], not web-checked]. The conduction crossover frequency of a conducting aqueous liquid, f_c = sigma / (2 pi eps0 eps_r), is 0.337 GHz for sigma = 1.5 S/m and eps_r = 80, i.e. a wavelength of 89 cm, essentially Kassner's serum band at "about 90 cm". At 333 MHz the loss tangent sigma/(omega eps0 eps_r) is 1.08 [calc, eps_r = 75]. This is a coincidence worth stating, not a demonstration: conductive loss (eps'' = sigma/(omega eps0)) falls monotonically with frequency and has no peak, so this crossover is a smooth change of regime, not a resonance. If Kassner's "serum frequency" tracked it, the band would be a broad conduction/Maxwell-Wagner feature (Q of order 1), which again conflicts with "half-width under 5%". I flag it as a hypothesis for a test (measure eps'(f) and eps''(f) of serum at 0.1-1 GHz), not as a finding.

1b. FR 788,428 (new member of the energy-content family), ES 135,727, GB 448,418, GB 435,643 (leads 20, 22; claims 2-5). [web: depatisnet note]. The examples read (pp.1, 6) match GB 417,501: gold sol, agar 116 cm at 10 W, milk (5 wavelengths from 455 cm), veal at 362/184/92.5 cm and 150/10/3.0 W, juice at 475/354/145/45 cm with 200/150/15/1.2 W, temperatures 20-24.5 C, serum about 90 cm. Arithmetic on the listed wavelengths [calc]: 475, 455, 362, 354, 184, 145, 92.5, 45 cm are 63, 66, 83, 85, 163, 207, 324, 666 MHz; so the 40-95 cm examples are 315-750 MHz and the 1.5-5 m examples 63-207 MHz. No new data, no controls, no spoilage criterion on the pages read. "Veal 2 weeks" in GB 417,501 reads "more than 15 days" in the French text: consistent within rounding. GB 448,418 (abstract only): ellipsoidal reflector with the liquid circulated through a glass sphere at the second focus; apparatus, no figures. GB 435,643 (abstract only), "Divided out of 417,501": two plate resonators beat against each other and one carries a light-sensitive layer whose dielectric constant shifts its frequency. Mathematical bearing: the detector is the first place where Kassner's plate resonator is used the way the theory suggests, as a frequency shift from a dielectric change. For a resonator whose mode is fixed by lambda = 2 pi R sqrt(eps_res) / x, a small change in eps_res shifts the frequency by delta f / f = -1/2 delta eps_res / eps_res [calc, differentiate]; for a layer that fills a fraction of the gap, delta eps_res is smaller again (series rule, eq. 11 of GB 483062). A 1 percent dielectric change of a fully filling layer is a 0.5 percent shift, which is an easily measured beat in a two-resonator difference circuit; this part is ordinary heterodyne engineering and is plausible. I have not seen the patent's numbers (abstract only). Verdict: Plausible, untested (device); no change to claim 4's verdicts.

1c. DE 1,128,930 (1960; applicant Wilma Hencke, Kassner named inventor with a dagger) (leads 10, 19; claim 4 and later work). [read: research/files/google-patents/DE1128930B.desc.txt, machine translation; web for the bibliographic data]. This is the only post-1951 Kassner document and the first use of the plate resonator for rotating fields, particle acceleration, plasma and "Kernfusionsforschung". What I can check: - The identity the patent invokes, that J0'(x) = -J1(x), is correct, so the first zero of dJ0/dx equals the first zero of J1 (3.832, second 7.016) [calc, re-run with mpmath]. The patent's "coincidence" (Entartung) at x = 3.83 pairs an axisymmetric mode with an m = 1 mode (E_z proportional to J1(kr) cos(phi)). With the rim shorted, the m = 1 mode has E_z = 0 at the edge, which requires J1(x) = 0, so x = 3.832; with the rim open, the axisymmetric mode has H_phi proportional to J1 = 0 at the edge, also x = 3.832. The degeneracy is real as algebra, but it requires the rim to behave as open for one mode and closed for the other. The patent says the rim loading (a gas-filled glass torus, ionised or not) selects between the two limits (its Fig. 3, cases I and II); I could not see that one loading serves both, because I have only the machine-translated description, not the figures or claims. - A field that rotates about the axis in the textbook sense needs two degenerate m = +/-1 modes in time quadrature: cos(phi) cos(wt) + sin(phi) sin(wt) = cos(phi - wt) [calc, sympy identity verified]. For a disc with an open rim these are the lowest modes (x = 1.841, my first-pass remark that the lowest mode is not axisymmetric); they are degenerate by symmetry with no special coincidence needed. A superposition of an m = 0 and an m = 1 mode in quadrature, which is what the passage I read describes at x = 3.83, gives E_z and in-plane H out of phase at the plate centre, i.e. reactive stored energy exchange, not a rotating Poynting flux (S = E x H averages to zero when E and H are in quadrature at one point). I therefore cannot confirm from the text read that the field "rotates"; this needs the full patent and its Fig. 3. This is a doubt about my reading, not a finding of error. - "Relativistic pinch effect ... much larger magnetic field than in known accelerators" with no beam current, energy or field value [read]. A self-pinch of a charged beam is cancelled to a fraction 1/gamma^2 by the beam's own electric repulsion unless the charge is neutralised by plasma [memory, high]. The patent's setting is a plasma, which can neutralise; but no number is given, so the claim is Not testable as stated. Verdict: the Bessel/degeneracy algebra: Established (as algebra). Rotating-field, acceleration and fusion claims: Not testable as stated from what I could read; no energy, current, field or yield figure is given.

1d. Kassner's death in Munich by May 1962 (lead 19; claims 8, 12). [web: depatisnet note, DE 1,128,930 title pages; dagger convention memory, high]. No mathematics. It bears on the "record goes dark" premise of claim 12: the record of Kassner does not end in 1937 or 1951 but runs, in patents, from 1921 to 1960-62. See Claim 12 below.

2. Support by others (priority 2)

2a. Arnold (US 2,522,082; In re Arnold 1950; Arnold v. Watson, 237 F.2d 584, 1956) (lead 3, 24; claims 1-3, 13). [web: research/2026-10-04-arnold.md; research/files/In-re-Arnold-.json and Arnold-v-Watson-.json]. A trained dielectric physical chemist (JACS 1936, J. Electrochem. Soc. 1938) claims the same principle in 1943-45: use the "critical frequency" at the centre of the anomalous-dispersion range; molecules at the surface "selectively activated without abnormally activating those in the interior"; "destructive heating is not required"; the critical frequency shifts with concentration, voltage and temperature and must be tracked. Result evidence: one sentence ("Excellent results ... alkyd resin monomers"), no data. The courts refused the broad claims as "too broad and indefinite"; they did not rule on whether the effect exists. The examiner cited Kassner's US 2,089,966. The 1955 judgment says it was given on "evidence" and that Arnold "exposed the error of certain assumptions ... by predecessors" [web, per lead 3]; the trial exhibits are not available. Mathematical weighing. (i) Arnold identifies the "critical frequency" with the centre of the S-shaped dielectric step, i.e. the Debye picture, whose loss peak is broad (Q about 0.3); so Arnold's own mechanism, like Kassner's French text, gives a broad, not a 2%, frequency selectivity. (ii) Arnold's procedure (measure eps'(f), locate the step, hold conditions constant or track the shift) is precisely the protocol whose absence I noted under claim 13; Arnold's lack of success was a patentability finding (indefiniteness), which is neither a test nor a refutation. (iii) The "selective surface activation without bulk heating" claim can be put in numbers: the penetration depth of a field into a conducting aqueous layer is the skin depth delta = sqrt(2/(omega mu0 sigma)), about 0.023 m at 333 MHz for sigma = 1.5 S/m [calc, [memory, medium] for sigma]; for a thin film or a surface layer of a few micrometres there is no mechanism in the Debye picture that heats the surface preferentially unless the surface layer has a different relaxation frequency from the bulk; Arnold's patent does not give one, and the claim is therefore Not testable as stated in the form the courts saw it. (iv) The independence is partial: Arnold cites Kassner's patent as prior art and cites his own published electrolyte dispersion work; I do not treat it as an independent replication of Kassner's examples. Verdict effect: claims 1-3: no change in label; Arnold is a second claimant (not a test), recorded.

2b. Heller and Teixeira-Pinto, Nature 183:905 (1959); US 3,095,359 (1959); Midwest Research Institute survey for the US Navy (1960) (leads 13, 23; claims 1-3). [web: research/2026-10-04-heller-pearl-chain.md and files/run3/ copies; US3095359A.desc.txt read]. Heller exposed garlic root tips to a pulsed 27 Mc/s field (pulses about 5 microseconds, 80-180 per second, "No temperature increase in the water was noted", 5 min, scored 24 h later) and reported chromosome aberrations "contingent upon frequency, pulse, power, exposure time, and the axis of the cell". The 1959 letter gives no cell counts, controls, field strength or statistics. US 3,095,359 says each organism "is responsive to a critical frequency and voltage" and lists frequency-specific outcomes (for example sex ratios shifting at about 25 and 30 megacycles, mutations at 18 and 31 megacycles) with no data in the passage I read; it cites Kassner. The 1960 Navy contractor survey (an interested party: a hazard-standards programme) wrote "A new specific nonthermal effect has apparently been found" and that growth enhancement in the 1-20 m band "is not because of heating" and shows "frequency specificity"; it also offers Maxwell-Wagner interfacial polarisation as the candidate mechanism. Arithmetic [calc]: - Spectral width of Heller's pulses: a 5 microsecond pulse has a bandwidth of about 1/tau = 0.2 MHz, which is 0.74 percent of 27 MHz. So a pulsed 27 MHz field is itself "narrow" to under 1 percent; frequency-dependence on the scale of a percent is measurable, and Heller's claim is not excluded on width grounds. (This is a statement about the source, not about the biology.) - Duty cycle 5 us x 80-180 /s = 4e-4 to 9e-4. Illustrative heating, with the Navy report's 300-1,200 V/cm (3e4-1.2e5 V/m) which is the unicellular experiment's field and not necessarily the root-tip field, water of conductivity sigma, power density sigma E^2 x duty over 300 s into water (4.19e6 J/m^3 K): for distilled-type water (sigma 1e-4 S/m) 0.003-0.09 K; for tap-type water (5e-2 S/m) 1.3-46 K. So the statement "no temperature increase" is credible only if the water was of low conductivity or the field low; the letter gives neither, so the thermal null explanation cannot be excluded from the printed information. This is a statement about what is reported, not about whether Heller's measurement was right. - Pearl chains (Navy appendix): the induced-dipole energy U = 1/2 p E, p = 4 pi eps0 eps_m K a^3 E, with |K| = 0.5 for an insulating sphere in water (eps_m = 80). For a = 1 um and E = 3e4 V/m, U/kT is about 470; for a = 5 um, 6e4 [calc, kT at 310 K]. So at those field strengths alignment energy far exceeds kT for micrometre cells, which is why pearl chains form and why the Navy report calls them real; the effect is broad in frequency (Maxwell-Wagner relaxation), not a molecular resonance. This is consistent with the mainstream account and does not support Kassner's sharp-band claim, though it does support the weaker statement that dielectric-orientation effects on suspended particles need no heating. Weighing: Heller is a second claimant of frequency- and pulse-dependent non-heating effects (priority 2); the Navy survey is a contractor's report of that claim, not a replication. Against it: Mittler (1976) reported no genetic damage in Drosophila at 2 and 10 m [web: PubMed title only; full text not read; a different organism, so not a direct test]. No repeat of the garlic root-tip result has yet been found by the Investigator. Verdict effect on claim 3: Never properly tested stays (non-thermal, frequency-specific part), with Heller's work and the Navy summary recorded as claims awaiting a controlled test; a mathematically coherent mechanism (induced-dipole alignment, Maxwell-Wagner dispersion) exists for the orientation part and is broad in frequency.

2c. Patent-office treatment of Kassner as prior art (lead 12; claims 5, 7). [web: google-patents note; USPTO scan files/US2495429.ocr.txt read by me: "2,094,602 Kassner Oct. 5, 1937" under References cited]. Spencer (Raytheon, US 2,495,429, 1945) lists Kassner's US 2,094,602; Copson (Raytheon, US 2,833,657, 1954) cites US 2,089,966; the 32 forward citations of US 2,109,843 are UHF-tube patents; a DOE Emitron patent (GB 2,120,008, 1983) cites GB 483,062. Weighing: a citation shows an examiner or applicant thought the document relevant, not that its numbers were checked. My check of the GB 483062 mathematics (claim 4: correct textbook radial-line theory, with slips) is more informative than the citation, and agrees with the fact that the DOE cites it as a plate-resonator reference. No change in verdicts.

2d. The Goodrich 1950 characterisation of the Kassner patents (lead 1; claim 7). [web: Rubber World, Oct 1950, per research/2026-10-03-internet-archive.md; interested-party statement: Goodrich bought the package and licensed the rubber field]. "Most of the work he reported specified frequencies about 150 million cycles per second" (150 MHz: lambda 1.9987 m [calc]). Check against the patents' tables: the apparatus tables run 0.30-4.9 m and the 2.05-2.90 m table is 103-146 MHz [calc], so the statement is accurate for part of the apparatus (the 2-3 m range) but not for the food and colloid examples, which I tabulated above as 63-207 MHz (the 1.5-5 m ones) and 315-750 MHz (the 40-95 cm ones) and, for the 18.6 cm gold sol, 1.61 GHz. It is a fair summary of the dominant apparatus range and an incomplete one of the examples; it is the buyer's characterisation, to be set beside Kassner's own statement that "the object is not to produce a rise of temperature" (GB 417,501). The Rubber World of April 1945 remark that results "may be connected in some way with electronic power itself" (lead 8) is an unquantified trade-press hint. No data, no mathematics; recorded, no verdict change.

3. Closely related work (priority 3)

3a. Sharp-resonance claims after Kassner, and tests (lead 27; claim 1). [web: research/2026-10-04-related-work.md]. For: Webb and Booth, Nature 222:1199 (1969) (sharp absorption by microorganisms in the millimetre range; abstract not read by the Investigator) and Grundler and Keilmann, Phys. Rev. Lett. 51:1214 (1983) (narrow windows near 41.7 GHz in yeast growth). Against: Gandhi et al., Bioelectromagnetics 1:285 (1980): a 26.5-90 GHz sweep of DNA, RNA and cells, including frozen samples, "Sharp spectra reported by other workers were not observed"; Gos et al., Bioelectromagnetics 18:142 (1997): concurrent controls at every 2 MHz step from 41.682 to 41.710 GHz, "no consistently significant differences". Mathematical weighing: these are the only designed tests of narrow biological spectral lines in the record, but they are at 26-90 GHz, about 100 times Kassner's 333 MHz serum band, and in cells and nucleic acids, not serum or electrolyte; so they do not test Kassner's numbers. What they do show is that narrow-band claims of the same kind were examined with sweeps and concurrent controls and not reproduced, so the method for testing claim 1 exists (a swept eps(f) measurement with the Q of the feature as the target). A Q of 20-50 at 333 MHz would show as a dispersion step of 2-5 percent in lambda that any modern vector network analyser resolves at ordinary sweep widths, a one-afternoon measurement [calc, bandwidth = f/Q = 7-17 MHz]. Verdict: claim 1's sharp-resonance part stays Never properly tested at Kassner's frequencies; the analogue claims at 26-90 GHz are Tested, not supported* (one sweep and one controlled repeat; not direct tests of this claim). Note this is a split by band; I add it to the claim 1 verdict.

3b. The 1930s "specific effect" dispute and Liebesny-Wertheim (leads 25, 26; claims 2-3). [web: related-work note; the German texts were seen only as snippets]. GB 417,863 (Liebesny and Wertheim, 1.8 mm-120 m, frequency chosen per organism, with cooling) and the Botanical Review 1944 (Benedetti: fermentation rates rose or fell "depending upon ... the frequency used") place Kassner's fermentation claim in a small cluster of contemporary claims; Schliephake/Compere (1933) and Kowarschik (1936, snippets) report an open dispute, with German physiotherapy text stating "no specific effect of short waves on bacteria". Liebesny's range spans a factor 6.7e4 in frequency (120 m to 1.8 mm [calc]); "choose the frequency to suit the organism" over such a range has no testable content unless the organism-frequency map is given. I treat all as claims and counter-claims; no mathematics to check, and none supplies a replication of Kassner's examples. No verdict change; recorded.

3c. Non-thermal microwave chemistry (lead 27; claim 3, claim 10). [web: Kappe et al., Angew. Chem. 2013, and a published reply, titles only]. The dispute over specific microwave effects on reactions continues. For rate effects the usual accounting is Arrhenius with a temperature measured at the right place (k = A exp(-E_a/RT)); a 10 K local error in T near 100 C changes k by about a factor 2.0 for E_a = 80 kJ/mol [calc: E_a/R = 80,000/8.314 = 9,622 K; 1/363 - 1/373 = 7.386e-5 /K; product 0.711; exp(0.711) = 2.04]. (Corrected 2026-10-04 in the QE remediation: this line first printed 1.30, which is not what the expression gives; example.py step 8d prints 2.04. The point is strengthened, not changed.) So apparent "non-thermal" effects are easily produced by temperature-measurement error, which is the usual mainstream view; this does not exclude real field effects. Claim 3's chemistry part keeps its verdict.

4. The historical record (priority 4)

4a. Company and money (leads 1, 2, 5, 14-16, 28; claims 7, 8). [web: SHAB, newspapers, USPTO, Federal Register, ETH library, per the notes]. Recorded for the review: Dipol A.-G., Arbon (same founding day, 18 Apr 1932, as Ternion) was reported as dissolved in 1933 ("Aufhebung der Dipol A.G.", three newspapers of 30 Dec 1933 to 3 Jan 1934), while its formal liquidation entry is 1938 [web]; Ternion's research account kept growing to Fr. 1,120,380.15 at 31 Dec 1936 [read: facts, my arithmetic in claim 8]; Dr. Alfred Wiegner (Dipol's signing chemist) was an analytical/dye chemist, not a dielectrics or radio specialist [web: ETH]; Vibranic Ltd (Glarus, chaired by Stoffel) bought Grell's foreign rights for Fr. 200,000 in Nov 1945, including FR 926,351 matching Grell/Richards US 2,415,025 (assigned to Firestone and Goodrich) [web, matched priority date 22 Apr 1943]; the Goodrich 1950 paper names US 2,089,966 and 2,109,843 in the portfolio; General Infra Co AG, Chur, appears in a Swiss federal "Schwarze Liste" file title 1946-48, with a "Kassner, Ernst (20.11.1900)" police dossier whose identity with E. E. W. Kassner is unconfirmed [web: BAR catalogue; the file contents are not read]. Arithmetic bearing. These add no new figure to the balance sheet I checked, but two consistency questions follow, both stated as questions: (1) if Dipol, the likely laboratory, ceased in late 1933 and the research account (93.6 percent of 1936 assets [calc]) still stood at Fr. 1.12 million three years later, the spending after 1933 must have been somewhere else (London, per Kassner's 1934-36 residence and his British and French filings), or the account was a book valuation (the 17 Jul 1936 minutes justifying the valuation are not in the folder, as claims.md notes); the data cannot decide between these. (2) The Fr. 200,000 Vibranic payment is 0.18 of the Fr. 1.12 million research account [calc], which says only that the 1945 market did not value the portfolio at the book cost (the 1937 liquidation already showed that). Neither point changes the verdict on claim 8, which is about the arithmetic of the register copies.

4b. The record after 1937 (leads 5, 10, 11, 19; claim 12). [web]. New dated traces of E. E. W. Kassner: 1937 "Phono-Vision" folder, 1938 visiting card to the harmonics theorist Hans Kayser, 1943 General Infra (Zurich), 1951 Montana-Vermala (US 2,558,568), 1960 DE 1,128,930, and death in Munich by 3 May 1962. Weighing under SOURCE HONESTY (absence of evidence): claim 12 (the essay's) argues from a record that "goes dark". The record is silent in papers and conferences but not in patents and archives, and it ends with a documented death rather than with a disappearance; a company dissolved for insolvency (my claim 8 calculation) and an inventor who kept filing for 30 years leave less room for the suppression explanation than I assumed in my first pass, though they do not exclude it (the Swiss "Schwarze Liste" file title and the unread BAR dossiers are the lead that could bear on wartime pressure; they are unread). The new records support the ordinary-explanation side by documents and leave the suppression side with no documents. Verdict on claim 12: Not testable as stated stays; I add that its factual premise (no record) is now partly contradicted by documents.

4c. Unread but pertinent (kept in the record). Goodrich Series VII (Research and Development) of the B. F. Goodrich Company Records, BIOS Final Report No. 866 "High Frequency Heating", the BAR files, the Landesarchiv Glarus Vibranic file, the Staatsarchiv Thurgau Dipol file, the Arnold trial and appeal records, Heller's 1959-61 conference papers, Mittler (1976) full text, and the Kowarschik chapter. Any of these could change what I can say about claims 3, 7 and 8.

5. Corrections to my own first pass arising from these findings

1. Claim 13 (temperature tolerance). I computed a drift of 0.9 percent in lambda for a 5 K change using the cavity scaling lambda proportional to sqrt(eps_res) and the temperature coefficient of eps of water (0.36 percent per K, [memory, medium], not web-checked). If Kassner's natural frequencies are relaxation frequencies, as his French texts and Arnold both say, the relevant temperature dependence is that of the relaxation time. For water tau falls from about 17.7 ps at 0 C to 8.3 ps at 25 C [memory, medium; not web-checked], i.e. d ln(tau)/dT of about 3 percent per K [calc], and the relaxation frequency rises by the same fraction. Against a quoted 2 percent bandwidth, a 1 K error moves the band by more than its full width and the control tolerance would have to be about 0.7 K or better (2/3). So the tolerance of "order a kelvin" I gave under claim 13 still holds as an order of magnitude (it is a little tighter by this route), and the conclusion stands: an attainable thermostat tolerance, a weak excuse for non-replication; but a relaxation of Q about 0.3 would not need temperature control at all, which is a further reason to doubt that the sharp-band claim and the relaxation claim describe one phenomenon. Arnold's 1945 statement that the critical frequency shifts with temperature and must be tracked is the same point made by a dielectric specialist.
2. Claim 4 correction to my first pass: I said the lowest mode overall (x = 1.841) was unused in GB 483062's example. The 1960 patent does not use it either in the passage read; it uses the J1-zero coincidence at 3.832 instead (see 1c). This is a statement about the patents, not an error in the first pass.
3. Claim 12: my first-pass "the evidence is absence" is softened to "the evidence offered is an absence that documents partly fill" (4b).

6. How each finding bears on claims a-d, and verdict changes

Summary of verdict changes in this pass: no verdict label is changed. Three refinements are recorded: claim 1 gains a band-split (Kassner-band sharp resonance Never properly tested; the analogue 26-90 GHz sharp-line claims Tested, not supported), claim 13's temperature tolerance is restated under the relaxation reading (about 0.7 K), and claim 12's premise of a silent record is softened by documents. New items outside claims 1-13, both Not testable as stated from what I could read: the rotating-field, acceleration and fusion statements of DE 1,128,930, and Arnold's selective-surface-activation claim.

Investigator findings (2026-10-08)

Scope. This pass weighs what the Investigator and the two follow-up investigators added after my 2026-10-04 section: sites.md "Leads for review" 30-40 (follow-ups Q03, 2026-10-06, and Q05, 2026-10-07), the notes research/2026-10-06-followup-Q03.md and research/2026-10-07-followup-Q05.md, and the answers A03 and A05 in followups.json. Nothing new was added to research/files/ after the last pass (checked by file date). Leads 1-29 were weighed on 2026-10-04 and are not repeated. Every pertinent finding is kept below, whatever my judgement of it. Tags: [read] project files, [web] as recorded by the Investigator in the cited note (I did not re-fetch; none of the web items was opened by me, and most are abstracts or search snippets), [calc] my arithmetic this pass (project venv), [memory] with confidence. Web verification this pass: none done. The verdicts below turn on thermodynamic constants (dG 237.1, dH 285.8 kJ/mol, [memory, high]) and the single-Debye parameters of water (eps_s 78.4, eps_inf 5.2, tau 8.27 ps, [memory, high]); I rely on no medium/low [memory] item for a verdict. Source gap unchanged: the new material is other people's related work on electrolysis; no replication or test of Kassner's own examples has appeared.

A. The inventor's own work (priority 1)

A1. Kassner wrote nothing on electrolysis, water splitting or bond energies (lead 30; claims 10, 11). [read: Investigator's full-text search of _text/, recorded in research/2026-10-06-followup-Q03.md; consistent with claims.md and my claim 11 check "the patents never mention electrolysis or hydrogen"]. His water band is the Debye band: "about 1.5 centimetres" (GB417501 p.2), "1.28 centimetre" (p.4, p.10). His chemical statement is "Purely chemical reactions can also be enforced which otherwise only proceed under the influence of heat or of catalysts" (p.4; acetylene plus water to acetaldehyde, p.5): a rate claim, with no yield, energy or control. Mathematical weighing: a rate (activation) claim and an energy-requirement claim are different quantities. The first changes a kinetic factor (an exponent exp(-Ea/kT)), the second would change the state function dG; nothing in his text speaks to dG. The essay's bond-weakening reading goes beyond Kassner's words, but the Investigator's 2026-10-07 revision records the point, put to the review, that water is a dipolar substance and so falls under his general claim 1. I accept that: the applicability of the principle to water is direct; the energy-saving conclusion is not his.

A2. Kassner: absorption is greatest at resonance (lead 36; claims 1, 11). [read: US2089966 p.3: "The excitation is especially strong and the absorption of energy therefore especially great in the case of resonance"; same page defines the "standing field" (substance in a plate or concentric-tube resonator) and the "radiating field"]. This bears on the Q05 "lightly loaded tank" premise (Q05) and it is the strongest internal test of that premise: by Kassner's own sentence the sample draws the most power at its natural frequency. Together with C1 below, it makes "water at its band" and "lightly loaded" mutually exclusive by Kassner's text as well as by Debye's.

A3. 1.28 cm may be the water-vapour rotational line (lead 31; claim 1). [calc: 22.235 GHz is 1.348 cm, 5.3 percent above 1.28 cm; the liquid Debye peak is 1.5-1.56 cm]. My arithmetic reproduces the Investigator's. Mathematical weighing: this is a possible explanation of the two water values in GB417501 (1.28 and 1.5 cm) that claims.md notes as unreconciled; it is an inference, and the 5 percent gap is large against Kassner's quoted band widths of about 2 percent, so the vapour line would not match his own number either. The water-vapour line was measured later than 1932 [memory, medium; not web-checked], so priority is unresolved. I record it as an unconfirmed lead; it does not change claim 1's verdict.

B. Support by others (priority 2)

B1. RF and microwave assistance of electrolysis is real at the catalyst (lead 32; claim 11, rate part). [web: ideas.repec.org and nature.com abstracts, per the Q03 note]. Niether et al., Nature Energy 3:476 (2018): high-frequency magnetic heating of FeC-Ni core-shell nanoparticles lowered the oxygen-evolution overpotential by 200 mV and hydrogen-evolution by 100 mV at 20 mA/cm2; "equivalent to a rise of the cell temperature to ~200 C" while the bulk rose 5 C. Serra et al., Nature Energy 5:910 (2020): microwaves reduce Gd-doped ceria, which then splits water below 250 C; the universities hold a patent application (ES2726028-B2), an interested party. Follow-on: Gatard thesis (Grenoble 2021, not read) and an ACS AEM 2022 paper (snippet). Mathematical weighing: 200 mV is 16 percent of the 1.229 V floor [calc], but it is a reduction of the overpotential, the voltage above the floor. It leaves dG at 237.1 kJ/mol. The abstracts do not say whether the field power was counted in an overall efficiency, so whether the trade pays is open. This is a tested rate effect from one group (plus its follow-on), not a replication by independent groups that I can see. See the claim 11 verdict below.

B2. Roy, Rao and Kanzius: polarised RF "catalysis of dissociation" of salt water (lead 33; claims 10, 11). [web: i-sis.org.uk, Chemistry World and ChEnected snippets]. Materials Research Innovations 12:3-6 (2008); Current Science 98:1500 (2010) (not read; behind a bot check). 13.56 MHz, about 300 W, the gas above 0.1-30 percent NaCl burns while the field is on and stops when it is switched off; Raman differences in the O-H stretch region; the claimants propose "specific resonant coupling" and, per Chemistry World and ChEnected, Kanzius "never claimed he could get out more energy than was put in". The Institute of Science in Society author (Mae-Wan Ho) writes "The phenomenon is real, but the mechanism is entirely unknown" and that the 13.56 MHz photon carries about 10^-8 of the energy needed per molecule; an anonymous reader comment calls the Raman spectra similar apart from "a minor difference in peak intensities". No independent replication was found in a short search; silence, not contradiction. Mathematical weighing [calc]: a 13.56 MHz photon is 0.0054 J/mol against 463 kJ/mol per O-H bond, a ratio of 1.2 x 10^-8, so any effect cannot be a single-photon bond weakening, and the frequency is about 1,700 times below Kassner's 23.4 GHz water band (22 m against 1.28 cm), so it is not a Kassner-type resonance either. Its energy books are not given in the text I can see. It is the only direct claim in the record of RF acting on water's bonding; I keep it as an untested claim, not a refuted one.

B3. Second Wien effect and bipolar membranes (lead 37; claims 2, 11). [web: PubMed, RSC and eScholarship snippets per the Q05 note]. A strong static field orients water and speeds its dissociation into H+ and OH- (Onsager 1934 [memory, high]; Mafe et al. 1998; Bui et al., J. Phys. Chem. C 125, 2021; Yamamoto et al. 2025; Stovall et al., EES Catalysis 2026 questions the model). Mathematical weighing: this is a measured field-orientation effect on water chemistry in the literature and is relevant to claim 2 (orientation by a field), but it is a rate effect in a DC field of about 10^8 V/m [memory, medium] and not a resonance at water's band. It supports the orientation half of claim 2 only; it says nothing about "energy content".

B4. Field-assisted electrolysis energy balances (lead 38; claim 11). [web: pubs.acs.org abstract; snippet of a paywalled 2026 review, ACS Appl. Energy Mater. 9(16):10362]. The abstract names energy consumption of field integration as a practical consideration; the snippet reads "power-supply losses of AC coils aggravate this negative energy balance even further" and "a net energy saving of 215.6 kWh was calculated" in a laboratory-scale assessment, context unseen. I cannot weigh a number whose method I have not seen; I record that at least one field-assisted method is described as a net loss once coil power is counted and at least one as a net saving, both concerning overpotential, not the floor.

C. Closely related work (priority 3)

C1. Water's own band is too lossy for a sharp or lightly loaded resonance (lead 40; claims 1, 4, 10, 11). [web: Kaatze, relaxation near 19 GHz, tau about 8.3 ps, snippets in the Q05 note; calc below]. With a single Debye term (eps_s 78.4, eps_inf 5.2, tau 8.27 ps) I reproduce the Investigator's figures [calc]: at 19.2 GHz (1.56 cm) eps = 41.9 - 36.6j, loss tangent 0.874; at 23.4 GHz (1.28 cm) eps = 34.7 - 35.9j, loss tangent 1.034; at 2.45 GHz 0.119; at 1 GHz 0.049. A resonator filled with water at its band has Q = eps'/eps'' of about 1.1 (1.14 at 19.2 GHz, 0.97 at 23.4 GHz), so its stored energy is dissipated in about one cycle, and its bandwidth f/Q is as wide as the frequency itself. Three consequences. (i) It confirms from a second direction my 2026-10-04 finding that a water band "of 2 percent" cannot be a relaxation band (Q of order 0.3-1, not 50). (ii) It makes Kassner's plate resonator of claim 4 with a thin water layer a heavily damped circuit, not a "sharp" one, unless water is a small fraction of the field (low filling factor), in which case little energy goes into the water per cycle. (iii) It disposes of "lightly loaded tank with water pumped at its resonant frequency" (Q05 premise) as a statement about water at 1.28-1.56 cm. The Investigator's heating figures also reproduce: absorbed power omega eps0 eps'' E^2 is 39 W/cm3 at E = 10 V/cm (rms) at 19.2 GHz, about 9 K/s in water [calc, specific heat 4.18 J/(cm3 K)].

C2. Established resonant bond weakening of water is infra-red, at a surface (lead 34; claim 10). [web: EPFL infoscience, AIP snippets]. Hundt et al., Science 344:504 (2014): infra-red excitation of the D2O stretch strongly promotes dissociation on Ni(111); later O-H against O-D selectivity in HOD (J. Chem. Phys. 2018). Mathematical weighing: this is the correct form of the idea and I accept it as Established for isolated molecules at a hot surface. Correction to the Investigator's ratio (see section E): the lead says the stretch photon is "about 35,000 times a 1.28 cm photon". My arithmetic gives 3,400-4,700 times (0.33-0.46 eV against 9.7 x 10^-5 eV) [calc]. The qualitative point (the established resonance is in a band thousands of times above Kassner's) stands.

C3. Later resonance-electrolysis claims (lead 35; claim 11). [web: Google snippets, Wikipedia]. Puharich US 4,394,230 (1983), "complex electrical wave form" water splitting (text not read by the Investigator, and not by me); Puharich's 1987 compilation names "22.3 GHz" as water resonance (that is the vapour line, see A3). Meyer's "water fuel cell": an Ohio court in 1996 found "gross and egregious fraud" after expert witnesses testified it used conventional electrolysis; that is the court's characterization in an adversarial proceeding, recorded as such. Non-thermal microwave effects in chemistry are contested in print (Kappe et al., Angew. Chem. 52:1088, 2013, and a published Correspondence). I have nothing mathematical to weigh in the Puharich snippets; I record them. They claim no more than the closed-cycle claim 11 already covers, and the court finding is about one device.

C4. Thermally regenerative electrochemical cycles (lead 39; claim 11). [web: NASA NTRS Morehouse 1986 snippet; Chum review]. Splitting water hot and recombining it cold is a heat engine; the second reservoir that Q05's "paid by the environment" requires. Mathematical weighing: the net work is bounded by the Carnot factor 1 - Tc/Th, 0.20 between 373 K and 298 K [calc]. This is a mainstream, bounded route to the Q05 asymmetry and is the exact form in which "the environment pays": a temperature difference, with a heat source.

D. Checks of the Q05 and Q03 arithmetic (claim 11; I recomputed each)

1. Heat-pump ratio. dH/dG = 285.8/237.1 = 1.205; T dS = 48.7 kJ/mol [calc]. Agrees with my first pass and with A05. Q05's "somewhat like air conditioning" is correct for this part: a reversible 1.229 V cell takes 48.7 kJ/mol of room heat, and the asymmetry lies in heat, not work.
2. Hydrogen bonds. Vapour dG 228.6 against liquid 237.1 kJ/mol: 8.5 kJ/mol, 3.6 percent [calc] (the Investigator wrote 8.6, rounding of the inputs). Removing the whole hydrogen-bond network lowers the electrical work by about 4 percent at most, and costs at least that to remove (state function). Agrees with A03.
3. Photon scales at 1.28 cm: 9.3 J/mol against RT = 2.48 kJ/mol, ratio 1/265 [calc]. Agrees. Against the O-H bond (463 kJ/mol) the ratio is 1 in 49,800 [calc], agreeing with "about 50,000".
4. Field energy stored in water. (1/2) eps0 (eps_r - 1) E^2 V_m with V_m = 18.07 cm3/mol and eps_r - 1 = 77: 0.006 J/mol at 10^6 V/m, 0.6 J/mol at 10^7, 62 J/mol at 10^8 V/m [calc]. Agrees with the Q05 note (10, 100 kV/cm and 1 MV/cm).
5. An error in the Q05 note. It says that lowering the work by a tenth (24 kJ/mol) by stored field energy "needs fields near 0.2 V per angstrom (2 x 10^9 V/m)". Those two numbers are not equal: 1 V/angstrom is 10^10 V/m, so 2 x 10^9 V/m is 0.2 V/nm = 0.02 V/angstrom. My calculation with the same linear formula gives E = sqrt(2 x 24,000 / (eps0 x 77 x 1.807e-5)) = 2.0 x 10^9 V/m = 0.02 V/angstrom [calc]. So the arithmetic (2 x 10^9 V/m) is right and the angstrom conversion is wrong by a factor of 10. Two further cautions. The linear formula fails at such fields (water saturates, dielectric breakdown and dissociation set in), so the number is an order of magnitude estimate only. And the comparison the note draws, "that is the scale at which simulations find water starts to dissociate" (Saitta et al., 0.35 V/angstrom [web: arxiv.org/abs/1204.1120]), is therefore off: 0.35 V/angstrom is 3.5 x 10^10 V/m, about 17 times the 2 x 10^9 V/m estimate, not the same scale. The correction does not change the conclusion (a field must itself supply the energy), but the sentence should read "about 0.02 V/angstrom, an order of magnitude below the simulated dissociation threshold". Correction (2026-10-08, QE remediation by the arbiter; arbiter.md ruling 4): this item is itself wrong and should not be carried forward. 1 V/angstrom = 10^10 V/m, so 2 x 10^9 V/m = 0.2 V/angstrom, as the Q05 note says; my step "2 x 10^9 V/m is 0.2 V/nm" was the slip: 2 x 10^9 V/m = 2 V/nm = 0.2 V/angstrom. Saitta's 0.35 V/angstrom is 3.5 x 10^9 V/m, not 3.5 x 10^10, so the estimate (1.97 x 10^9 V/m [calc: sqrt(2 x 24,000 / (8.854e-12 x 77 x 1.807e-5))]) is about 1.8 times below the threshold [calc: 3.5e9 / 1.97e9 = 1.77], the same order, not 17 times below. The Q05 note's sentence stands. My cautions about the linear formula and the conclusion (a field must itself supply the energy) are unaffected; indeed the estimate sits at the dissociation scale where the linear formula fails.
6. Second reservoir by ambient RF. 24 kJ/mol at 1 mol per hour is 6.7 W; at 1 microwatt/cm2 that needs 667 m2 of perfect collector [calc]. Agrees (the 1 microwatt/cm2 level is from an aggregator snippet; Piñuela et al. 2013 not read).
7. Debye numbers: reproduced in C1. The note's Q about 1.1 is right to the precision of the single-Debye model (real water has a second, faster term at higher frequencies that changes the 23 GHz values by a few percent [memory, medium]; not web-checked).
8. A03's 2.45 GHz and 13.56 MHz photon energies (0.98 J/mol, 0.0054 J/mol) agree with mine [calc: hf N_A].

E. Corrections to earlier documents

1. research/2026-10-06-followup-Q03.md, section D, and sites.md lead 34 (and A03 if it repeats it): "roughly 35,000 times a 1.28 cm photon" is wrong. 0.33-0.46 eV over 9.7 x 10^-5 eV is 3,400-4,700 [calc]. It looks like a slip of a factor of about 8. Correct to "roughly 3,400-4,700 times" (this line said 3,500-4,700 until 2026-10-08; 3,407 rounds to 3,400). The ratio of the mean O-H bond energy to the same photon, 50,000, is right and may be the source of the confusion.
2. research/2026-10-07-followup-Q05.md part A and A05 (if repeated): "0.2 V per angstrom (2 x 10^9 V/m)" should be 0.02 V/angstrom, and the comparison with Saitta's 0.35 V/angstrom threshold should say the estimate lies about 17 times below it (D5). [Withdrawn 2026-10-08: this correction is wrong; 0.2 V/angstrom = 2 x 10^9 V/m and 0.35 V/angstrom = 3.5 x 10^9 V/m, about 1.8 times the estimate. The Q05 note is right. See the correction under D5 and arbiter.md ruling 4.]
3. My own 2026-10-04 claim 11 (above) said the weak form "RF fields assist electrolysis" is Plausible, untested "as a rate effect". That was written before the Niether and Serra papers were in the record; the weak form is no longer untested at the catalyst (B1). See the verdict in F. This is a statement overtaken by new evidence, not an arithmetic error.
4. My claim 11 deep-read comment, "Landauer misapplied" and "cold products" points, are not affected. The Q05 note's own point that the essay draft predicts the environment cools (old-unexplored-technology drafts, p.1) is consistent with T dS = 48.7 kJ/mol drawn from the room; I had not weighed it and it is correct, but it is the established, bounded heat-pump effect (COP up to 1.205), not an extra.

F. How each finding bears on claims a-d, and verdict changes

The scale has no label for "tested, supported in one form"; the nearest honest wording within it is a split verdict, which I give: the catalyst-surface rate effect is a measured, published effect (so not "Plausible, untested"), and no scale entry says "partly supported", so I state it in words and keep "Never properly tested" for the Ternion-specific part. A reader should not take it as a verdict for Ternion's method.

Summary of verdict changes in this pass: (1) claim 11 weak form is split: the catalyst-surface RF/microwave rate effect is no longer "Plausible, untested" (published, measured, field power not yet counted in what I could read), while the Ternion-style standing field at water's band is Never properly tested; the strong form stays Refuted by calculation. (2) claim 10 is made two-part: single-photon RF/microwave bond change stays Refuted by calculation; infra-red resonant bond weakening at a surface (Hundt 2014) is Established but is not a Ternion band. (3) claims 1, 2, 4, 12, 13 keep their labels with added support (water's Q about 1 at its band; Second Wien orientation; Kassner's "absorption greatest at resonance"). Two numerical errors in the Investigator's notes are recorded in E (35,000 should be about 3,400-4,700; 0.2 V/angstrom should be 0.02 V/angstrom). [Note 2026-10-08: the second of these is withdrawn; the Q05 note's 0.2 V/angstrom is right. See D5.]