Su-CC: Mathematician review (Step 2)

Reviewer: PhD mathematician. Project: Ching-Chuan Su (C.-C. Su), National Tsing Hua University, Hsinchu: the "local-ether" model and "Quantum Electromagnetics". Date of review: 2026-10-06.

Tags: [read] = from a source document, [read: deep/NAME] = from a Step 1b deep read that I re-read and, where noted, re-computed, [calc] = my own arithmetic or algebra, [web] = web source with URL, [memory] = recalled, with confidence.

Source gap (repeated from claims.md): the 2005/2008 book is present only as an outline and summary. Su's earlier papers on radar echo time (JEWA 14, 1525), explicit field definitions (Eur. J. Phys.), the AP-S digests on Sagnac, and the railgun paper are not read. None of the experimental papers Su cites is in the folder. Where I compare with an experiment I say whether it rests on Su's citation, on [memory], or on a web check. Nothing in this review rests on [memory] alone for a verdict except where stated.

How I worked: I read all 14 deep reads (f2a, f3a, f3c, f4a, f5a, f5b, f5c, f6, f7, f8a, f8b, f8c, and the EPJC paper), claims.md, sites.md, all research notes, and the Investigator's downloads f1b (EPL 2001, Michelson-Morley), f2d (Barnett) and the Marsen 2019 text. I re-ran the key numbers (below). The deep readers worked from page images for the equations, and I found no arithmetic error of theirs that changes a conclusion. I did not re-render the page images myself.

0. What the mathematics is, in plain terms (for the reader)

Su's programme has five layers. Keep them apart, because they have very different mathematical status.

1. Frame bookkeeping. Light travels at c relative to a chosen frame (his "local ether": the Earth-centred inertial frame, ECI, which does not spin with the Earth; the Sun-centred frame between planets). The time a signal takes is (distance travelled in that frame)/c. Because the receiver moves while the signal is in flight, "distance travelled" differs from "distance between the endpoints at one instant"; the difference is the Sagnac term, of first order in v/c. This layer is ordinary kinematics. In an inertial frame it gives the same numbers as special relativity (SR) for closed loops and for the GPS range correction.
2. A wave equation for matter (his eq. 1, a Klein-Gordon-type equation with a "natural frequency" omega0), declared valid only in the ether frame. Algebra from it gives m0 = hbar omega0/c^2, the de Broglie relations, and f = f0 sqrt(1 - v^2/c^2), with v measured in the ECI frame.
3. A velocity-dependent force law (the "augmented potentials", a Weber/Riemann-type interaction) that reduces to F = q(E + v x B) with v measured relative to the magnet or wire ("the matrix").
4. Gravity as an optical index n_g = 1 + 2GM/(c^2 r). This is the weak-field metric of general relativity written as a refractive index.
5. Applications: Compton scattering as wave scattering, quasar redshift as gravitational redshift of a huge gas cloud.

A reader's key to everything below: where Su's formulas agree with SR/GR, they agree because they are the same formulas with a different meaning given to "v". The disagreements are few, small, and mostly untested.

1. Corrections to Step 1

1. claims.md, claim 6 (NGC 7319). The "0.7 arcsec" is the quasar's angular diameter estimated by Su from an HST image; the quasar lies about 8 arcsec from the galaxy centre [read: deep/f5c sec. 2 item 4 and sec. 4]. claims.md can be read as saying the quasar is 0.7 arcsec from the galaxy. Also, the 300 million light-year distance is the galaxy's, taken from Wikipedia; applying it to the quasar is the ejection hypothesis itself.
2. claims.md, claim 5 (62 Hz vs 34 Hz). Wording "one old measurement showed about 34 Hz peak-to-peak attributed to a spurious signal" is right as to Su's text [read: deep/EPJC sec. e], but incomplete: Su does not say the phase of the reported term (lowest frequency when the cavity points east-west) matched, and does not try to explain the factor of about 1.8 between 62 Hz and 34 Hz. The 34 Hz is 0.55 of the prediction, not an agreement. Modern evidence on this is in section 3 below.
3. claims.md, claim 2, "one-way GPS gravitational delay (about 43-60 ps)". Su's own formula, applied with his own inputs, gives 42.2 to 62.2 ps [calc, confirmed by deep/f5b]. The printed 43 and 60 are 2 to 3 percent off at each end. Cosmetic.
4. claims.md, claim 2 / deep/f5b. Su's statement that eclipse deflection was "first confirmed in 1917" is wrong; the first confirmation is the 1919 eclipse expeditions [memory, high]. Not load-bearing.
5. EPL 2001 (f1b), "orbital speed about 100 times that of rotation". The ratio is 30 km/s / 0.464 km/s = 64 [calc]. The conclusion is unaffected (an uncorrected 30 km/s term would still be tens of times the 30 m correction).
6. Step 1 gap now filled. claims.md said the EPL Michelson-Morley paper was not in the folder. The Investigator downloaded it (research/files/wayback-qem/f1b.pdf). I read it: it contains no derivation beyond what the EPJC deep read already records (its eq. 4 is the classical-ether round-trip time, which I checked below). So the EPJC deep read's account of the Michelson-Morley argument stands.
7. Citation oddities the deep readers flagged and which remain unchecked: in f7 the Cedarholm and Townes reference (Nature 181 vs 184 depending on which Su paper), in f5c a doubled and a malformed identifier. These are bibliographic, not mathematical.

No Step 1 verdict-bearing claim needed reversing. The deep reads are careful and I found them reliable.

2. Findings I verified myself

All with the project venv.

3. The central claims

Claim 1. A local ether, not a universal one, carries light (ECI frame near Earth; heliocentric between planets)

I split it into a weak form and a strong form.

Weak form: the formulas. Light-travel times and Sagnac terms for GPS, intercontinental links, Sagnac loops and Fizeau computed in the ECI frame, with the Earth's orbital motion absent from earthbound results.

a. Internal consistency. Yes. The propagation-range formulas (EPJC eqs. 2-8, round trip to second order), the GPS range formula R = R_t + 2 S.omega_E/c, the loop result delta-tau = 4 omega.S/c^2 and the Fresnel-drag derivation all check [read: deep/EPJC, deep/f3a; calc]. Two hidden assumptions to record: - The derivation of the electric-field wave equation (f3a eq. 9) needs the matrix velocity to be uniform and constant, so that the matrix-frame time derivative commutes with the wave operator. It is then applied to rotating loops where it varies [read: deep/f3a sec. 3.1]. At first order in v/c the effect is probably small, but Su does not show it. - For one-way links, "the time" of emission and reception is read from clocks synchronised in the ether frame. That is a convention (absolute simultaneity) built in, not derived.

b. Established experiments. The same ECI-frame first-order formulas are used by mainstream GPS practice and derived there from SR [memory, high; Ashby, Living Reviews in Relativity 2003, not re-fetched]. The data Su cites (GPS Sagnac correction, Japan-USA two-way link about 0.3 microseconds, Michelson-Gale 1925, fibre gyros, Fizeau) are reproduced equally well by SR with an inertial frame chosen consistently [read: deep/EPJC, deep/f3a "closed-loop tests do not discriminate"]. So agreement here shows consistency, not preference. A real weakness in Su's argument: that the orbital motion must not enter earthbound results is also what GR gives (the Earth is in free fall around the Sun; its orbital velocity is a boost, and only tidal terms remain) [memory, high]. So "no orbital Sagnac term" is not a distinguishing prediction, though Su and the Investigator's advocates present it as one.

c. Tested? Not as a distinguishing claim. No neutral test exists for the weak form because it coincides with the standard result.

d. What would have to change. Nothing. The weak form is mainstream physics with a different narrative.

Strong form: a physical preferred frame (an ether at rest in the ECI frame), distinguished by second-order terms. The two clean mathematical predictions:

(i) Lab-fixed quadrupole in an optical cavity, fractional size beta^2/2 where beta = (Earth-rotation speed at the site)/c: 62 Hz at 3.39 microns, 40 deg N (about 7e-13 fractional). (ii) Transverse radar Doppler -2v^2/c^2 (a few to 12 Hz at 10 GHz, LEO).

On (i), I looked beyond Su's single 1979 comparison. - Brillet and Hall (1979) reported a limit of delta-c/c = (1.5 +/- 2.5) x 10^-15 [web: https://vivo.colorado.edu/display/pubid_108412]. Their lab-fixed twice-rotation-rate term, about 17 Hz amplitude at 88 THz (3.9e-13 peak-to-peak fractional) according to Su, is about half of Su's prediction; Su and Marsen both read it as a possible positive signal, and the experimenters called it spurious. I have not seen the Brillet-Hall paper itself (single report of their attribution, via Su; the Investigator's note says the paper is not yet obtained). Su's own words: "It seems too early to make a decisive conclusion" [read: deep/EPJC]. - A modern rotating-table cavity experiment, Herrmann et al. (arXiv:1002.1284; Phys. Rev. D 80, 105011, 2009) rotates two orthogonal 282 THz cavities on an air bearing and fits separately (a) sidereal modulations and (b) the constant, laboratory-fixed 2 omega_table amplitudes S0 and C0. In the extracted figure axes, S0 and C0 run within about +/- 2e-15 (single points) and about 4e-16 in the yearly overview; the paper says these lab-fixed terms are the ones most affected by residual systematics and that they "vary in magnitude and phase and thus average out" over a year [web: https://arxiv.org/pdf/1002.1284, text extracted locally; I read the axis ranges and the quoted sentences, not a tabulated number]. Their summary says systematic signal amplitudes were reduced below 1 Hz, a factor 10 to 100 below previous measurements [web, search summary]. Su's lab-fixed effect would be about 4.5e-13 (Berlin, 52.5 deg N, [calc]), i.e. of order 130 Hz at 282 THz, constant in lab phase. Its absence at the 1e-15 level in a lab-fixed amplitude is a discrepancy of 2 to 3 orders of magnitude from Su's prediction, if the apparatus and Su's effect are geometrically equivalent (two orthogonal horizontal cavities on a vertical-axis turntable, beat-note between them; I believe yes, but I have not derived Su's prediction for a two-cavity difference with a monolithic block). I mark this as a provisional, strong indication, not a closed test: the Investigator and the Physicist should confirm it against the full text of that paper. It also bears on the Brillet-Hall residual: a lab-fixed term of 3.9e-13 in 1979 and under 2e-15 in 2009 with better systematics control suggests the 1979 term was a systematic (an inference, not a documented fact). - Su's own derivation of the structure (that a quadrupole exists at all) rests on one fact: that in his model the round-trip time through a cavity arm depends on the arm's orientation relative to the ether velocity at order beta^2. That is classical-ether mathematics and is correct as algebra [calc].

Verdict on the strong form of the cavity prediction: Never properly tested by anyone who set out to test it in 2001; the 1979 residual is a single, unexplained, lab-fixed term of about half the predicted size. My reading of the later literature is that the effect is excluded by about two orders of magnitude (see above), pending a check of the paper's lab-fixed amplitudes.

On (ii) (transverse radar Doppler at -2v^2/c^2): not tested. Su cites no data; the standard formula has no such term for transverse motion [memory, medium].

The annual stellar aberration problem is admitted unsolved by Su once the Earth's local ether is included [read: deep/EPJC sec. g]. In plain words: if starlight enters a medium (Earth's local ether) that co-moves with the Earth, the telescope has no velocity relative to the medium and the annual aberration of about 20.5 arcseconds should vanish. Su names the "interface problem" and leaves it open. This is a mathematically unresolved gap, not a verdict by itself, but it is the oldest objection to any dragged-ether model [memory, high].

Verdict, claim 1 - Weak form (ECI-frame Sagnac, GPS, no orbital term): Established as calculation, with the proviso that it is mainstream SR/GR in an inertial frame and does not prove an ether. - Strong form (a physical ether at rest in the ECI frame, with second-order lab-fixed signals): Never properly tested as of Su's papers (single ambiguous residual in 1979, not dismissed without discussion by Su himself); on my reading of the later literature, Tested, not supported (provisional) for the cavity quadrupole. Annual aberration unsolved. - Priority note (Investigator): Beckmann (1986) proposed the same local-ether postulate independently [web, per Marsen and the Natural Philosophy Wiki; not verified from Beckmann's text]; Su's EPJC text does not cite him [read: grep, sites.md].

Claim 2. Gravity is an optical index, not curvature

a. Internally consistent. Eq. n_g = 1 + 2GM/(c^2 r) is postulated, not derived [read: deep/f5b]. The deflection integral gives 2/b exactly and hence 4GM/(c^2 b) [calc]; the delay formulas have the right logarithms and reproduce the standard GR (gamma = 1) results [calc, memory high]. The "19.5 microsecond disagreement with Kenyon" Su reports is, in the deep reader's reading, a coordinate-convention constant in textbook formulas, not an observable [memory, medium; deep/f5b sec. 5a]. I agree with the logic: a constant offset in the echo time is absorbed into fitted ranges. b. Consistent with Shapiro 1971, Viking, Mariner and Fomalont-Sramek, because numerically identical to GR in those cases [read: deep/f5b; memory medium for the measured ratios]. c. Tested by others as GR. The only claimed difference is the choice of frame (geocentric, heliocentric) and instants. Su gives no size and proposes no test [read: deep/f5b sec. 6]. I could estimate one: the Sun's motion relative to the solar-system barycentre is about 10 m/s [memory, high], so any heliocentric-versus-barycentric difference is of order (10 m/s / c)-level effects, far below spacecraft ranging precision; Su does not attempt this. d. If true as a replacement for curvature, one would need an account of the other GR effects (perihelion precession, gravitational waves, strong-field behaviour). None is given. The index form is a known approximation to GR to first order in GM/(c^2 r), so for the tests listed nothing in mainstream physics would have to change [memory, high].

A mathematical remark: the paper makes gravity enter matter waves only through n_g multiplying the same Laplacian and time-derivative as for light (f5a eq. 3). That gives a gravitational redshift of f0/sqrt(1 + 2 Phi_g/c^2), which differs from GR's 1/sqrt(1 - 2GM/rc^2) at second order. Both agree to first order, which is all that Pound-Rebka, GPS and Gravity Probe A can test [calc; read: deep/f5c sec. 3].

Verdict, claim 2: Established as numerical agreement with GR at first order (and equal to GR by construction); the claim that this removes the need for curvature is Not testable as stated (no measurable difference stated), except the second-order redshift difference and the unsized frame effects, which are Never properly tested.

Claim 3. Matter waves obey the same preferred-frame equation; mass is a frequency

a. Internal consistency. Mostly yes, with identified weak points. - The wave equation (f4a eq. 1) is the Klein-Gordon equation linearised in the potential, with the cross term frozen at the rest frequency and omega0 = m c^2/hbar (deep/f4a sec. 3). That is a fair reading and I agree. Su presents the coefficient 2/(hbar omega0) as a postulate chosen "so that the electrostatic force comes out right"; therefore m0 = hbar omega0/c^2 is a calibration, not a derivation, and the sentence "unveils the physical origin of inertial mass" has no measurable content in these papers. The charge-of-the-electron sentence is ordinary electrostatics. - The step to the Schrodinger equation (drop the second time derivative of the envelope) is the standard non-relativistic limit and correct [read: deep/f4a sec. 4; calc]. - Group velocity gives k = omega v/c^2 and the Lorentz-factor relations; correct algebra [calc]. - The identity of gravitational and inertial mass (f5a): the gravitational potential enters with no particle-dependent coefficient while m0 is defined from omega0, so it follows from the form postulated; it is not an independent derivation. This is circular in the same way as the mass relation [read: deep/f5a sec. 5]. - The augmentation operator U is postulated, not derived, and the ordering q Phi (1 + U) makes the Hamiltonian non-Hermitian, so norm conservation and the Ehrenfest formula used afterward are not exact (effect small for slowly varying fields) [read: deep/f4a sec. 6; the deep reader checked with SymPy, I accept it]. - The frequency formula f = f0 sqrt(1 - v^2/c^2) is shown only for electronic states; Su admits it is assumed for hyperfine and nuclear (Mossbauer) transitions, and that spin cannot be treated [read: deep/f6, deep/f7]. The Cs and H-maser clocks used for Hafele-Keating and GPS are hyperfine clocks, so for them the formula is an expectation. - Compton paper (f8c): the algebra is correct, but the derivation inserts the electron's final energy and momentum through the de Broglie relations with free v, and the sum rules (omega_s = omega_i - (omega - omega0), k_s = k_i - k) are exactly Compton's energy and momentum balances; same unknowns, same number of equations [calc, read: deep/f8c sec. 5]. So it re-derives rather than replaces conservation. The one new element, a weak "direct radiation" at wavelength lambda_C/(gamma - 1), is 2 to 7 nm for 70 pm X-rays at 45 to 180 deg [calc, read: deep/f8c]; no intensity is given, so it is not a usable prediction. - f8b (neutron interferometer): the rotation phase 2 m omega_E.S/hbar and the gravity phase follow algebraically from "reflection off a moving lattice" (checked symbolically by the deep reader); unstated assumptions include omission of an energy (frequency) term at moving-lattice collisions and fixed path vectors.

b. Consistent with established experiments. The numbers reproduced are the standard SR/GR numbers: Hafele-Keating (-40 and +275 ns; these are HK's own predictions, not an independent calculation by Su) [read: deep/f6], GPS clock offset 4.45e-10 [read: deep/f6], Ives-Stilwell (0.36 percent self-consistency, equally SR), ammonia maser null, Mossbauer rotor at second order (omega^2 (r_a^2 - r_s^2)/2c^2), Sagnac and COW phases [read: deep/f7, f8a, f8b]. The Mossbauer references Su cites as having "demonstrated" the rotor formula include first-order drift null tests (Champeney et al.) that do not test the (v_r^2 - v_t^2) dependence, per the deep reader's memory (medium/low, unverified). Kundig, the best rotor test, is not cited.

c. Tested? Not as distinguishing claims. Su's distinguishing predictions here: - East-west dependence of neutron Bragg angle (about 1.4 deg between two symmetric orientations, f8a). Su compared it with Staudenmann et al. (1980): "the agreement is not good quantitatively" [read: deep/f8a]. My reading of the deep reader's numbers: with Su's stated zero of the rotation scale the measured asymmetry has the opposite sign; with the opposite zero it matches; and the only zero-independent quantity (the separation 140.49 deg) gives theta_B = 19.755 deg, matching the standard 19.761 deg [calc, read: deep/f8a sec. 3.3]. The wavelength 1.134 angstrom may itself have been derived from those same readings under the standard law, which would make the comparison circular (inference). So: a testable prediction; the one test Su cites is inconclusive and Su himself says it fits poorly; a decisive test needs an independent wavelength and a known zero. - Third-order Mossbauer-rotor orientation anisotropy about 1e-18 [calc: 1.4e-18 to 2.7e-18], five orders below the Fe-57 line width: not feasible with Mossbauer precision [read: deep/f7 sec. 6a]. - Constant -11.5 Hz offset at 2.3 GHz in interplanetary links: arithmetic correct (30 km/s, 2.3 GHz); Su says the existing data cannot test it (fitted oscillator bias absorbs a constant) [read: deep/f6]. The paper also does not say how the Sun's potential at the ground clock is handled, so the full predicted offset is ambiguous. - Turntable one-way link: sinusoid in the phase at the turntable rate (f3a eq. 33; EPJC eq. 31, 0.14 deg for 10 GHz over 10 m). This depends entirely on clock transport: in SR slowly carried clocks pick up compensating offsets and the effect reduces to a Sagnac term of order omega_E d^2/c^2. The paper does not discuss synchronisation [read: deep/f3a sec. 4.2, deep/EPJC sec. g]. A genuine difference exists only if the oscillators at both ends are rotated with the table; not yet tested.

d. What would have to change. Special relativity's principle that there is no preferred inertial frame; the Lorentz transformation of space and time would be replaced by a Galilean one plus frame-tied physics for matter. Concretely, the mass-energy relations would have to be frame-dependent in the ECI sense, with measurable consequences at 1e-12 to 1e-18 in the places above.

Verdict, claim 3 - Algebra from the postulated wave equation to the de Broglie and Lorentz-factor relations: Established (as algebra, equal to Klein-Gordon/SR with the frame relabelled). - "Mass is a frequency, origin of inertia, identity of gravitational and inertial mass derived": Not testable as stated (calibration/postulate; no measurable difference). - Distinguishing predictions (Bragg east-west anisotropy; rotor third order; -11.5 Hz; turntable link): Never properly tested. The one data comparison (Staudenmann) is, by Su's own words, quantitatively poor and by the deep reader's analysis is within a zero-offset ambiguity. - Compton reinterpretation: Not testable as stated (conservation laws are inserted through the same relations, the single new prediction has no intensity).

Claim 4. Magnetism can be Galilean (augmented-potential force law)

a. Internal consistency. The algebra of the reduction is right: eqs. 12-13 and 21-22 of f2a, and the Lagrange-type law, which is the Euler-Lagrange equation for a Weber/Riemann-type velocity-dependent potential (1/R times (1 + relative speed^2/2c^2)). I checked the deep reader's identities [read: deep/f2a sec. 4, 5, 6; calc]. For two point charges in the instantaneous limit the third law holds (momentum conserved) [read: deep/f2a sec. 8]. Weak points: - Frame independence by labelling. Every velocity, derivative and position is defined relative to a named physical object (ether, matrix, effector), so no observer change can alter it. That is not form-invariance of equations under a Galilean boost. In the quasi-static limit the retardation drops out and the law genuinely depends only on relative velocities [read: deep/f4a sec. 11], which is the correct statement. - The "hidden restrictions" claim. Su says the Lorentz law holds only if the matrix frame is the lab frame, speeds are low, drift speed is very low and the Sagnac term is omitted. At first order this is the known magnetic limit of electrodynamics (Le Bellac and Levy-Leblond, 1973 [memory, medium; cited by the deep reader]), in which a moving magnet produces a lab electric field E = -u x B so the net force on a charge depends on velocity relative to the magnet. For a neutral wire both agree [calc: a stationary charge near a magnet moving at u feels q E = -q u x B = q (0 - u) x B]. So the claim that the Lorentz law is "only valid under hidden restrictions" is true of the low-speed limit of the Lorentz law with the fields held fixed between frames; it is not a discovery that the Lorentz law fails. - Gauge and absolute potential. The augmented vector potential contains -v_em Phi/c^2 (f2a eq. 13). Phi is the retarded integral of the charge density with zero at infinity, so the force law is not invariant under Phi -> Phi + constant: the term F3 acts as an acceleration-dependent change of inertia, effective mass m0 - q Phi/c^2 [read: deep/f2a sec. 9; calc: |q Phi|/m0c^2 = 0.196 for an electron at 100 kV]. In ordinary electrodynamics only potential differences matter. Su's escape is the neutralisation assumption (Phi approximately 0 inside neutral matter) and the order-of-magnitude argument v/c << 1, but at accelerator voltages the correction is not small and the paper does not say what sets the zero of Phi for a laboratory on a charged Earth. - Asymmetric approximations. The low-speed reduction treats source drift (v_sm "<<< c") and effector speed (v_em "<< c") differently, and the reaction on the yoke is never computed, so the paper's headline reduction (the Lorentz-like force on the beam) and its third-law claim rest on different approximations [read: deep/f2a sec. 8]. - Non-Hermitian operator ordering in the quantum derivation (see claim 3), and the use of expectation values of the effector's own momentum inside the "potential" (Su acknowledges these potentials "tend to be different for different effectors"). - Moving-medium (Fresnel drag). Derivation correct to first order (verified, section 2). Drag in a purely magnetic moving medium is zero in Su's model but is the standard SR first-order drag with n^2 = mu/mu0 [read: deep/f3a sec. 3.5; memory, high]. Su gives no experiment on it. Equation (9) of f3a (the electric wave equation) is used with the unstated uniformity assumption noted above. - Barnett experiment (Investigator, f2d). I read it. Su derives that with a long rotating solenoid and the capacitor inside, induction vanishes (as Barnett and Kennard observed), and that with the capacitor outside or a short solenoid it does not. The derivation uses the general force form (eqs. 13-14), explicitly noting that the vector-potential form is "not applicable" when the matrix velocity is non-uniform [read: f2d sec. 3]. The result V = (mu0 I/4 pi) integral (v_em . dl')/R is then reduced by symmetry. I could not check the geometry-specific outcome (the paper's later sections) beyond the structure; it is a testable, quantitative new prediction, and the paper gives no sizes. [read: f2d sec. 2-3] - Riemann force law (Investigator, f2c): not read in full; the abstract says the relative-speed law matches the Lorentz law for quasi-static cases and obeys action-reaction. It places Su in the Weber-Riemann tradition. Magnitude and sign of the 1/c^2 term in Su's potential: Su uses (1 + v_es^2/2c^2); a Darwin-type expansion of the Lorentz interaction has -(v1.v2)/(2c^2) plus a (v1.r)(v2.r) term, so the cross term matches only after integrating around closed circuits [calc, memory medium]. I would flag this for the Physicist: for single moving charges (no neutralising matrix) Su's law and the Lorentz/Darwin result may differ at order v^2/c^2 even in the instantaneous limit. That is also where F1 lives.

b. Consistent with established experiments? For neutral currents at low speed: yes by construction. For electrostatic forces on fast electrons it makes a definite prediction F1 = +v_em^2/2c^2 times the electrostatic force (4.6 percent at 25 kV) [calc]. A crossed-field velocity selector would select a speed lower than E/B by 4.3 percent at beta 0.3 [calc]. Su concedes F1 and F3 "could present a problem" at high speed and argues that cyclotron acceleration is by many small passages with no per-passage measurement known to him [read: deep/f2a sec. 10]. Bertozzi (1964) did measure the kinetic energy of electrons accelerated through a known potential up to 15 MeV (calorimetry plus time of flight) and found agreement with relativity [web: https://en.wikipedia.org/wiki/Tests_of_relativistic_energy_and_momentum, search summary; not the original paper]. Whether Su's tentative high-speed extension of eq. 26 conflicts with this is not settled in Su's paper; his own text restricts the force law to low speed and calls the high-speed extension tentative. I leave the full comparison to the Physicist.

c. Tested? Not as a distinguishing claim; the one explicit disagreement Su names (F2: a force on a charge at rest next to a neutral loop with steady current, size v_sm^2/c^2, about 7e-8 V/m at 1 cm from a 10 A copper wire [calc by deep reader]) is far below any measurement and unmeasured. Barnett-type short-solenoid induction: no replication or test on record in the review files.

d. What would have to change. The Lorentz force law would be replaced by an ether-frame-dependent law. Mainstream view: not required, since SR gives the low-speed magnetic limit already.

Verdict, claim 4 - Low-speed reduction to F = q(E + v_em x B): Established (as agreement with the standard magnetic limit; algebra correct). - Claim that "the Lorentz law holds only under hidden restrictions": Not testable as stated (equivalent predictions in those regimes). - Extra terms (F1, F2, F3), frame-dependent inertia, Barnett short-solenoid induction, magnetic-medium no-drag: Never properly tested (F1/F3 are in tension with high-energy electron work at high speed, which Su acknowledges and which I rate Refuted by calculation in outline only if the tentative high-speed form is taken seriously; I do not so rule because Su restricts the law to low speed). - Gauge dependence of the full law (absolute potential): a mathematical defect, Internally inconsistent with gauge invariance of electrodynamics (the force depends on the zero of Phi). I mark this as a defect of the full (not the reduced) law.

Claim 5. The model makes testable predictions that differ from relativity

a. The predictions follow from the formulas as stated, with arithmetic correct (list in section 2). Hidden assumptions: all depend on frame-tied velocities (ECI), absolute simultaneity for one-way links, and for the Bragg and rotor items on first-order terms in v0/vp being kept. b/c. Each prediction, its status:

The Investigator's lead (Marsen 2019) proposes a Michelson-Morley experiment in low Earth orbit (about 7.6 km/s) and in solar orbit (about 30 km/s). In Su's model the cavity quadrupole scales as v^2/2c^2: 3.2e-10 in LEO, 5e-9 at 30 km/s [calc], about 450 and 7000 times the ground value. Marsen's readings of Brillet-Hall are his own advocacy reading (Marsen promotes Su's work). The proposal is internally consistent with Su's model and would be a sharp test; I note that Marsen's claim that the 1979 residual "was averaged out" (his words) is not a statement I could check, and that later experiments (above) report the lab-fixed term as a systematic that averages out over a year.

d. SR's second postulate (no preferred frame at any order) and the equivalence of inertial frames for clocks would have to fail at second order, in the ECI frame specifically.

Verdict, claim 5: Never properly tested for most items (several unreachable); for the cavity quadrupole, Tested, not supported (provisional) per the 2009 rotating-cavity data, to be confirmed by the Physicist and Contrarian. Mathematically each prediction is derived correctly from the postulates; the postulates are the issue.

Claim 6. Gravity-as-potential explains discordant quasar redshifts

a. Internal consistency. The algebra is correct: z = sqrt(1 + 2 Phi_g/c^2) - 1; the halving rule scales Phi by 2^(-2/3) and gives eq. 11; Karlsson's 1.227 spacing is ln = 0.2046; the 14 predicted values reproduce [read: deep/f5c sec. 3, 6; calc]. But: - Newtonian potential used at Phi_g/c^2 = 4.2. GM/(R c^2) = 4.3 means the Newtonian escape speed is 2.9 c [calc]. A Newtonian formula Phi = GM/R, derived for weak fields (n_g - 1 << 1), is applied far outside its range. The model's index n_g = 1 + 2 Phi/c^2 is weak-field by construction (f5a: "Phi_g/c^2 << 1"), and Su's redshift formula (his eq. 9) is a different function from GR's 1/sqrt(1 - 2GM/rc^2) (finite where GR diverges). At Phi/c^2 = 4.2 the choice of function decides the answer, and nothing in the paper tests it in the strong-field regime [read: deep/f5c sec. 3, 5]. - Free parameters. The density (6e-11 kg/m^3) is chosen, not measured, and Su says "a slight adjustment in the size or density" fixes any residual. At D = 1000 ly, z = 2.058; at D = 1018 ly, z = 2.108 [calc]. So the computed 2.07 versus observed 2.114 is a fit, not a prediction [read: deep/f5c sec. 4]. The 0.7 arcsec size is Su's estimate from an image. - Stability. The cloud has a free-fall time of about 270 years and a mass of about 1.4e16 solar masses (2.8e46 kg), about 2.7e4 times Su's own figure for the Milky Way [calc]. The paper gives no pressure or rotation support and answers the classic "gravitational implosion" objection only by saying the surface gravity (below 1 percent of Earth's) is small. Surface gravity small and potential large is arithmetically consistent, but a cloud whose escape speed is about 3 c has no Newtonian equilibrium and Su offers no relativistic one. - Preferred values. The fragmentation series (z0 = 1.956 taken from Karlsson as input) gives nine values between 1.96 and 0.06 where Karlsson has five; they agree at n = -1 to 2 only. The Karlsson 0.60 peak is absent and explained as a merger of 0.71 and 0.49; three "new" values 0.22, 0.14, 0.09 have no cited data [read: deep/f5c sec. 6]. A fit with an adjustable ratio and an input seed will always overlap a handful of peaks. - Observational basis. The paper cites Arp, Burbidge and collaborators for physical associations; the Gutierrez et al. results it cites as supporting an abrupt redshift change "may be viewed instead as evidence for the projection effect", as Su himself notes [read: deep/f5c item 12]. I record that evidence as Su states it; the physical association of quasars with low-redshift galaxies is a contested observational question for the Physicist and Contrarian, not for me.

b/c. No quantitative comparison with a redshift survey is made. Karlsson periodicity itself is contested in the literature [memory, medium; not web-checked here]. No test by others of Su's mechanism is on record in the review files. d. If the formula held for quasars, the standard cosmological redshift interpretation of high-z quasars would fail for that subset, and the potential well of an object of 1e16 solar masses would need a stable structure, none known.

Verdict, claim 6: Plausible, untested is too generous because of the stability and strong-field problems. I split it: the algebra is Established as arithmetic; the physical mechanism (a gas cloud with Phi_g/c^2 about 4, escape speed about 3 c, stable for cosmic times) is Internally inconsistent with the paper's own weak-field premises (Newtonian potential at Phi/c^2 = 4.2; n_g derived for Phi/c^2 << 1), and the preferred-value agreement is Never properly tested (a fitted seed, no survey comparison, no citation for the new peaks).

4. Investigator's findings I weighed (kept in the record whatever the verdict)

Priority 1, the inventor's own work: - EPL 56, 170 (2001) (f1b, read): contains the classical-ether round-trip formula (correct) and the argument that the orbital term is absent; the rotational second-order term is "too small to observe". The key step ("the propagation mechanism in the Michelson-Morley experiment in no way can be different from that in GPS") is an assumption of uniform mechanism, not a derivation. - Barnett (f2d, read): new prediction, unsized, not tested. - Riemann/Lorentz (f2c), AP-S 2001 digests (f2b, f3b), physics/0208083 (f4b): not read in depth; I rely on abstracts. The Schrodinger-equation paper claims the derived equation is "substantially identical to Schrodinger's equation incorporating the vector potential if the latter is observed in the atom frame" [read: Investigator note]: consistent with the frame-labelling reading of Galilean invariance above. - Not obtained: the railgun paper (IEEE Trans. Magn. 42, 2193, 2006), Eur. J. Phys. 22 explicit definitions, JEWA 15, 945 (Sagnac), Electron. Lett. 36 (radar Doppler), and the book.

Priority 2, support by others: - Gift (2021), Applied Physics Research: argues from GPS timing that light speed is constant in the ECI frame and calls Su's nested ethers "a reasonable working hypothesis". Gift is himself a proponent of preferred-frame readings of GPS; this is his characterisation, and it rests on the same ECI-frame formulas which SR reproduces. I did not read the whole paper. - Marsen (2019, 2021): advocacy; proposes orbital Michelson-Morley tests; reads the Brillet-Hall residual as a positive signal. Marsen is the single source for Su's death c.2007 (see below). - Engineering citations of the EPL formulation (TWSTFT, GNSS handbook, SAR synchronisation, 2015 to 2025): uses unknown; likely the ECI-frame Sagnac correction, not the ether interpretation (unread).

Priority 3, related work: Beckmann (1986, Galilean Electrodynamics); Field (2019, IJMPA) and Kipreos (2024, IJMPA), mainstream-journal discussions of preferred-frame and differential-simultaneity assumptions that cite Su; Marsen's "Tron Theory". The existence of this related work shows the preferred-frame idea has had a continuing, small, published literature. Field and Kipreos not read.

Priority 4, the historical record (absence of evidence): Su's record stops in 2006 (Crossref, arXiv, Wayback). Marsen says he died c.2007; no obituary found; the book appeared from NTHU Press in March 2008 (ISBN registered 2005). For the mathematical review the relevance is that no response from Su exists to any criticism and no Comment or Reply was found on his EPJC or EPL papers; the competing explanations (death, illness, withdrawal after limited reception) are recorded in sites.md and cannot be decided by mathematics.

5. Summary of the mathematics

• Where Su is correct: ECI-frame first-order Sagnac and Fresnel-drag algebra; Weber/Riemann-type force law reduction to the Lorentz force at low speed; GPS clock arithmetic; Shapiro and deflection integrals; Klein-Gordon algebra.
• Where he is calibrating, not deriving: m0 = hbar omega0/c^2; the identity of gravitational and inertial mass; the operator U; "mass from frequency".
• Where the mathematics is not self-consistent or is outside its range: gauge-dependence of the full force law; non-Hermitian ordering; Newtonian potential at Phi/c^2 = 4.2 in the quasar paper; unsolved annual aberration; one-way clock synchronisation unspecified.
• Where an actual experiment bears on it: the cavity quadrupole (provisional exclusion), Bragg east-west anisotropy (one poor comparison), fast-electron electrostatics (tension, not settled), and the many predictions below any feasible precision.

6. Verdicts

Open items for the arbiter: (1) read Herrmann et al. 2009 Table and figures for lab-fixed 2 omega_table amplitudes and decide whether Su's quadrupole is excluded; (2) obtain Brillet-Hall 1979 for the phase and amplitude of the 17 Hz term; (3) a one-way-link test with synchronised oscillators on a rotor would settle the clock-transport difference between Su and SR; (4) check F1/F3 against the velocity-selector and linac literature if the high-speed extension is to be taken seriously.