Distinti Robert: PhD mathematician review (Step 2)

Reviewer role: checks derivations, notation, units and hidden assumptions. Inputs: facts.json, claims.md (verified against the PDFs), plus my own calculations (scripts in the session scratchpad, results quoted below).

Source gap (repeated from Step 1)

All ten PDFs have a text layer. I read the key derivations myself: ne.pdf section 6 (BMP), the_secrets_of_qvxb.pdf (full), ng.pdf section 6 (derivation, plus page image p.14 [read: page image p.14]), ne_hydrogen.pdf sections 2-5, anomolies.pdf items 1, 7, 17-20 (page image p.17), nm.pdf chapter 10 (corner effect), neThesis.pdf abstract, chapter 6 and Tables 8-4/8-5, paradox2.pdf in full. NOT read: nm.pdf chapters 4-9, nia1.pdf derivations, the dipole-antenna derivation, and the cited-but-absent papers (displacement_dilemma.pdf, ni.pdf, homopolar.pdf, ind_jackson.pdf, ron.pdf). The Paradox 2 raw data and any independent replication are absent. Conclusions about independent testing rest on absence of evidence in the folder, not on a search of the literature.

Corrections to Step 1

1. ng.pdf time-dilation formula: Step 1 said the paper's gravitational factor has "no square root" (facts.json ng.pdf summary). Wrong. The page image shows Dilation = sqrt(1 - 2K_G M/(r C^2)) [read: page image p.14]. The text layer drops the radical. This matters: the factor then equals the exact Schwarzschild static-clock factor, not a first-order approximation.
2. nm.pdf corner formula: facts.json writes E = K_M I V_S^2 / h. The page image (anomolies.pdf p.17) and nm.pdf step 16 give E = K_M I_S V_S sqrt(2) (-1/h) a_x, one power of V_S, with the sqrt(2) lost by the text layer. The squared version is dimensionally wrong (T m^2/s^2, not V/m); the printed version is dimensionally fine. Also nm.pdf says the impulse is a_S t = V_S sqrt(2) [read].
3. claims.md claim 2 writes the NM law with (v_T.r), (v_S.r), r (no hats). The papers use unit vector r-hat. Without hats the expression is dimensionally inconsistent. Use r-hat.
4. claims.md claim 3 lists "the Paradox 2 disk generator makes DC power with no net flux linked or cut". That is the author's assertion, not an established property of the device; see the calculation under Claim 3.
5. facts.json ne_hydrogen: Step 1's note is right that the 1.0000 g/mol comparison value is wrong. Confirmed [web] https://physics.nist.gov/cgi-bin/Compositions/stand_alone.pl?ele=H gives 1H = 1.00782503223 u. Proton radius check [web] https://physics.nist.gov/cgi-bin/cuu/Value?rp gives CODATA 2022 r_p = 8.4075(64)e-16 m (0.84 fm), so Step 1's [memory high] is now [web].
6. Step 1 said the ne.pdf "derivation" of the electron mass from r_e is circular. Confirmed, and it is stronger than stated (see Claim 4).

Common mathematical results used below

(All units: K_E = 1/(4 pi eps0), K_M = mu0/(4 pi), K_E = K_M c^2. A "slow" charge means v << c.)

R1. Textbook induction is already "spherical". The standard law is E = -dA/dt with A = K_M q v / r for a moving source charge (Neumann/quasi-static form, [memory high]; Griffiths ch.7, Jackson ch.5). Differentiating: dA/dt = K_M q [ a/r + v (v.r-hat)/r^2 ] (r-hat from source to target, target at rest). So E = -K_M q a/r (full vector a, no component removed) - K_M q (v.r-hat) v /r^2. The first term is Distinti's New Induction (NI); the second is exactly the term -(v_S.r-hat)v_S that he adds to Biot-Savart to make New Magnetism (NM). So NI + that NM term = textbook -dA/dt.

R2. Numerical check that the "transverse-only" form is NOT textbook. I integrated both forms over two coaxial unit circular loops (script neu.py). Neumann mutual inductance integral oint oint (t.t')/r gives 11.126, 4.941, 1.419 (units K_M x length) at separations 0.5, 1, 2. The transverse-only integral oint oint [t.t' - (t.r-hat)(t'.r-hat)]/r gives 0 (to 1e-17) at all three. It vanishes identically for closed loops because it is -oint oint d^2 r/(dl dl'), a total derivative. So the claim "classical induction removes the longitudinal component" cannot be what textbook circuit theory uses: with it, no loop would have any inductance. Distinti's "classical" is the radiation-zone a_perp part of the Lienard-Wiechert field, not the law used for circuits.

R3. Exact classical field of an accelerated charge. I computed the exact Lienard-Wiechert E for a charge starting at rest with small constant acceleration a (script lw.py, c=1), subtracted the Coulomb field at the present position, and divided by a. Results at r=1: on axis (theta=0 or 180 deg) the remainder is -a/r (matches NI); at theta=90 deg it is -a/(2r) (NI says -a/r); at 45 deg it is (-0.25, -0.75). These fit E_accel = -(K_M q/(2r)) [a + (a.r-hat) r-hat] to 1e-4 (the Darwin form, [memory medium], not web-verified, see "web checks"). So the exact classical O(1/c^2) near field has a longitudinal part, equal to NI on axis, with a different angular dependence elsewhere. NI is neither textbook nor exact-classical off axis.

R4. Dimensions. NI: K_M Q^2 a / r has units of (N s^2/C^2)(C^2)(m/s^2)/m = N. OK. NM: K_M Q^2 v^2 / r^2 = N. OK.

---

Claim 1: New Induction, F = -K_M Q_S Q_T a_S / r

a. Internal consistency. As an algebraic law it is dimensionally fine (R4). Two structural problems. (i) Newton's third law: F on T is proportional to a_S, F on S is proportional to a_T; these are not equal and opposite unless a_S = -a_T, so momentum is not conserved by NI alone for two charges (in classical theory the missing momentum is in the field; Darwin's form removes this at O(1/c^2) via a velocity-dependent momentum). Distinti's papers do not discuss this. (ii) The law is instantaneous (no retardation), but ne.pdf lists "field changes propagate radially (retarded)" as a rule of the theory, and section 6 admits the BMP "requires electromagnetic fields to travel much faster than the speed of light". The theory therefore contradicts its own propagation rule when used in section 6.

b. Experimental consistency. Where NI is used for closed circuits (thesis), it reduces to Neumann's formula (R1/R2; thesis eq. 6-1 is L = K_M/(HW)^2 oint oint dL_m.dL_n / r [read: neThesis.pdf ch.6]), so it agrees with every inductance measurement that Neumann's formula agrees with. For a single accelerated charge, R3 shows NI matches the exact classical field only on the acceleration axis, and is a factor 2 off at 90 deg. I know of no measurement that distinguishes these; none is cited by the author.

c. Tested? The only tests in the folder are the 32 inductance measurements in the thesis (Fairfield University M.S., advisors named in the thesis), average absolute error 1.9% (std 1.3%) without a ground plane, 4.1% (3.3%) with one [read: neThesis.pdf Tables 8-4, 8-5 and Figs 8-13/8-14]. Fitted slopes are 0.9874 and 0.9393, i.e. a systematic offset, larger with the plane. These test the Neumann integral, not NI-versus-classical. No independent replication in the folder; no comparison against partial inductance or a field solver on the same traces was in the sections I read.

d. If true. Nothing in the closed-circuit regime would change, since the formula coincides with Neumann. A genuinely different single-charge force would require revising the Lienard-Wiechert/Darwin results, which are derived from Maxwell's equations and tested through radiation and near-field measurements ([memory high]).

Verdict: Split. Weak form (NI equals the quasi-static induction law for closed circuits): Established, but it is a restatement of Neumann/Faraday, not new. Strong form (the textbook law is "transverse only" and NI corrects it): Internally inconsistent with its own premise, because the textbook law is already the full-vector form (R1, R2). Single-charge angular form: Refuted by calculation (R3), off by factor 2 at 90 deg from the exact classical field; no experiment needed.

Claim 2: New Magnetism, spherical force replacing Biot-Savart/Lorentz

a. Internal consistency. Source passage [read: the_secrets_of_qvxb.pdf pp.3-7]. Steps 1-7 reproduce Biot-Savart plus F = Q_T v_T x B, giving K_M Q_S Q_T/r^2 [(v_T.r-hat)v_S - (v_S.v_T) r-hat]. This is correct and is textbook (BAC-CAB identity). The author then says "a third term is added to the equation" to account for the effect of moving the source toward a stationary target: -(v_S.r-hat)v_S. It is added by hand, "to account for this known effect in a manner consistent with experiment". By R1 that term is the convective part of -dA/dt, which classical theory already contains as part of Faraday induction (it is the same as the motional/transformer emf that a moving source induces). So the NM law is not a new law; it is the textbook Lorentz force on a moving charge plus the textbook induced field of a moving source, written as one force. Other problems: (i) Section 3 "dogmatic" expansion obtains an extra +v_S^2 r-hat term, which the author then discards without a derivation, noting it would conflict with experiment. (ii) The wording "no relative motion" is misleading. In section 2.1 the author sums Coulomb and the parallel-motion term for two charges moving side by side and gets F = (Q Q/4 pi eps r^2)(1 - v^2/c^2) [read]. This is the standard lab-frame result with one slip: the Coulomb field of a moving charge at transverse separation is gamma times the static value, so the exact transverse force is gamma(1 - v^2/c^2) = 1/gamma times the static value. At low v the paper's expression and the correct one agree to O(v^2/c^2); at the "v approaches c" extrapolation the author draws conclusions from, they differ. (iii) Nothing is Galilean or Lorentz covariant in NM; at O(v^2/c^2) it is not invariant, and the paper does not claim a transformation law.

b. Experimental consistency. For closed steady currents NM reduces to Biot-Savart/Ampere (author's own statement in section 2.2: net force on a stationary charge is zero). So it agrees with the well-tested magnetostatics (the ampere force between wires, mass spectrometers; [memory high], not individually cited). The claimed extra novelty (force without relative motion) is explained by relativity: in the lab frame the magnetic attraction partly cancels Coulomb repulsion; in the co-moving frame there is no magnetic force and the Coulomb force is the whole story. Both frames agree [memory high, standard special relativity, Purcell ch.5]. The B field is frame-dependent, so "static B is a contradiction in terms" is not a contradiction in the mainstream view.

c. Tested? No test distinguishing NM from Lorentz is in the folder. The homopolar and corner "tests" are discussed under Claim 3.

d. If true. If B, flux lines and the Lorentz force were obsolete, the experiments behind the Lorentz force (cyclotron/synchrotron orbits, mass spectrometry, particle accelerators) would need a different explanation; but NM reproduces the Lorentz force in the cases above so nothing would actually need to change for them. The conflicts occur only in the added -(v_S.r-hat)v_S term, which is a transformer-emf term already present classically.

Verdict: Split. NM = Lorentz + Biot-Savart (terms 1 and 3): Established (not new). Added term 2: Established as already part of Faraday induction (R1); its use as proof that the classical field is wrong: Internally inconsistent (the author compares against a truncated "classical" law). "B, flux lines, cutting/linking are obsolete": Not testable as stated (an interpretive claim: NM and Lorentz make the same predictions in the cases examined).

Claim 3: Classical electromagnetism is anomalous

Sub-claims examined, in order.

3a. Self-inductance undefined / "Level 5 Test" (anomolies.pdf item 1). A single-turn loop of thin wire has a log-divergent self-inductance for zero wire radius, a well-known and well-understood feature: for wire radius a and loop radius P, L ~ mu0 P [ln(8P/a) - 2] [memory high; Jackson problem; Landau-Lifshitz ECM sec.33], finite for any real wire. A finite answer needs the wire radius; this is a regularisation, not an inconsistency. The thesis does the same ("seed" size; eq. 6-1 diverges as the seed shrinks, as the author concedes [read]). Verdict for 3a: Established as a mathematical idealisation limitation of the classical theory, not an inconsistency; the same is true of NE.

3b. Corner emf "hot spot" (anomolies.pdf item 7; nm.pdf ch.10). The "classical" calculation uses the transverse form F = -K_M Q (a - (a.r-hat)r-hat)/r applied to the centripetal acceleration of carriers rounding a sharp corner, giving E = K_M I V_S sqrt(2)/h (dimensionally correct). Magnitude: I = 1 A, V_S = 7e-5 m/s (copper drift speed, [memory medium] for a 1 mm^2 wire), h = 1 cm gives about 1e-9 V/m, orders of magnitude below any measurement in the folder. But the more important point is that it is not what classical theory predicts. For a steady current the vector potential A is time independent, so E = -dA/dt = 0 everywhere, with no exception at corners (stationary distribution of carriers). I verified numerically on a unit square loop with a test point at h = 0.1 and 0.01 above a corner (script corner.py): the sum of the four corner impulse terms (full-vector NI) is (9.29, 9.29, 0) and (99.3, 99.3, 0) in units K_M I V; the convective term (the second NM term) integrated along the four straight sides is the negative of this to 6 digits; the total is 2e-9 and 2e-6 (discretisation error). Analytically, oint d(t-hat/r) = 0 for a closed loop. In other words, the cancellation the author takes as "proof of the spherical field" is a total-derivative identity that holds whenever E = -dA/dt is used, and any force law of the form -dA/dt (including the textbook one) satisfies it. The hot spot appears only if one keeps the acceleration term and drops the convective term. The "proof" therefore cannot discriminate spherical from toroidal fields. Appendix A's "corner effect transformer" is described as a device "which does not work"; no data in the sampled pages.

3c. Antenna patterns. Classical Maxwell theory gives the half-wave dipole pattern cos(pi/2 cos th)/sin th, which agrees with measurement ([memory high], standard antenna texts; not re-checked on the web). Claimed NI improvement is in nia1.pdf, which I did not read beyond the summary; no data tables for it were in the sections read. Not verified.

3d. curl H = 2J. The derivation is in displacement_dilemma.pdf, which is absent. My check: for a slow point charge, Biot-Savart B = curl A with A = K_M q v/r. Then curl B = grad(div A) - laplacian A = grad(div A) + mu0 q v delta^3(r - r_q). With div A = -K_M q (v.r-hat)/r^2 and phi = K_E q/r one finds grad(div A) = mu0 eps0 dE_c/dt (E_c the Coulomb field of the moving charge). So curl B = mu0 [J + eps0 dE/dt], with J counted once. No factor 2 arises. Not a verified refutation of the missing derivation (I cannot see it), but with the stated premises (real charge distribution, Maxwell's equation) the claim is contradicted by this calculation. I suspect a double count of the delta-function current and the local part of the displacement current (a 1/3-type delta term in the ball average of E), but that is a guess.

3e. Homopolar generator and Paradox 2. Calculation (the author gives no classical estimate; I supply one). The flux rule is a shortcut valid for closed loops of fixed material; it fails for sliding contacts (Feynman, Lectures vol. II, sec. 17-2, [memory high]; web check failed, 403). The correct classical tool is the Lorentz force on charges in each segment, emf = integral (v x B).dl taken along the circuit with v the lab-frame velocity of each material element and B the lab-frame field. For a brush arm rotating with the rotor through a magnet's field: v = omega r phi-hat, B = B_z z-hat, v x B = omega r B_z r-hat, so a radial arm over a magnet contributes omega integral B_z r dr. In Paradox 2 the path goes outward over the N-up magnet (B_z > 0, dl along +r), through the stationary ring (v = 0, no emf), and inward over the S-up magnet (B_z < 0, dl along -r): both terms have the same sign, so they ADD. This predicts, qualitatively, every observation in paradox2.pdf: no magnets gives zero; opposite polarities gives a DC emf; reversed rotation reverses sign (emf is linear in omega); both North-up gives (nearly) cancellation (outward over +B, inward over +B); one magnet gives about half. Order of magnitude: the magnets are 1.125 in (28.6 mm) in diameter [read: paradox2.pdf p.17]. Take B_z ~ 0.1 T along the arm (assumed, not stated), arm span 28.6 mm at radius ~40 mm (assumed): emf per magnet ~ omega x 1.1e-4 V. The rotor speed is not given (toy gearmotor on a 6 V cell); at omega ~ 1.6 rad/s (about 0.25 rev/s) this is ~180 microvolts per magnet, the same order as the reported 150-180 microvolts. These inputs are assumptions, so this is a plausibility estimate; it shows the observation does not need new physics, not that the reading is exactly predicted. Because the author's classical analysis ("from the top/side": counting flux lines through areas A, B, D) uses the flux rule on a circuit with sliding brushes, the conclusion "no classical explanation" is not established. Further weaknesses: no rotor speed, no field map, no uncertainty analysis, no replication, a 10 kohm load, a 1 Hz low-pass filter and a x1000 amplifier read by a scope at 100 uV/div (so thermal and brush-contact drift of tens of microvolts is not excluded; only an 8 microvolt Seebeck argument is given), and the "one magnet" cases differ from "half" by factors of 4.5 (20 uV) and 2 (80-90 uV), explained by rotor grinding.

The homopolar disk in the_secrets_of_qvxb.pdf (section 2.3): the mainstream explanation is that the emf is the Lorentz force on charges in the rotating disk, whose velocity relative to the lab frame is omega r irrespective of whether the magnet rotates, given a (cylindrically symmetric) magnet whose rotation does not change the field. This is exactly the author's own "better explanation" in section 2.3, i.e. the Lorentz force gives the answer he wants; he presents it as a consequence of NM's "parallel motion" term, but the physics used is the ordinary v x B on the disk.

3f. "curl H = J only valid for infinitely long currents" (item 20). Ampere's law in integral form for a closed path is general in magnetostatics; the point form curl B = mu0 J holds for any steady current distribution (derived above by R1-style vector calculus, Griffiths sec.5.3). Not a valid objection [memory high; derivation standard].

a-d summary for Claim 3. a. Math: the classical side is mis-stated (3b, 3e), the 2J claim contradicts a short calculation (3d). b. Experimental: all known classical results stand; the single experiment (Paradox 2) is consistent with the Lorentz force (3e). c. Tested: only by the author; no replication; no independent evaluation in the folder. d. If true: Faraday's law, Maxwell's equations and the Lorentz force would be wrong in a regime accessible with a 1.125 in magnet and a toy motor, which implies a century of motor/generator engineering is mis-modelled.

Verdict: Split. Self-inductance infinity of an ideal filament: Established as a known idealisation. Corner emf as a classical prediction: Refuted by calculation (R1 and the numerical total-derivative check). curl H = 2J: Refuted by calculation under the stated premises (3d), with the caveat that the author's derivation is not in the folder. Paradox 2: Never properly tested (no independent test, no quantitative model; consistent with the ordinary Lorentz force by estimate, so "anomalous" is not established); it was not dismissed by a test either: I found no record of a response in the folder. Antenna anomaly: Not verified (source not read).

Claim 4: Mass and energy from charge (BMP)

a. Internal consistency. Source passage [read: ne.pdf section 6.1]. Force balance, with S and T diametrically opposite on a circle of radius r_P (separation r = 2 r_P), source charges Q, orbit speed V_t: Coulomb K_E Q^2/(2 r_P)^2 repulsive; NM term K_M Q^2 V_t^2/(2 r_P)^2 repulsive (I checked the vector algebra: v_S = V_t y-hat, v_T = -V_t y-hat, r-hat along x gives +V_t^2 r-hat); NI term K_M Q^2 a/r with a = V_t^2/r_P, which equals K_M Q^2 V_t^2/(2 r_P^2) attractive. Multiply through by 4 r_P^2/Q^2: K_E + K_M V_t^2 - 2 K_M V_t^2 = 0, so V_t^2 = K_E/K_M = c^2. This agrees with the paper's result. The printed equations in the paper (K_E/(2 r_P) + K_M V_t^2/(2 r_P) - K_M V_t^2/r_P) are not the same expressions (they drop the squares of r and a factor Q^2); they have the correct ratios 1:1:2 but wrong powers of r_P (1/r_P^2 required for a force); sloppy notation but not an error in the conclusion. Effective mass: set NI from the partner equal to -M a: M_each = K_M Q^2/(2 r_P), total M = K_M Q^2/r_P [read]. Energy: KE = (1/2) M c^2 = K_M Q^2 c^2/(2 r_P); PE = K_E Q^2/(2 r_P) = K_M Q^2 c^2/(2 r_P); sum = M c^2 [read, arithmetic correct]. But E = Mc^2 here is equal parts KE and PE because V_t = c made them equal; it follows from the definition M = K_M Q^2/r_P and K_E = K_M c^2. It is an identity, not a derivation of E = mc^2; no independent definition of M (e.g. by response to a force) is used for the energy, only by NI on the partner charge. The mass-from-radius step is circular: the classical electron radius is defined by r_e = K_E e^2/(m_e c^2) = K_M e^2/m_e, so K_M e^2/r_e = m_e identically. Numerically: 1e-7 x (1.602177e-19)^2/2.817941e-15 = 9.1094e-31 kg [read: ne.pdf p.27; recomputed]. Nothing about the model predicts r_P = r_e; the force balance is independent of r_P, so the model has a free parameter and M can take any value. "A more precise model" with half charges and r_e/4 gives the same M (K_M (e/2)^2/(r_e/4) = K_M e^2/r_e); again no new content. Two inconsistencies with the paper's own premises: (i) charges moving at exactly c, yet the NI, NM and Coulomb forces are the low-velocity O(v^2/c^2) expansions (the author derives NM from Biot-Savart, valid to O(v^2/c^2)), applied at v = c where all orders matter; (ii) instantaneous forces at separation 2 r_P with source speeds c, while the paper's own rule is retarded propagation, and the paper concedes fields must travel faster than c (the retardation angle over the separation is then of order 1 radian). The "binary antimass" (opposite charges, negative M) is the same algebra with signs flipped; a negative inertial mass has no experimental counterpart.

b. Experimental consistency. Electron: scattering shows no structure to far below r_e (about 3e-15 m); the electron is point-like to < 1e-18 m ([memory medium], web check failed, budget exhausted). So the r_P = r_e identification conflicts with data, if r_P is a real size; the author calls the model "hypothetical". The charge-to-mass ratio is measured, not derived. Proton: the same formula with the proton mass gives r_P = K_M e^2/m_p = r_e m_e/m_p = 1.5347e-18 m (recomputed: 2.81794e-15/1836.15 = 1.5347e-18) [read]. The measured proton rms charge radius is 8.4075(64)e-16 m [web: https://physics.nist.gov/cgi-bin/cuu/Value?rp, CODATA 2022], about 5.5e2 times larger than the "BMP radius" 1.5e-18 (1.5e-18 vs 8.4e-16: ratio 548). Step 1 wrote "500,000 times"; that figure is wrong. 8.4075e-16/1.5347e-18 = 547.8. Correction: the discrepancy is a factor of about 550, not 500,000. The model also assigns the proton a charge e and the same force law, so no quark substructure; the proton has measured internal structure (deep inelastic scattering, [memory high]). Hydrogen: M_H = K_M e^2 (1/r_P - 7/r_e) = m_p - 7 m_e. Verified: 1.67262e-27 - 7 x 9.10938e-31 = 1.66624e-27 kg, times N_A x 1000 gives 1.00344 g/mol [read, recomputed]. The sign counting is arithmetic: 4 charges, 12 interactions: ++ pair 1/(2 r_P), -- pair 1/(2 r_e), four unlike pairs -4/r_e at separation ~r_e (the paper neglects r_P in r_e +/- r_P), total 2 K_M e^2 [1/(2 r_P) + 1/(2 r_e) - 4/r_e] = K_M e^2 [1/r_P - 7/r_e]. But since K_M e^2/r_P = m_p and K_M e^2/r_e = m_e by construction, "predicting" the hydrogen mass is the identity m_p - 7 m_e: nothing is predicted. The comparison value "1.0000 g/mol" is wrong. The 1H atomic mass is 1.00782503223 u [web: https://physics.nist.gov/cgi-bin/Compositions/stand_alone.pl?ele=H], and the hydrogen atom is m_p + m_e - 13.6 eV/c^2 (binding energy; [memory high]). The model is below the true value by 8 m_e = 0.44%, so the correct comparison is 1.00344 versus 1.00783, an error of 0.44% (4.4e-3), which the paper presents as 0.34% against a wrong reference. The "agreement" is that m_p - 7 m_e differs from m_p + m_e by only 8 electron masses, i.e. 0.4% of m_p, because the electron mass is small. In particular, the paper's reasoning that the periodic-table value (1.00794) is for "isotope mixtures" and that the exact value should be 1.0000 confuses the old chemical scale with a physical constant. The magnetic-moment "radius" argument (section 4.1) treats the nuclear/electron magnetic moments as current loop moment e v r/2 at v = c and gets 3.9e-13 m for the electron; this is a classical-loop model of a quantum spin-1/2 moment (the electron moment is ~one Bohr magneton, mu_B = e hbar/(2 m_e) = 9.27e-24 J/T [memory high]); the result r = 2 mu/(c e) is the reduced Compton wavelength, hbar/(m_e c) = 3.86e-13 m [memory high]. No new size information.

c. Tested? Nothing is tested; the author calls it "hypothetical". No experiment distinguishes it from the standard picture. The one numerical "test" (hydrogen) is an identity against a wrong reference value.

d. If true. The electron and proton would be composed of massless charges orbiting at c, the electron mass would be explained as electromagnetic (this is the old 1900s electromagnetic-mass idea of Abraham/Lorentz, in which m ~ K_E e^2/(r c^2) with a numerical factor depending on the model: 2/3 for a shell, the "4/3 problem"; [memory high]). Mainstream: electron mass comes from the Yukawa coupling to the Higgs field and the proton mass mostly from QCD binding energy (about 99% not from quark masses); [memory high]. The model would also require superluminal field propagation, overturning special relativity.

Verdict: Split. "Two massless like charges at speed c balance at any separation" (given the NE force laws): Plausible, untested in the sense that the algebra is right under its own premises; but the premises violate retardation and are applied outside their validity range (v = c). "M = K_M Q^2/r_P gives the electron mass": Internally inconsistent as a derivation (circular: r_e is defined by it), and the proton "radius" 1.5e-18 m is Tested, not supported by size measurements (factor ~550 below the measured charge radius, 8.4e-16 m). E = Mc^2: an identity of the model (Refuted as a derivation: it follows from the definitions used). Hydrogen 1.0034 g/mol: Refuted by calculation (identity m_p - 7 m_e; true mass 1.00783 u, 0.44% off, and the paper's reference value is wrong).

Claim 5: Gravity is induction in a flowing ether

a. Internal consistency. Source passage [read: ng.pdf sections 5-6, p.14 page image]. Ether acceleration a_P = -K_G M r-hat/r^2 and infall speed v_P = -sqrt(2 K_G M/r) r-hat (equal to the Newtonian escape speed, 11.2 km/s at Earth's surface) are consistent with each other (v dv/dr = a, integrates to v^2 = 2 K_G M/r). This is the Gullstrand-Painleve "river" picture of Schwarzschild spacetime: space flowing at the escape speed ([memory high], Hamilton and Lisle, Am. J. Phys. 2006). In that picture a static observer's clock rate is exactly sqrt(1 - v_flow^2/c^2) = sqrt(1 - 2GM/(r c^2)), which is what the paper obtains by substituting v_P into its time-dilation factor. So the final formula is correct for a static clock (and the Schwarzschild radius r = 2GM/c^2 follows by setting v_P = c), but that is built in by the choice of the escape-speed flow, not derived from NE; any model with that flow field would give it. In the paper's text the factor sqrt(1 - V^2/c^2) arises from the BMP: with axial speed V the NM term adds -K_M V^2/(2 r_P) (I checked the vector algebra: the parallel-motion term gives (V_t^2 - V^2) r-hat), so the balance gives V_t^2 + V^2 = c^2 (correct algebra under NE), and V_t'/V_t = sqrt(1 - V^2/c^2) [read]. This is a ratio of orbital speeds of the model, taken to be the clock rate; period ~ r_P/V_t gives gamma only if r_P is fixed, which the paper postpones to a missing paper ("Ethereal Mechanics"). Inconsistencies: (i) the paper says there are "two factors" (ether speed and a reduced light speed in less-dense ether) that each reduce the clock rate, but the displayed formula contains only one; either the second factor is already in the first (then the explanation is redundant), or it is missing (then the formula is wrong). (ii) The energy: E = K_M Q^2 (c^2 - V^2)/(2 r_P) + K_E Q^2/(2 r_P) = M c^2 - (1/2) M V^2 (checked), adding the translational kinetic energy (1/2) M V^2 gives M c^2 for all V. In special relativity the energy is gamma M c^2, which grows with V; the paper's "constant energy for all V" contradicts relativity, including the time dilation it claims to reproduce, and the effective M = K_M Q^2/r_P is held constant in V whereas relativistic inertia grows with speed. So the framework reproduces the clock-rate factor but not E = gamma m c^2 or p = gamma m v. (iii) NI is a force between charges proportional to the source charge's acceleration; ether particles are said to be "mathematical abstraction" and no charge assigned to them, yet gravity is the NI force from ether acceleration, with a coupling equal to the internal one so that the gravitational force is M a, i.e. equals inertia by construction. The equivalence principle is assumed, not derived. (iv) The ether incompressibility argument (v = -Z/(4 pi R^2), a = -Z^2/(8 pi^2 R^5)) is right for incompressible flow from a sink of strength Z; it is inconsistent with escape-speed infall (v ~ R^(-1/2)); the author concludes the ether is compressible, which merely says the model needs a density profile that is never derived. (v) Collapse beyond c "for BMPs" and the Schwarzschild radius: the radius equals 2GM/c^2 by setting v_P = c; but GR's Schwarzschild radius is the horizon of a vacuum solution; whether a BMP collapses at that speed is an assertion, not a calculation.

b. Experimental consistency. Time dilation and gravitational redshift: the formula matches GR to the order tested (Pound-Rebka, GPS, [memory high]). But the ether claims conflict with experiment in other ways: ether infall at 11.2 km/s at Earth's surface relative to Earth plus an ether wind at the orbital speed (30 km/s) and the Sun's infall at ~620 km/s at the Sun's surface: a locally detectable anisotropy of light speed that tests of Lorentz invariance (Michelson-Morley and later experiments, [memory medium; web check failed]) constrain to tiny levels. The author's escape is that Earth "rides" on the ether (section 3), which just means the ether is dragged with local matter, hence undetectable by that class of tests; the paper gives no quantitative model of the drag. Light faster at altitude is "consistent with Einstein's theories" in coordinate terms only; locally c is constant (GR) [memory medium].

c. Tested? No tests of the ether model itself in the folder. Time dilation/gravitational redshift are tested for GR but not discriminating between GR and this model (which reproduces the static-clock factor by construction). No test of the "faster-than-light work-around".

d. If true. It would replace GR's geometric account by an ether with variable density and flow, retaining only the static-clock factor; moving-body energy and momentum would need to be redone to restore E = gamma m c^2, and the equivalence principle would need an explanation of why NI has the same coupling for ether-induced and internal inertia.

Verdict: Split. Static clock factor sqrt(1 - 2GM/rc^2) and r_S = 2GM/c^2: Established (as GR results; the paper reproduces them by choosing the escape-speed flow, so the derivation adds no independent support: the Gullstrand-Painleve reformulation). Ether/induction mechanism of gravity: Not testable as stated (no stated measurable difference from GR in static fields; the ether is admitted to be a "mathematical abstraction"), and Internally inconsistent in its energy treatment (E = Mc^2 independent of V versus its own time-dilation factor; one-versus-two dilation factors). FTL work-around: Not testable as stated.

Claim 6: Longitudinal EM waves and the engineering payoff

a. Internal consistency. The longitudinal component follows from using the full-vector NI form in the radiation zone. Under Maxwell's equations in vacuum, div E = 0 away from sources forces the free-wave field to be transverse for a plane wave (k . E = 0). A longitudinal component with a 1/r falloff would violate Gauss' law in empty space unless a charge density is present; for NI, the term -K_M q a/r with a along r-hat has no companion field-equation in the papers, so there is no check. In my calculation (R3), the exact classical field does contain a longitudinal part in the near zone (it equals -a/r on axis), but it is the O(1/c^2) near-field correction, not a propagating wave; at large r the Coulomb-minus-retardation pieces cancel the 1/r longitudinal term (it enters only through the time-retarded velocity field). Thus "radiation has longitudinal parts" is true only in the sense of near-field/induction terms, which classical antenna theory includes. Thesis result: eq. 6-1 is Neumann's integral (see Claim 1); thesis eq. 6-4 compares it to partial inductance, and the argument that PI "contradicts CE" rests on the absolute value / sign function convention that Ruehli used for non-closed segments, which is a bookkeeping choice, since segment partial inductances are defined only up to closing the loop at infinity. The thesis's own statement of this is "closed loop requirements of VMP are dropped" [read, Table 6-1]. The claim of "no singularities" refers to the finite seed size, which is the usual wire-radius regularisation and is the same as geometric mean distance methods ([memory medium], not web-checked). The "10x faster" claim (adaptive numerical integration) has no benchmark in the sections I read. Ground plane: negative images with 97% reflectivity for copper is a valid engineering approximation (method of images for a perfect-conductor plane; for a real conductor at frequency f the image depth depends on skin depth) [memory medium].

b. Experimental consistency. The inductance results (average absolute error 1.9% without plane, 4.1% with plane, 32 traces) are consistent with the Neumann formula; they are the kind of agreement partial-inductance and field-solver tools also give. No tabulated comparison with competing methods on the same traces was in what I read. Dipole radiation patterns: the classical result is confirmed by measurement; the NI-based claim of better patterns is in nia1.pdf (not read in detail).

c. Tested? By the author, with an LCR meter (Agilent) in an M.S. thesis; no independent replication in the folder. Longitudinal far-field waves: no test described.

d. If true. A propagating longitudinal EM wave in vacuum would contradict Maxwell's equations in source-free space and every radio measurement of polarisation (transverse). If only the engineering formula is meant, nothing in mainstream physics has to change because it is the same integral.

Verdict: Split. Engineering inductance formula (NI integral for traces within 5-10%): Established (it is Neumann's formula, previously known; the agreement is a modest, plausible result; claimed speed advantage never properly tested in what I read). Longitudinal radiation: Never properly tested (not dismissed after a test; no test or measurement of a longitudinal far-field component is in the folder) in the strong form; contradicted by Gauss' law for source-free space in the far zone, so in the strong form also Refuted by calculation as a propagating free wave. Weak form (longitudinal near-field terms exist): Established (they are in classical theory; R3).

Summary table

Web checks

• Done: proton rms charge radius 8.4075(64)e-16 m, CODATA 2022 [web] https://physics.nist.gov/cgi-bin/cuu/Value?rp
• Done: 1H relative atomic mass 1.00782503223 [web] https://physics.nist.gov/cgi-bin/Compositions/stand_alone.pl?ele=H
• Failed (fetch 403 / search budget exhausted): Feynman Lectures vol. II sec. 17-2 flux rule exceptions (https://www.feynmanlectures.caltech.edu/II_17.html); Darwin Lagrangian form; electron point-like bound < 1e-18 m; Michelson-Morley-type limits. These remain [memory], confidence as marked (the Darwin form is additionally supported by my own numerical match in R3).
• Conclusions resting on [memory] alone: the antenna-pattern formula, the Lorentz-force tests, the electromagnetic-mass 4/3 history, the Higgs/QCD origin of masses, partial-inductance history, the river-model correspondence.

Scripts (scratchpad, not deliverables)

[scratch file] (exact Lienard-Wiechert vs NI/Darwin), neu.py (Neumann vs transverse-only), corner.py (corner total-derivative check).