Mills-Randal · Source catalogue

Mills's single-author monograph, published by his company's circle (ISBN 978-0-9635171-5-9). The printed title page says 'December 10, 2018 Edition, Volume 1 of 3', but the PDF runs to 1,876 pages and covers all three volumes: Vol. 1 Atomic Physics (Introduction, Ch. 1-10), Vol. 2 Molecular Physics (Ch. 11-23), Vol. 3 Collective Phenomena, High-Energy Physics and Cosmology (Ch. 24-42), then Appendices I-VI. The reference list includes a 2022 paper (Hagen and Mills, EPR), so the file is later than the printed 2018 date. Text extraction worked for 1,826 pages; 50 pages were OCR'd. Equations are mostly garbled in the text layer, so every numerical check by the deep readers used page images. Thesis: the electron is a zero-thickness spherical shell of charge and current that obeys Maxwell's equations and Newton's laws; Schroedinger/Dirac/QED are said to be unnecessary and in places inconsistent; from this model Mills claims closed-form results for atoms, molecules, solids, particles and cosmology using integers and fundamental constants only, plus a new physics of hydrogen states below n = 1 ('hydrinos') that is the basis of his company's (BlackLight Power / Brilliant Light Power) power technology. The Preface and Introduction list the claimed successes (g factor, Lamb shift, hyperfine, 1-20 electron atoms, organic and inorganic molecules, lepton and nucleon masses, accelerating universe predicted in a 1995 edition, top quark mass) and the claimed new disciplines (hydrino chemistry, 'new energy source'). QE update (2026-10-09): the central claims that rested on digests alone have now been deep-read. Claim 7 (collective phenomena, Ch.24-30), the hydrogen-molecule and dihydrino chapter (Ch.11), the general-relativity half of claim 6 (Ch.31-34), Ch.35 (fifth force) and the Introduction's evidence statements are summarised in the per-part entries. New items carried into the record: (a) the book's statements that gravity has no far-field transverse waves (p.1642, p.1678) and that the Higgs boson 'will not be observed' at the LHC (p.1678), both resting on 2009-2010 sources in an edition dated 2018; (b) the claim that a free electron has zero gravitational mass, with the Witteborn-Fairbank 1967 free-fall result ('less than 0.09 m_e') as support, and the pseudoelectron / fifth-force proposal (Ch.35); (c) hydrino catalysed fusion (pp.272-274); (d) the Introduction's headline sentence that hydrino states are confirmed 'by the data presented in over 100 published journal articles and over 50 independent test reports and articles [22]', where ref 22 is the company website (p.37). These are the author's statements; his company has a commercial stake in the hydrino claim.

Key claims

• Classical physics with a zero-thickness spherical-shell electron reproduces atomic, molecular, particle and cosmological observables in closed form.
• Hydrogen has stable states below n = 1 (hydrinos) that form by resonant energy transfer to a catalyst and release energy.
• Schroedinger/Dirac quantum mechanics and QED are unnecessary and internally inconsistent.
• Gravity has no transverse far-field wave ('absence of the observation of gravity waves'; p.1642, p.1678), and the Higgs boson 'will not be observed' at Fermilab, the LHC or any future collider (p.1678).
• A free electron has zero gravitational mass (Witteborn-Fairbank: 'less than 0.09 m_e'); a negatively curved 'pseudoelectron' feels a repulsive fifth force (Ch.35).

Relevance: The only source document in the project: it is the inventor's own statement of every claim. Author has a commercial stake (BlackLight Power / Brilliant Light Power sells hydrino technology); the book is the author's characterization of his own results and of mainstream theory.

Mainstream conflict: Fundamental: no states below n = 1, QED and the Schroedinger/Dirac equations are accepted and tested to many digits, QM spin is intrinsic and not a classical rotation, Bell tests rule out local hidden variables, cosmology uses general relativity and a Big Bang with dark matter particles.

Contents of all 42 chapters and 6 appendices. The Preface contrasts first-year classical physics (intuitive, closed-form) with quantum mechanics, which the author calls non-physical, with infinities removed by discretionary algorithms, and with the Dirac sea equated to an ether. The Introduction summarises the whole programme: the bound electron as a 'bubble-like' two-dimensional charge-current layer (atomic orbital), nonradiation condition (Haus 1986), spin and Bohr magneton from a 'current-vector field' of great circles, g factor, Table I.1 (lepton masses and neutron/electron mass ratio from alpha only: 206.76828 vs 206.76827 etc.), a claim that CP predicted the top quark mass and the accelerating expansion (1995 edition), Table I.5/I.6/I.7 (molecules, particles, cosmology and 'disruptive technologies' solved), hydrinos with energy 13.6 eV/n^2 and n = 1/p, catalysts accepting m x 27.2 eV, EUV continuum edge at 91.2 nm / [(p+m)^2 - p^2 - 2m], hydride ion 0.75418 eV (vs Lykke 6082.99 cm-1), NMR upfield shift as 'direct evidence', hydrinos as dark matter (Bournaud 2007, Jee 2007/2012), and a claim that hydrino states are 'confirmed by several analytical techniques [22-42]' (references are Mills, Brilliant Light Power and coworkers, plus Hagen and Mills 2022). The author calls this 'disproof' of Bohr, Schroedinger and Dirac theory. QE deep read of pp.1-86 (22 evidence statements listed with their reference numbers). The hydrino evidence is cited as refs [22]-[42] (and [23-29, 31] for the continua). Ref 22 is the company website (brilliantlightpower.com) and is the only reference attached to the sentence 'The existence of such states has been confirmed by the data presented in over 100 published journal articles and over 50 independent test reports and articles [22]' (p.37). Refs 23-42 are by Mills with company-linked co-authors; ref 29 (Bykanov, file name 'GEN3_Harvard.pdf', hosted on blacklightpower.com) is the only item without Mills as an author; ref 30 is Hagen and Mills 2022. The reference list prints no affiliations, so the text names no non-company laboratory. From memory (medium to low, unverified): Hagen is at Delft, Scharer at Wisconsin, Phillips and C. K. Chen at Los Alamos, Mayo at North Carolina State, Nansteel at Penn State; all are Mills co-authors. The Introduction describes no instrument, sample, run, power figure or spectrum, and mentions no negative result or failed replication. It states 'Hydrinos have been isolated in the laboratory and confirmed by a number of analytical techniques [22-42]' (p.83); the Investigator found a Scientific American 2014 report that Mills said hydrinos had not been isolated (see sites.md). Table I.2 reference numbers refer to Chapter 11, not to the Introduction list. Other unsupported-by-number statements: Lamb shift, fine and hyperfine structure, muonium and positronium hyperfine, elastic electron scattering from helium, superconductivity, quantum Hall and Aharonov-Bohm 'agree with experimental observations' (p.75, no numbers); about 800 organic molecules 'match the experimental values typically to the limit of measurement' (p.80, ref 4, Mills et al. 2010); H0 = 78.5 km/s/Mpc (p.44); 'the basis of the antigravitational force is presented with supporting experimental evidence' (p.75).

Key claims

• Hydrino states with n = 1/p exist and are confirmed experimentally by EUV continua, hydride-ion data and NMR.
• Hydrinos explain dark matter and cosmic EUV/X-ray features.
• The theory predicted the top-quark mass and the accelerating expansion before they were measured (1995 edition).
• Hydrino states are confirmed by 'over 100 published journal articles and over 50 independent test reports and articles' (sole reference: the company website, p.37).
• Hydrinos have been 'isolated in the laboratory and confirmed by a number of analytical techniques' [22-42] (p.83).

Relevance: Frames every later claim and gives the inventor's own list of what he says is solved. The evidence cited for hydrinos is mostly the author's company's papers.

Mainstream conflict: Direct conflict with accepted quantum mechanics (ground state n = 1) and with particle-dark-matter cosmology.

Electron source current, nonradiation, the atomic orbital as a delta-shell charge/mass density, the angular momentum hbar assumed as an 'inalienable' input, spin hbar/2 built from great-circle currents spread over one hemisphere (Mills 0.495 hbar numerically), resonant precession and a trapped Larmor photon to reach a full Bohr magneton, magnetic field and energy of the orbital, g-factor derivation (Eq. 1.228: g/2 = 1 + alpha/2pi + (2/3)alpha^2(alpha/2pi) - (4/3)(alpha/2pi)^2), radii, energies, relativistic correction (Eq. 1.293 = Dirac 1s). Deep-read results: arithmetic of the shell model is right; hbar is an input; mu_B needs an extra postulate (the resonant photon); N = 3/2 inserted by hand; printed fields and energy are 4pi and (4pi)^2 too big in SI (0.0572 eV vs 3.6e-4 eV at a0) because Gaussian field forms are combined with SI mu_B; three conflicting wavelength definitions (lambda = 2 pi r, = r); factor-of-two between stated Larmor frequency eB/2m and the flip photon. Reproduction: with the book's alpha^-1 = 137.03604, g/2 = 1.0011596521215 (book ...120); against modern data the equation is off by 2.9e-10 (about 2,000 sigma), but the claimed 'eleven-figure agreement' used 1973-era constants. No fitted decimals; discrete modelling choices (2 pi radius scaling, v = c in one term and v = alpha c in another, sign of dissipative term); the first term equals Schwinger's alpha/2pi and the next two have different coefficients from QED (-0.3285, +1.1812 in (alpha/pi)^n) with errors that nearly cancel. Chapter 1 also gives the Bohr reduced-mass results and Table 1.5 relativistic ionization energies for hydrogen-like ions, which match Dirac's 1s formula; deviation at high Z is attributed to Lamb shift and nuclear size, not calculated.

Key claims

• The electron g factor follows from a classical shell model: g/2 = 1 + alpha/2pi + (2/3)alpha^2(alpha/2pi) - (4/3)(alpha/2pi)^2 = 1.0011596521 (agrees with experiment to about eleven figures with 1973-era constants).
• Spin 1/2 and the Bohr magneton follow from a current-vector field of great circles plus a resonant Larmor photon, not from a postulate.
• The bound electron is a nonradiating two-dimensional shell at radius r_n with angular momentum hbar.

Relevance: First test of the theory: the g factor and spin are the best-known quantum results; the deep read separates what is derived from what is input.

Mainstream conflict: Spin as intrinsic quantum property and QED's perturbation series for g-2 are mainstream; Mills's series agrees to 2.9e-10 only coincidentally (the next-term coefficients differ from QED and the errors nearly cancel).

Chapter 2: photon absorption as trapped photon in the orbital, selection rules from photon multipole conservation, Stark and Zeeman splitting, state lifetimes, Lorentzian line shape, Lamb shift from radiation-reaction (RR) radius change, muonic-hydrogen Lamb shift, fine structure, hyperfine structure (21 cm), muonium hyperfine. Deep-read results (arithmetic reproduced): H Lamb 1057.09 vs 1057.845 MHz (7.1e-4); muonic H 2P3/2(F=2)-2S1/2(F=1) 49,879.0 vs 49,881.88 GHz (5.8e-5; about 3.8 sigma, uses two QED literature terms from Pohl 2010); fine structure 10,968.46 vs 10,969.05 MHz; H 21 cm 21.10610 vs 21.10611 cm (0.75 ppm); muonium 4.46330328 vs 4.463302765(53) GHz (0.115 ppm, about 10 sigma); H Knight shift 157.29 T untested; Lyman-alpha lifetime 1.49 ns (not compared; memory 1.596 ns measured). No decimal constant is fitted, but several structural choices differ case by case (muonic H three-term expansion where one unit in the last coefficient moves the result by about 94 GHz, larger than the proton-radius discrepancy; H vs muonium stored-magnetic-energy factors; the Lyman-alpha recoil term). Mills's quoted residuals are larger than the uncertainties of the constants. Chapter 3: free electron as a two-dimensional plane lamina with force balance from the radiation-reaction force, de Broglie relation 'classically', Stern-Gerlach, free-electron g factor and binding; Chapter 4: photon as spherical standing-wave field built from great-circle fields, photoelectric and Compton effect, 'photon torpedoes', free-electron photon absorption (digest only). QE deep read of Chapters 3-4. Free electron: a flat disc with mass and charge density sigma = (3 m_e / 2 pi rho0^2) sqrt(1 - (rho/rho0)^2) delta(z) (Eqs. 3.7-3.8), thickness the Schwarzschild radius 1.3525e-57 m. p.205 says this charge distribution 'has recently been confirmed experimentally [3,4]' at KEK. Ref 3 is J. Gribbin, New Scientist, 25 Jan 1997 p.15; ref 4 is Levine et al., Phys. Rev. Lett. 78, 424 (1997). The deep reader could read only web snippets: the paper (TOPAZ detector, TRISTAN e+e- collider at KEK) measures how the electromagnetic coupling strengthens with momentum transfer (about 57 GeV) by muon-pair production, and its stated conclusion is agreement with electroweak predictions; mainstream reading is vacuum polarisation (running of alpha). The book gives no alpha(Q) value and no derivation from Eq. 3.8; 'confirmed' is the author's characterisation. Stern-Gerlach (pp.215-223): the electron's intrinsic L = hbar and a resonant Larmor photon carrying hbar/2 projection give the full Bohr magneton; the apparatus (inhomogeneous field, beam splitting) is not treated. Photoelectric and Compton effects (pp.235-238): the derivations are the standard photon ones (E = h nu, p = h/lambda); hbar is imposed by the boundary condition that the photon angular momentum is hbar (p.229, p.232, p.239); Compton shift 0.0485 sin^2(theta/2) Angstrom reproduced [calc]. Free-electron photon absorption (pp.243-246): the electron gains 1.73e-27 kg m/s from a 5 GHz photon of momentum 1.1e-32, 'five orders of magnitude greater', with 'spacetime' conserving momentum; the book proposes a 'space drive'. Standard physics: a free electron cannot absorb a photon with energy and momentum both conserved [memory, high]. No experimental data of the book's own appear in Ch.3-4; every experimental statement is a citation.

Key claims

• The Lamb shift, fine structure, hyperfine structure and muonic-hydrogen intervals follow from classical radiation reaction without adjustable parameters, to 1e-4 to 1e-7.
• The de Broglie relation, Stern-Gerlach result and the photon (including Compton and photoelectric effects) are classical.
• A free electron is a planar disc/lamina that precesses into a bi-conical cavity.
• The free-electron charge density (a disc increasing toward its core) 'has recently been confirmed experimentally' at KEK (p.205, refs 3-4).
• A free electron absorbing a photon gains about 1.6e5 times the photon's momentum, conserved by 'spacetime', enabling a 'space drive' (pp.244-246).

Relevance: Large block of numerical claims that can be checked against measured intervals; also contains the first appearance of the electron/photon models used later.

Mainstream conflict: QED explains the Lamb shift and hyperfine/fine structure with perturbation series; the muonic-H proton radius puzzle is a recognised discrepancy that Mills claims to resolve without changing the proton radius.

The central hydrino chapters. Claim: hydrogen has states n = 1/p (p = 2, 3, ... 137) with radius a_H/p and energy approximately p^2 x 13.6 eV, made by resonant nonradiative energy transfer of m x 27.2 eV from H to a catalyst (He+, Ar+, Sr+, K, Li, NaH, H2O, or H itself via disproportionation), releasing [(p+m)^2 - p^2 - 2m] x 13.6 eV, with continuum edges (91.2 nm, 10.1 nm = 122.4 eV, 22.8 nm). Force balance with Z_eff = p + m from a 'trapped photon' standing wave. Table 5.1 (image-only) and Table 5.2 (catalysts) transcribed; ionization potentials agree with the printed table digit for digit. Hydride ion H-(1/p): 0.75418 eV (p = 1) vs Lykke 0.754195 +/- 0.000019 eV (about 1 sigma) using a special reduced mass m_e/sqrt(3/4); NMR shift -(p 29.9 + p^2 1.59e-3) ppm, no measured value on these pages. H2(1/p): bond 4.478 eV (rests on using 27.20 eV), NMR -28.01 ppm vs measured -28.0 ppm for ordinary H2, vibration p^2 0.5159 eV, rotation p^2 x 0.01509 eV. Evidence classes cited on pp.252-253 are the company's and the author's papers (EUV continua, fast H, lack of emission, NMR, Raman/FTIR, XPS, ToF-SIMS, power measurements by calorimetry). pp.265-286: disproportionation cascades (3.48 keV line = H[aH/4] + H -> H[aH/17], 3481.6 eV, compared with Bulbul 2014 / Boyarsky 2014), Foerster-type dipole-dipole rate (8e21 /s, with orientation factor, overlap and efficiency set to one), power examples (100 kW/m^3 for hydrino-hydrino, 144 kW/m^3 Li catalyst; both conditional on assumed populations), hydrino catalysed fusion (HCF) as single events needing a ~7 keV vibrational state, p <= 137, hyperfine A coefficients for hydrinos (34.3 GHz predictions). Deep reader flags: no laboratory spectrum, no hydrino power measurement and no independent replication in pp.265-286; arithmetic slips (Sun power density 272 W/L should be 2.72e-4; 0.1 MeV paired with 1.16e7 K); relation between the 2 pi factors in Eq. 6.13 and 6.14. Mainstream (memory, high): there is no state below n = 1 in Schroedinger/Dirac theory; the departure is the existence of a lower state at all, not selection rules. QE additions (2026-10-09). 3.48 keV line: the book compares the 3481.6 eV disproportionation line with Bulbul 2014 and Boyarsky 2014 only. The arbiter's correction: the line is unconfirmed rather than excluded; Hitomi (Perseus cluster) and the later XRISM ten-cluster stack set limits (XRISM 3-4 times tighter than Hitomi, still about 5 times above the Bulbul rate), Dessert-Rodd-Safdi find no signal in a large blank-sky sample (contested by Abazajian) [memory, medium; arbiter web-checked]. Hydrino-catalysed fusion (HCF, pp.272-274) in detail: after catalytic cascades to high p the internuclear distance of D or T hydrino molecules is 1/p of the ordinary one; p = 137 is the limit (radius 8.85e-15 m [calc, agrees]); the book says p = 115 gives dimensions comparable to muonic molecules (vibrational energy 6840 eV) and that only the lowest vibrational state is likely populated (about 7 keV would need roughly 1e8 K), so 'the cross section to populate the molecule hydrino vibration state is essential' and is not computed; no HCF rate, neutron, tritium or 3He yield is given. Footnote 2 on p.272: arc-current detonation of hydrated silver shot 'yielded power densities comparable to those of nuclear weapons [50-54]' (refs are Mills and company papers and reports; no numbers on these pages). Book arithmetic slips: 0.1 MeV x 11,600 K/eV is 1.2e9 K, not 1.16e7 K; Sun 272 W/litre should be 2.72e-4. Fast-H evidence class (pp.85, 1689; refs 36-42, 2005-2010): the book says the catalyst reaction gives fast H atoms by 'an inverse Franck-Hertz mechanism' whose excitation gives broadened Balmer-alpha lines 'observed experimentally [19-25]' (Ch.35 numbering); authors are Mills and company-linked co-authors. Related outside work found by the Investigator: Phillips 2008/2009 (a Mills co-author) and Loureiro and Amorim 2010 (Phys. Rev. E) on whether hot H atoms exist in discharges (sites.md).

Key claims

• Hydrogen atoms can drop to states n = 1/p (hydrinos) by resonant energy transfer to a catalyst; the energy released is [(p+m)^2 - p^2 - 2m] x 13.6 eV.
• The hydride ion H-(1/p) and molecular hydrino H2(1/p) have binding energies p^2-scaled (e.g. H- 0.75418 eV, H2 bond 4.478 eV).
• Hydrino disproportionation produces the 3.48 keV line, the 10.1 nm EUV continuum, 511 keV emission and gamma-ray bursts.
• Hydrino-catalyst reactions can produce power densities of 100-144 kW/m^3 (conditional estimates) and hydrino-catalysed fusion.
• Deuterium or tritium hydrinos at high p fuse more readily (hydrino-catalysed fusion, HCF), observable as neutrons, tritium and 3He; no rate or yield is given (pp.272-274).
• Broadened Balmer-alpha lines come from fast H atoms formed by an 'inverse Franck-Hertz' resonant transfer in the hydrino reaction (refs 36-42; author and company papers).

Relevance: The commercial and physics core of the project: if hydrinos exist, this is where the energy source and dark matter claims come from.

Mainstream conflict: Fundamental conflict: Schroedinger, Dirac and QED place the ground state at n = 1; the nuclear charge seen by the electron is exactly +e; energy conservation and photon-less resonant transfer are not accepted as a new energy source.

Helium: both electrons at r1 = 0.567 a0 by a force balance with a spin-pairing term (Eq. 7.35). Helium ionization energy 24.58750 eV vs 24.58741 eV measured; reproduced exactly, but it uses a helium-only formula whose correction bracket (1 - (1/2)((1/3)^2 + alpha)) is taken from the muonium hyperfine section and whose magnetic term has the opposite sign from the ion formula (the ion formula would give 23.68 eV). Table 7.1 (isoelectronic He-like ions): reproduces row for row from one formula, errors a smooth -0.5 to +0.4 percent trend (0.8 eV at Be2+, 37 eV at Cu27+), far larger than experimental uncertainty at low Z. H- 0.75418 eV (again). Hydrino-hydride numbers: NMR shift p x 29.9 ppm, hyperfine; predictions, with Mills-group plasma spectra as the only data cited; NMR formula pi/2 larger than the standard Lamb shielding formula for the same shell. Chapter 8: classical electron scattering from helium; the formula drops the nucleus and a 1/s^4 factor, has a free scale, fits Bromberg 500 eV data from about 10-30 degrees, diverges at zero angle where data are finite. Chapter 9: helium excited states (singlet/triplet, l = 0 and l != 0) with spin-orbit energies, tables with r2 and energies. Appendix VI checks: 2^1S 1.71132 a_He, -3.97465 eV vs NIST -3.97161; 2^3S -4.78116 vs -4.76777; 2^1P -3.36941 vs -3.36936; 2^3P -3.61957 vs -3.6233. Appendix VI derives only the pure-number angular-momentum factors; the scale, multipole factor and sign rules are stated or imported; cross products in Eqs. (7.12)-(7.13) do not follow one handedness. QE deep read of Chapter 9 (helium excited states). Method: classical force balance with electron charge e/n and fixed factors (2/3 correction, s = 1/2, triplet x2, orientation sign, Z = 2); no fitted parameter. The deep reader recomputed all 61 distinct rows: the tabulated energies follow the book's equations to better than 1e-5 relative, so the arithmetic is consistent. Against NIST the mean absolute relative error is about 1.0e-3 (three figures), not the book's 'about 5 significant figures'. Worst rows: 1s2s 3S -4.78116 vs -4.76777 eV (13.4 meV, 2.8e-3) and n = 3 3P (-3.4e-3, 5.4 meV); 1s2p 1P matches to 1.4e-5. Errors are systematic by series (singlet S all too deep; triplet S changes sign at n = 5). For l >= 3 agreement of 1e-4 to 1e-6 is the hydrogenic limit -13.6/n^2. The claimed r^2 = 0.999994 is reproduced (0.9999936), but plain -13.6/n^2 with zero parameters already gives 0.967, a 12-number quantum-defect fit gives 0.99997, so r^2 hardly discriminates. Structurally the book's formula is a quantum-defect form with fixed defects 0.144 (singlet S; observed about 0.145) and 0.289 (triplet S; observed about 0.305), which come from geometric factors, not from NIST (a non-trivial hit or a numerical coincidence to be tested on other atoms). Standard quantum mechanics reproduces these levels far better than 1e-3 [memory, medium-high]. The boxed sidebar on p.346 says the helium and hydrogen excited-state agreement 'strongly supports' the hydrino states; no state below the ground state is tested in Chapter 9 and no hydrino detection is cited there (the author's own sidebar; stake: the BlackLight Process). Spin-orbit: hydrogen 2P fine structure 10,968.46 vs 10,969.05 MHz; the helium 1snp 1P spin-orbit energies of Table 9.6 are not compared with data.

Key claims

• Helium and all two-electron ions are solved exactly in closed form: r1 = 0.567 a0 and ionization energy 24.5875 eV.
• The electron-scattering intensity from helium is predicted classically and fits data where the Born approximation fails.
• Helium excited-state energies and spin-orbit couplings follow from the same classical force balance.
• More than 100 helium excited states are reproduced with r^2 = 0.999994, which 'strongly supports' the hydrino states (p.345-346).

Relevance: Tests whether the 'exact classical solution' extends beyond hydrogen; the first place where a formula must be reused with changed signs and brackets.

Mainstream conflict: Helium has no closed-form solution in mainstream theory, but variational/QED calculations reach 1e-9 relative accuracy; Mills's 4e-6 match is well within a few-parameter-choice fit.

Each atom is solved shell by shell with the radius of the outer electron from a force balance containing electric, spin-pairing, paramagnetic, diamagnetic and relativistic terms, integers A, B, ... chosen atom by atom from prose angular-momentum arguments. Neutral atoms: ionization energies matched to 0.03-0.65 percent (3p atoms) and similarly for Li-Ne. Isoelectronic ion tables 10.12-10.20 (116 entries in pp.401-444): mean absolute relative error 1.73 percent, 43 entries within 1 percent, 20 above 3 percent, worst Ar3+ -4.64 percent, with a smooth drift with Z (positive 3-4.6 percent for the first ions, crossing zero near Cr-Fe, to -2 to -3 percent at Zn) that the text does not remark. The text defends the larger errors by saying the reference values at large Z are interpolations ('no assurances can be given that these techniques are correct'). Ad hoc rules stated in the text: the 2p-3s-3p interaction exception for third-row atoms; induced charge-density waves in the 3s orbital; Hund-like filling with unenumerated exceptions; orbital ordering borrowed from helium excited states (4s before 3d); doubled/tripled forces for K and Ca ions; a magnetic-energy correction applied to Al but not to Si-Ar. The book calls the results an 'exact solution' of multielectron atoms and 'remarkable agreement' with 400 atoms and ions; 'exact' means closed-form, not zero error.

Key claims

• All one- to twenty-electron atoms can be solved exactly in closed form, with ionization energies in remarkable agreement with about 400 atoms and ions.
• Electron configuration (Pauli exclusion, Hund's rules, 4s before 3d) follows from classical force balance and an energy-minimum rule.

Relevance: Largest body of atomic numerical comparison; the key question is how many free per-atom choices stand behind the agreement.

Mainstream conflict: Mainstream solves many-electron atoms with approximations (Hartree-Fock, CI, DFT) at spectroscopic accuracy; Mills's tabulated errors of up to 4.6 percent are far larger than those methods' errors for ions of this size.

Chapter 11: H2+ and H2 as prolate spheroidal molecular orbitals (MO) with protons at the foci; total energies H2+ 16.2527 eV, H2 31.6776 eV; ionization energies and bond energies; vibration with a Doppler energy term; NMR; dihydrino molecule H2(1/p) with p^2 scaling. Chapter 12 (deep read): excited states of H2+/H2 as in helium, rotation, centrifugal distortion. Chapter 13 (deep reads): H3+, OH, H2O, NH, NH2, NH3, CH, CH2, CH3, CH4, N2, O2, F2, Cl2, CN, CO, NO. Table 13.1: all 18 rows NH to NO match bond energies within 1.5 percent (typical 0.3 percent, 0.01-0.04 eV). Bond angles: NH3 106.67 (exact), CH3 120 (symmetry), CH4 109.5 (asserted); CH2 100.22 vs 102.4 and NH2 105.97 vs 103.3 miss by 2-3 degrees; the 'experimental' CH2/CH3/CH4 values come from a computational paper. Vibrations: only CH, CD, NH, ND, OH, OD and Cl2 calculated (CH 0.15 percent, Cl2 -3.8 percent; omega_e x_e 3-27 percent off); others use experimental or reused omega_e as input. Extra adjustments noted by deep reader: CH2 magnetic energy 0.14803 eV, sp3 hybridization factors 0.91771 (C) and 0.93172 (Cl), 0.75/0.25 charge split, double-bond multipliers for CO and NO, experimental sub-radical bond energies as inputs in the CH2-CH4 and NH3 chains. QE deep read of Chapter 11 (H2+, H2, dihydrino H2(1/p)). Reproduced: bond energies H2 4.4778 eV (printed 4.478), H2+ 2.6541, D2+ 2.6958; D2 gives 4.5549 from the book's numbers versus 4.556 printed (1-2 meV slip). The H2 match depends on rounding 2 x 13.59844 to 27.20 eV (27.19688 gives 4.4809) and on using a0 for the neutral molecule (aH gives 4.461-4.464); the 'Doppler' term (-0.0426 eV) is needed to come within 1 percent. Inputs in Section 8 of the deep read: measured atom energies, rounding, a0 versus aH by species, empirical Morse and Lavrov-Weber formulas, Purcell's 2/3 factor, and table distances (0.7411 and 1.0577 Angstrom) not computed in the text (the derived values are 0.7484 and 1.0584). Vibration: H2 0.517 and D2 0.371 eV reproduce; H2+ 0.270 and D2+ 0.193 do not (recipe gives 0.280 and 0.200). NMR: -28.01 ppm reproduces from a chain of choices; the 'experimental' -28.0 ppm is Mills's composite of -28.5 (Suarez, gas-phase TMS) plus 0.48 ppm from two papers, and the same paragraph uses a second TMS reference (-31.5 ppm); the deep reader recalls an accepted absolute shielding of gaseous H2 near 26.3 ppm [memory, medium; needs a web check]. Quadrupole: the printed integral gives 1.70127 a0^2 (0.476e-16 cm^2) vs Ramsey 1950 0.38 +/- 0.15; the deep reader finds the integral omits the surface-element factor, and Mills's own charge density integrated correctly gives 1.3333 a0^2 (0.373e-16 cm^2); both lie inside Ramsey's range; the convention of Ramsey's number needs a check. Dihydrino: the p^2 scaling of energies, vibration and rotation requires postulates beyond Chapter 5: an integer two-centre field (asserted), the field also multiplying the proton-proton repulsion (needed for exact p^2; otherwise ET(H2(1/2)) would be -165.2 eV not -126.71 eV), a Doppler term divided by p^2 in some places and p^3 in others (1.3 eV at p = 2, 15.7 eV at p = 4), and EPR activity imported from Chapter 16's unpaired-electron 'doublet' state, which contradicts the paired-electron force balance of Chapter 11. The hydrino vibration and rotation signatures of Ch.5 and Ch.16 use measured H2 constants times p^2. No experiment by Mills or his company is reported in Chapter 11.

Key claims

• Molecules are solved as ellipsoidal molecular orbitals (MOs) by the same force balance; the H2 bond energy, bond lengths and vibrations follow in closed form.
• Small molecules (H2O, NH3, CH4, N2, O2, ...) have total bond energies, bond angles and vibrations calculated from integers and constants alone.
• The dihydrino H2(1/p) energies, sizes, NMR shift and vibration scale as p^2, p, and so on, from an integer two-centre field (Ch.11).

Relevance: Establishes the molecular method and the p^2 scaling that gives hydrino molecule predictions.

Mainstream conflict: Mainstream chemistry uses quantum-chemical (ab initio/DFT) calculations with 0.04 eV (chemical accuracy) typical; Mills's 0.3 percent is a few hundredths of an eV on small molecules but misses angles by 2-3 degrees.

Chapter 14 solves CO2, NO2, ethane, ethylene, acetylene, benzene and n-alkanes up to octadecane; Chapter 15 derives general geometrical and energy equations (Eqs. 15.1-15.127) for functional groups and applies them to alkanes, alkenes, alkynes, halides, alcohols, ethers, amines, carbonyl compounds, nitrogen, sulfur, phosphorus compounds, aromatics, ions, sugars, DNA/RNA bases, amino acids and polypeptides. The deep reader tallied the summary tables 15.9 (431 rows): mean absolute relative error 0.17 percent, median 0.056 percent; n-alkanes 0.019 percent; most other classes 0.03-0.3 percent; worse: thiols (HS radical -3.3 percent), DNA bases 0.47 percent (cytosine 1.73 percent), phosphines 0.96 percent (trimethylphosphine 2.27 percent), D-ribose 2.4 percent, amino acids 1.6 percent (13 of 20 are +1 to +3 percent; 12 compare against crystal data). The n-alkane CH2 increment is exactly 12.1577 eV (= CH2 7.83016 + C-C 4.32754), vs experimental 12.16-12.18. Printed relative errors do not follow (exp - calc)/exp in 9 rows (e.g. guanine printed -0.00055 vs recomputed +0.00693); several formula labels are wrong (fluorobenzene as C6H5Cl; cysteine as C3H7NO4S); isomers receive identical calculated totals while experiment differs, so errors measure isomer scatter. Chapter 14 deep read found whether parameters are fitted: 'closed-form equations having integers and fundamental constants only', but sp3 hybridisation factor 0.91771 appears with a 25 percent donation rule chosen for an energy minimum, geometric integers assigned per group. No overall accuracy claim is stated in the summary range. QE deep read of Chapter 15 pp.801-1082 on the question whether parameters are fitted. Findings: about 19 distinct E_T(atom-atom) values form a menu from which each functional group is assigned a value with a verbal justification (for example 0.92918 is 'maximum single-bond contribution' for bromides but 'mean of primary and secondary amine' for tertiary amines); about 22 hybridisation numbers are computed by one formula (rule-derived); about 85 freshly specified group choices; each class has its own vibrational input E_Kvib or E_osc. Poly-halo groups (CCl4 0.92918, CBr4 0.36229, CH2I2 0.18114, CHI3 0) are separate groups; the two iodide groups (ii) and (iii) serve exactly one compared molecule each (errors 0.195 and 0.444 percent). Fourteen heterocycle and DNA-base classes are single molecules with 3-11 group types each against one experimental total (thymine 10 types and one total; adenine 11; cytosine 10, error 1.7 percent). The text never says E_T or an integer was adjusted until a total matched, and never gives a rule fixing it independently of the experimental total; the deep reader calls the procedure 'selected from a small lattice with verbal justification' and neither fitted nor derived. No held-out molecule was found. Fits quoted 0.006 to 0.44 percent for iodides, 0.03 to 0.08 percent for thymine and adenine. Pentacene AFM image (Gross et al., ref 53) is shown against the classical solution (p.983-984). Many table cross-reference and label errors are listed in the deep read (section 7).

Key claims

• Bond energies, bond lengths and angles of several hundred organic molecules (alkanes, alcohols, amines, carbonyls, aromatics, amino acids, DNA bases) follow from two closed-form equations with integers and fundamental constants only.
• Mean relative error in total bond energies is about 0.1-0.2 percent over the summary tables.

Relevance: The book's biggest numerical sweep: the claim that a single method works across organic chemistry is what makes the theory impressive to the reader.

Mainstream conflict: Total bond energy errors of 0.1 percent of 40-220 eV are a few hundredths of an eV to 0.2 eV, comparable to or worse than chemical accuracy but obtained with no basis sets; the physics assumption (molecule as shells of 2-D MOs) is not accepted. Whether the group energies are tuned to the data is undetermined. The group-parameter question (fitted or derived) is now documented: choices are made from a small menu with verbal justification and the procedure is unstated; whether any were tuned is not recorded in the book.

Pharmaceutical molecules, bond and dipole moments, hydrogen bond in ice, van der Waals cohesive energies of noble gases (solid Kr 0.1189 vs 0.11561 eV; solid Xe 0.18037 vs 0.16608 eV: 3 and 9 percent high), H2 dimer, solid H2, H2(1/4) dimer and solid H2(1/4), end-over-end rotation, Raman/diffuse-interstellar-band ideas, EPR of a white fibrous material grown in 4 M KOH from Ga2O3 recovered from a SunCell hydrino run, identified as GaOOH:H2(1/4). Deep-read: X-band CW EPR at 9.820295 GHz by W. R. (Fred) Hagen (TU Delft), co-author with Mills [ref 131], 'replicated by Bruker using two instruments on two samples' (no further detail); principal peak g = 2.00445 vs predicted 2.0046386; mean peak-position error 0.097 G over Tables 16.49-16.50 (peak count not given). Stated controls: control GaOOH dissolves and gives no EPR signal; not stated: SunCell-without-hydrino blank processed the same way, impurity analysis, spin counting. Theory: line splittings Delta B = m x 3.99427 G (m = 1/2, 1, 2 ...) with sub-combs of 0.31/0.62/0.93 G and an unbounded integer j, one-sided magnetic term; all printed numbers reproduce, no continuous fitted parameter, but many discrete choices make the predicted line set dense (random-match benchmark s/4 about 0.08-0.23 G vs 0.097 G). Transition-state-theory section uses only literature SN2 data.

Key claims

• Hydrino molecules H2(1/4) are detected by EPR in a gallium oxyhydroxide product (g = 2.00445, splittings m x 3.99427 G) measured by Hagen and replicated by Bruker.
• Van der Waals and hydrogen-bond energies, dipole moments and transition-state energies are calculated from the classical MO model.

Relevance: The one place the book points to an independent laboratory (Hagen, Delft; Bruker) observing a hydrino signature; the assessment depends on the underlying paper [131] which is not in the project folder.

Mainstream conflict: EPR peaks at g ~ 2.004 are common for oxide defects and organic radicals; H2(1/4) assignment contradicts the accepted ground state; no independent theory predicts the line pattern.

Same method applied to bulk matter: diamond, C60, graphene/graphite; alkali hydrides including 'potassium hydrino hydride'; fluoride and chloride ion ionization energies in lattices (e.g. F- 3.40603 vs 3.4011895 eV); alkali metals as free-electron 'membranes'; silanes; the semiconductor bond as insulator-type and conductor-type; boranes with bridging bonds; organometallics. Deep-read (boron and Al hydrides): totals within about 2 percent for all 91 boron compounds (mean 0.3-0.75 percent per class; worst B5H11 -1.78 percent); geometry: diborane B-H 1.202 vs 1.19 A, B-H-B 1.307 vs 1.32 A, B-B 1.797 vs 1.798 A. Bridge modelling: one H2-type MO per bridge contact with donation factors (25 and 50 percent) chosen to give an energy minimum; bridge angles use experimental B-H-B 85.4 and B-B-B 58.9 degrees as inputs; some 'experimental' references are AM1 semi-empirical computations; +/-1 percent of 25-300 eV is several tenths of an eV, larger than the bridge bond energy itself (0.87-0.88 eV). No explicit accuracy claim beyond the relative-error column.

Key claims

• Solids and ionic, metallic, semiconductor and organometallic bonds are solved by the same closed-form MO equations with energies agreeing to the limit of measurement.
• Boranes and organoaluminium hydrides (bridging bonds) are solved with total energies within about 2 percent.

Relevance: Extends the claim from molecules to materials; the potassium hydrino hydride compound is a claimed hydrino product.

Mainstream conflict: Condensed-matter physics explains these properties by band theory and quantum chemistry; the free-electron 'membrane' and 2-D MO models have no mainstream counterpart.

Chapter 24 re-derives Maxwell-Boltzmann, Bose-Einstein and Fermi-Dirac distributions, blackbody (Planck) radiation, specific heats and free electrons in metals, with the bound electron as a resonator cavity trapping photons. Chapter 25: a cubic array of magnetic dipoles on lattice nuclei is a 'band-pass filter' for electrons in a superconductor; Tc of 3D conventional metals about 30.8 K (vs 23.2 K for Nb3Ge, as printed), ceramic oxides 7 K (3D), 22 K (2D), 180 K (1D); Josephson junction. Chapter 26: integral and fractional quantum Hall effect R_H = h/(n e^2) = 25812.807 ohm from a transverse 2-D superconductor and flux quantum h/2e. Chapter 27: Aharonov-Bohm effect via flux linkage. Chapter 28-29: pair production as LC resonance of spacetime, alpha as a pair-production constant. Chapter 30: positronium radius 2a0, levels E_n = -6.795 eV/n^2, hyperfine interval 8.41155110e-4 eV (203.39041 GHz as printed in the digest). Equation text mostly garbled in the text layer; these chapters carry claims that have NOT been checked by a deep reader. QE deep read of Chapters 24-30 (replaces 'digest only'). Corrections to the earlier summary above: Chapter 27 is a ring magnetoresistance plus a damped oscillation with an assumed period h/2e and a free damping factor (Eq. 27.13); Eq. 27.8 is dimensionally inconsistent; the fine-structure constant is 'identified' (Eq. 29.9 is the identity alpha a0 = hbar/(m_e c)), not derived; positronium E_n = -6.795 eV/n^2 is 0.11 percent below the leading-order value 6.8028 eV that the book's own formula gives. Ch.24: textbook derivations (Beiser) with E = h nu, de Broglie h/p and counting rules supplied. Ch.25: T_c = 0.0091253 E_F/(k_B f^3) with h, m_e, k_B, a round-number density (1e29 or 1e28 per m^3) and a chosen dimension f = 1, 2, 3 (factor 27 between f = 3 and 1); printed values 30.81, 6.64, 22.40, 179.2 K reproduce; applied to real cubic metals it gives Cu 28 K, Ag/Au 22 K, Na 13 K, Al 46 K (observed 1.18 K) though none of the first four superconducts at ordinary pressure and Al does at 1.18 K; Eq. 25.6 gives 2 pi not 4 pi at k_rho = k_z. Ch.26: R_H = h/(n e^2) = 25812.807 ohm follows from Eqs. 26.38-26.39 but hbar enters through v = hbar k/m_e and the integer n is postulated (omega_z/omega_rho = n); misprinted factor 2 in Eq. 26.40; the fractional case adds three postulated integers and permits any rational n, with no selection of odd denominators. Ch.27: period h/2e assumed; the cited Chandrasekhar et al. paper reports h/e as well as h/2e; the model has no h/e term. Ch.28-29: hbar declared an axiom (p.1566); printed eta = 376.730519 ohm should be 376.730313; no measured pair-production quantity is computed. Ch.30: the 'positronium' g/2 = 1.001159652137 on p.1578 is the free-electron g factor (Eq. 1.236) compared with Van Dyck, Schwinberg, Dehmelt 1987 (1.001159652188(4)): -5.1e-11, 12.75 sigma at the printed uncertainty, 11.9 sigma at 4.3e-12, 335 sigma against the 2023 value; with present alpha the formula is +2.9e-10 off (about 2,200 sigma). Positronium hyperfine 203.39041 GHz is reproduced with modern alpha; it is +1.8 sigma from Ritter 1984 and about 1.3 MHz below QED theory, but is built from an alpha^4 coefficient of 0.393 (QED: 7/12), a large alpha^5 term and five chosen factors, with no annihilation term. Lifetimes are misprinted (para 125 ps, ortho 142 ns actual). Answer to the deep reader's question: no derivation in these chapters avoids supplying hbar (or h, or Phi_0 = h/2e) and the integers by hand. The chapters cite no BCS, von Klitzing, Tsui-Stormer-Gossard, Laughlin, Aharonov-Bohm 1959 or post-1987 electron g measurement.

Key claims

• Superconductivity, the quantum Hall effect and the Aharonov-Bohm effect are classical effects of dipole-array electron membranes and flux quantisation.
• Pair production and positronium follow from the classical photon and electron models with the fine-structure constant derived.
• The superconducting transition temperature follows from T_c = 0.0091253 E_F/(k_B f^3) with a chosen dimension f = 1, 2, 3.
• The positronium (free-electron) g/2 is 1.001159652137, compared with a measured 1.001159652188(4) (p.1578).

Relevance: Shows the breadth of the 'solved by classical physics' claim; unchecked by a deep read.

Mainstream conflict: BCS/Ginzburg-Landau theory, Landau levels and the Berry phase in quantum mechanics; positronium is treated by QED with high-order corrections.

Chapter 32: finite gravitational velocity, particle production when the Planck energy equals mc^2, spacetime contraction of 2 r_g per particle (Schwarzschild metric from the classical wave equation, 'conservation of spacetime'), an oscillating universe with period 2 pi G m_U/c^3 = 3.10e19 s (9.83e11 yr) from m_U = 2e54 kg, present radius about 3.2e11 light years, H0 = 78.5 km/s/Mpc, acceleration from t = 0 (claimed in the November 1995 edition, ch. 22), mass density 1.7e-32 g/cm^3 at 10 Gyr, T_CMB 3.08-3.09 K from the equations, CMB peaks 77 sinc[pi(l-197)/140] at l = 197, 541, 824 (observed about 220, 540, 810), B-mode r = 0.16 (BICEP2 2014, since withdrawn), large-scale power peak 880 million light years. Deep-read verdict on numbers: arithmetic reproduced; H0 is 7-16 percent above Planck/SH0ES; T_CMB 13 percent above FIRAS; mass density below the book's own luminous density; CMB peak positions are a two-parameter fit that works only with a 10 Gyr age (with 13.8 Gyr it fails by the deep reader's calculation); BICEP2 prediction conflicts with r < 0.036 (2021). Book errors: 1 Gyr = 3.1358e16 s (should be 3.156e16), factor 1229 vs 12,290, 'km/s^2 = km/s/Mpc', cosmology digest entries corrected in the corrections section. Chapter 33-34: equal periods of expansion and contraction; absolute space 'confirmed experimentally'; Chapter 35: negative-mass 'pseudoelectrons', photonic super-bound hydrogen states and the EUV continuum, tri-hydrogen cation mechanism (digest only). QE deep reads of the general-relativity half and Ch.34-35. (1) How the Schwarzschild metric is obtained: the wave equation supplies only a light-speed front; the metric then comes from assuming reciprocal time and radial coefficients (asserted, Eqs. 32.11-32.12) and a light-clock argument with the Newtonian escape velocity; the result (Eq. 32.38) is the textbook Schwarzschild metric. The claim that it differs from Fock's form (32.41) by being 'not conservative' is a coordinate relabelling (r to r + GM/c^2) [calc]. (2) Table 32.1 perihelion advances (Mercury 43.11 +/- 0.45 observed, 43.03 'theoretical'; Venus, Earth, Icarus) and Table 32.2 light deflection (1.57-1.87 arcsec; Fomalont-Sramek 1.761 +/- 0.010) reproduce the GR numbers (42.98; 1.751 arcsec [calc]); the 'observed' columns are 1970s compilations. Because the metric is GR's, these data cannot distinguish Mills's theory from GR; the solar-oblateness paragraph (J2 = 1.84e-6) has not been updated. Mills's own new element is that light has zero gravitational mass. (3) Gravity waves: p.1678: 'no transverse time-dependent gravity wave effect in the far field consistent with the absence of the observation of gravity waves [32-33]'; p.1642: 'no physical basis for a transverse light-speed propagating gravity field ... consistent with the absence of the direct experimental observation of gravity waves [128,129]'. Refs are LIGO 2009 and Shawhan 2010. The page also cites 2017 results (refs 134-136), so it was edited after 2017. LIGO detected GW150914 on 14 Sept 2015 (announced 11 Feb 2016) and GW170817 in 2017 arrived with a gamma-ray burst; binary-pulsar orbital decay (Hulse-Taylor, 1974 onward) fits GR's emission rate [memory, high; web check pending in the arbiter's QE revision]. (4) Higgs: p.1678: 'Such a mass conveying particle will not be observed in experiments performed at Fermilab, the LHC, or any future collider [31]' (ref 31 = Science 2010 news item); the next sentence reinterprets the CERN 126 GeV boson as 'a high-energy neutron resonance' predicted at 128.75 GeV (Eq. 37.47), +2.8 percent from the measured 125.20 GeV [memory, medium]. (5) 'Absolute space confirmed experimentally' (p.1678): quasars show no time dilation (Hawkins 1993-2010) and supernova ejecta show it; the SN 1997ex dilation matches 1 + z = 1.36, whereas ejecta at 0.07 c give a Lorentz factor of 1.0025 [calc]; Lewis and Brewer (Nature Astronomy 2023) report the (1 + z) dilation in quasars [memory, medium]. (6) Speed of gravity: p.1592 says the speed of gravity was measured to be c (a 2003 New Scientist item); agrees with GW170817. (7) Chapter 35, fifth force: three curvature states of an electron (bound positive, free flat, pseudoelectron negative). The free electron has inertial mass but zero gravitational mass 'in the limit of the electron being absolutely free' (p.1686); support offered: Witteborn and Fairbank, PRL 19, 1049 (1967), 'less than 0.09 m_e' (an upper limit; the book rejects the Schiff-Barnhill shielding explanation as 'untenable' and gives no equation or citation for it), and a CERN Courier item (Amsler, March 2014) saying electron drops gave g 'consistent with zero' because shielding fields can counterbalance gravity. The pseudoelectron (metric with the sign of v_g and r_g reversed, hyperbolic orbits, repulsive force) is formed by photons of at least 44.2 eV [calc: 44.23 eV] in the field of a massive body whose M/R exceeds a threshold: the book prints 9.39e17 kg/m twice (Earth's own ratio), whereas its inequality gives about 1.17e23 kg/m [calc]; Earth does not qualify and the book names only black holes. Proposed laboratory route via H3+ + e- collisions (Eq. 35.106) needs a gravitating body that the chapter does not supply; black-hole jets and fast H2 (Tadhunter et al., Nature 2014) are reinterpreted as pseudoelectron effects. No acceleration, curvature or negative gravitational mass is computed. Matching patents found by the Investigator: 'antigravitational force' (1989, 1994) and 'Fifth-force apparatus and method for propulsion' (2007) (research/2026-10-09-google-patents.md).

Key claims

• The universe oscillates with a 9.8e11-year period and accelerates from t = 0; H0 = 78.5 km/s/Mpc; the CMB acoustic peaks come from the same equations.
• The Schwarzschild metric and gravity follow from the classical wave equation with particle production; inertial and gravitational mass are equal because of absolute space.
• Dark matter is hydrinos concentrated at galaxy centres and in halos.
• Gravity waves do not exist as transverse far-field waves ('consistent with the absence of the observation of gravity waves', p.1642, p.1678); the Higgs boson 'will not be observed' at the LHC (p.1678); the Schwarzschild metric (Eq. 32.38) is the textbook one, so perihelion and light-deflection agreement does not separate the book from GR.
• A free electron has zero gravitational mass (Witteborn-Fairbank, < 0.09 m_e); negatively curved pseudoelectrons feel a repulsive fifth force, formed by photons of at least 44.2 eV near a very dense body (Ch.35).

Relevance: Contains the claimed 1995 prediction of cosmic acceleration and the hydrino-dark-matter link; the numerical cosmology can be checked with a calculator.

Mainstream conflict: Conflicts with general relativity, Big Bang cosmology with cold dark matter and inflation (BICEP2 withdrawn); an oscillating closed universe with a minimum radius equal to r_g is not supported by CMB flatness and nucleosynthesis data.

Lepton masses from photons whose energies are the Planck energy, potential energy and magnetic energy, each equal to mass energy; muon-to-electron ratio from alpha only, with field corrections (Eqs. 36.12-36.22) that make it match to 1.6e-8 (bare formulas are off 0.35, 0.44, 0.09 percent); absolute electron mass uses h, c, G, alpha and a time unit 'sec', 0.11 percent low unless 1 sec = 0.9975 s is fitted (Eq. 36.4); proton/neutron masses (m_n 0.15 percent off, 1838.674 vs 1838.68366 m_e after the fitted sec); magnetic moments mu_p = (8 pi/9) mu_N = 2.792527 vs 2.792847 (-1.15e-4), mu_n = 1 - 8pi/9 - 3/25 = -1.912527 vs -1.913043; Z 91.16, W 80.51, Higgs 128.75 GeV vs measured 91.188, 80.369, 125.20 (+2.8 percent); X17 17.11 MeV published after ATOMKI reports; top quark mass 187 GeV vs 172.57 +/- 0.29 GeV measured (8-9 percent off; book compares with CDF 186 +/- 10); neutron beta decay energy 0.78241 vs 0.78233 MeV; deuteron binding 2.181 vs 2.2246 MeV (-2.0 percent); alpha decay is the standard Gamow derivation. Book errors: experimental proton moment printed 2.79268 (correct 2.792847), proton mass printed 1.672648e-27 kg, neutron half-life '12 minutes' (about 10.2), OPERA 2011 described wrongly, Eq. 38.20 gives 197 not 196 GeV. Whether the correction factors were fixed before comparison is open; the deep reader calls for a look-elsewhere count.

Key claims

• The lepton and nucleon mass ratios and magnetic moments follow from alpha and a few geometric factors: m_mu/m_e matches to 1.6e-8.
• The theory predicted the top quark mass and the X17 mass (17.11 MeV) before measurement.
• Neutron beta decay, deuteron binding and alpha decay follow classically.

Relevance: Particle-mass claims are the most easily falsified numerical claims; the predicted top mass is 8-9 percent off the modern value.

Mainstream conflict: The Standard Model takes lepton and quark masses as free parameters (no known formula); the Higgs mechanism, QCD and weak interaction are accepted and tested.

Chapter 40: the Schroedinger charge density 'must radiate' by Haus's condition, via a Fourier transform of the radial factor r exp(-r/a0) (a factor-2 slip in Eq. 40.5), but the argument depends on the premise that the charge density oscillates at omega_n, which is asserted not derived (|psi|^2 is static for a stationary state in standard QM). Chapter 42: the Aspect coincidence curve R(phi)/R0 = 0.2490 + 0.2178 cos 2 phi and violations delta = 5.8e-2 (13 sigma) and S = 0.118 (9 sigma) are claimed predicted classically from extended photons with the same linear polarization, formally by adopting Horne's Eq. 5.17 with p_f = 1; the deep reader found (42.23) is the QM prediction formula of the Aspect paper (medium-confidence memory), and the verbal mechanism gives half the modulation and satisfies Bell inequalities. Bell's theorem 'does not apply'; the book cites nothing on Bell tests after 2007 (no loophole-free 2015 tests). Other sections treat Wheeler's delayed choice, Monroe 1996 Schroedinger cat ions, Friedman 2000 SQUID (calc 0.139 K vs 0.14 K, depends on the alpha factor; about 120 K without it), O'Connell 2010 (6.187 GHz), free electrons in superfluid helium (bubble radius 6.7 A, 15 mobility peaks of Ihas and Sanders matched with mean deviation 3.4 percent but about 69 candidate values), quantum bouncer neutrons (z1 12.6 micrometres). Book errors: mis-numbered cross-reference in Eq. 42.132/42.160, Josephson constant units, Table 42.3 peak 15 vs text.

Key claims

• The Schroedinger charge density must radiate, so the quantum-mechanical electron is inconsistent with Maxwell's equations.
• The Aspect experiment and Bell-inequality violations are predicted classically, so there is no spooky action at a distance.
• Wave-particle duality, Schroedinger-cat SQUID and ion experiments, and electron mobility peaks in superfluid helium are explained classically.

Relevance: The book's direct attack on quantum mechanics; two of the three claims depend on postulates beyond Maxwell's equations.

Mainstream conflict: Bell-inequality violations have been confirmed in loophole-free tests (2015); local hidden variable theories are ruled out; the stationary Schroedinger state has a static charge density.

Appendix I: Fourier-transform proof of nonradiation. Deep read: the transform vanishes only because the wavelength is set equal to r_n (lambda_n = r_n) by a light-speed-frame postulate with v replaced by c (for hydrogen k r1 = alpha, transform about 0.99999 of maximum); a zero of the sinc factor is said to make a convolution vanish, which does not follow; for l >= 1 the correct factor j_l(k r_n) is not zero at k r_n = 2 pi (j_1 = -0.159); the l = 0 static state is nonradiating, trivially because it is time-independent. Poynting-vector proof assumes its conclusion (a_E set to zero by dropping a term that charge continuity makes nonzero; the l = 1, m = 1 case is a rotating dipole). Appendix II: the shell has finite self-energy but the outward self-stress sigma^2/(2 eps0) (the Poincare problem) is removed by postulate; direct shell integral at r = a gives a factor 1/2 the book rejects as 'nonphysical' although the same 1/2 is measured on conductors; with the self force included the book's force balance gives r = 2 a0; the field-energy derivation of 13.6 eV silently includes the self-energy. Appendix III: muon g/2 = 1 + (g_e/2)(1 - beta_mu^2) with beta_mu^2 = 2/g_mu taken from the measured g_mu itself, so 1.001165923 is returned within 7e-9 for any input and cannot be a Fermilab test; crossed-field assumption not the BNL apparatus. Appendix IV: great-circle rotation matrices; the printed Y_0^0 construction has an invalid substitution (Eq. 27 drops R_y(-pi/4)) and a false equality (Eq. 30), and is not uniform in polar angle (density 0.82-1.35 of the mean for N = M = 200) unless the Bujnak-Hlucha normalization of Chapter 1 is applied; rotation matrices themselves are correct. Appendix V: photon fields algebra (E_0 algebra correct given a mixed Gaussian/SI prefactor convention; Eq. 19's H gives zero mean power flow with Eq. 18's E if i and j are both sqrt(-1)). Appendix VI: helium force balances (see Ch. 7-9 entry).

Key claims

• The Schroedinger-theory and classical orbitsphere nonradiation condition follows from the spacetime Fourier transform of the current density (wavelength = radius).
• A zero-thickness charged shell has no self force or self-energy problem.
• The muon g factor follows from an electric term g_mu/2 = 1 + (g_e/2)(1 - beta^2).

Relevance: The foundational proofs: every chapter depends on the nonradiation and stability conditions. The deep reads show where these rest on postulates.

Mainstream conflict: The electron's stability in QM comes from the uncertainty principle and quantised states; a charged shell experiences a Poincare stress in classical electrodynamics; muon g-2 is calculated in QED/SM.