Gardi-Lori · Source catalogue

Conference essay (Proceedings of the CNPS, Vancouver 2017, 6 pp, ResearchGate preprint). Argues by analogy with sound that all waves need a medium, so light needs an aether. It rewrites c = 1/sqrt(eps0 mu0) as sqrt(mu0^-1/eps0) to mimic the sound-speed formula v = sqrt(stiffness/density), then borrows Menahem Simhony's NaCl-lattice picture: for NaCl it computes v = sqrt(A/(B+C)) = 3700 m/s from a bond binding energy A = 1.3052e-18 J and ion masses B, C (the arithmetic checks: about 3699 m/s). It then plugs in the electron-positron pair binding energy 1.637e-13 J (1.022 MeV) and pair mass 1.8219e-30 kg (2 m_e) and gets exactly c, concluding that vacuum is a lattice of bound electron-positron pairs (Dirac sea). The same formula is said to work for proton-antiproton or quark pairs. The Michelson-Morley null result is dismissed as circular because light is used to detect the medium for light; an unofficial ultrasonic 'acoustic MM' test (Feist) also gave a null in air. Further claims: light may have a faster longitudinal 'P-wave' component; the 2015 LIGO event GW150914 is read as the aether P-wave, followed 0.4 s later by a gamma-ray transient (Fermi GBM) read as the S-wave, justified by visual similarity of the LIGO strain trace to a seismic P-wave. Prediction offered: if all future 'gravitational waves' are followed by gamma-ray signals the aether idea should be revisited.

Key claims

• Light requires a material medium (aether) to propagate, as sound does.
• The vacuum is a medium of bound electron-positron pairs whose wave speed sqrt(binding energy / pair mass) equals c.
• The same formula gives c for any particle-antiparticle pair (proton-antiproton, quark-antiquark).
• The Michelson-Morley null result does not rule out an aether because light is used to detect the medium of light.
• Light has an undiscovered longitudinal component travelling slightly faster than c.
• LIGO's GW150914 signal was an aether P-wave and the Fermi gamma-ray transient 0.4 s later was the matching S-wave; every future LIGO event should be followed by a gamma-ray signal.

Relevance: Earliest paper in the set; sets up the aether / Planck-pair medium that later papers (OM particle, spacetime lattice) develop. Cites Simhony and Hotson (Dirac-sea aether authors).

Mainstream conflict: Conflicts with special relativity (no preferred frame, MM and later cryogenic-resonator nulls), with vacuum Lorentz invariance, and with the standard reading of GW150914 as a tensor spacetime wave from a black-hole merger. The pair-binding 'derivation' is E = mc^2 rearranged (A = 2 m_e c^2, so sqrt(A/2m_e) = c identically), not an independent check.

CNPS 2018 (Storrs, CT) paper comparing four classical equations (E = mc^2 vs Coulomb force; Newton's second law vs 'New Induction'; electron magnetic moment vs 'New Magnetism'; gravity/centripetal force) with independent researcher Robert Distinti's equations and Jeff Yee's wave-constant model of particles (standing longitudinal waves, after Milo Wolff). Central result: F = m c^2 r_e / r^2 is declared 'equivalent' to Coulomb's law k_e q^2 / r^2 and numerically checked at several distances for one electron; the maximum force is 29.1 N at r = r_e. The authors conclude the standard equations are 'simple and elegant' but lack detail, and that Distinti's and Yee's are better. Check: m c^2 / r_e = 8.187e-14 J / 2.818e-15 m = 29.05 N, equal to k e^2 / r_e^2 because the classical electron radius r_e is defined by m c^2 = k e^2 / r_e, so the equivalence holds by definition and tests nothing. Deep read: each 'equivalence' (Coulomb vs mc^2 r_e/r^2; 'New Induction' F = K_M q1 q2 a/r; 'New Magnetism' F = K_M q1 q2 v^2/r^2) is an identity once r_e is defined by m c^2 = k_e e^2/r_e; the tables evaluate the identity at four inputs, always at r = r_e, and the 'energy conservation' equalities in Fig. 14 are built in because every row uses a = v^2/r_e. The 'gravitational energy three ways = 1.97e-56 J': Eqs 9 and 10 are the same quantity by definition, and Eq. 11 cannot be checked because its constants (delta_e, K_e, O_e) are defined only in an outside viXra paper. The Discussion concedes the models 'evaluate to the same force', so no testable difference from standard physics is stated. New finding: the stated constant K_M = mu0/(2 pi) gives twice the tabulated values (K_M e^2/r_e = 2.000 m_e); the numbers in Fig. 7 need mu0/(4 pi). The standard counterpart of 'New Induction' is the radiation (acceleration) field of an accelerated charge, which is a field on a second charge and not an inertial force; 'New Magnetism' at point-charge level is the standard F_mag/F_Coulomb = v^2/c^2 up to that factor of 2. The authors read m = K_M q1 q2/r as 'the cause of mass has to do with charges at distance', which is the classical electromagnetic-mass idea read backwards (circular with q1 = q2 = e, r = r_e).

Key claims

• F = m c^2 (r_e/r^2) equals the Coulomb force for an electron at all distances.
• Distinti's 'New Induction' and 'New Magnetism' equations are equivalent to Newton's second law and to the electron magnetic-moment equation respectively.
• Particles are standing longitudinal waves and Coulomb force is the amplitude of the same waves travelling outward.
• Yee's wave-constant equations give all of these results from one common equation, with more detail than the standard equations.
• The gravitational energy of an electron computed three ways equals 1.97e-56 J (Eqs 9-11); two of the three are the same definition and the third rests on constants defined outside the paper.
• The stated constant K_M = mu0/(2 pi) in 'New Induction' and 'New Magnetism' is inconsistent by a factor 2 with the tabulated numbers, which need mu0/(4 pi) (found by recomputation, not claimed by the authors).

Relevance: First paper in the Yee-Gardi collaboration; introduces the wave-constant / standing-wave electron that later papers turn into the spacetime lattice.

Mainstream conflict: Contradicts nothing numerically only because it re-expresses the definition of r_e; its claimed superiority of the alternative equations has no stated testable difference. Treating charge as wave amplitude departs from the standard picture.

Preprint (Nov 2018, 7 pp). Presents complex numbers a + bi as 2x2 real matrices: scalar [a] = diag(a,a) and the imaginary unit as a rotation-type matrix with entries on the backward diagonal. Says this explains why 'i' is linked to rotations and phase, shows the Mandelbrot set can be generated using only the matrices, and writes Euler's formula in matrix form, applied to robot kinematics. The mathematics is the standard isomorphism between C and a subring of 2x2 real matrices (a well known fact), and so is pedagogy rather than new physics.

Key claims

• Complex numbers can be represented exactly by 2x2 real matrices, removing any need for a mysterious imaginary unit.
• Euler's formula in 2x2 matrix form simplifies robotic kinematics.

Relevance: Mathematical background tool for the project's wave and Mandelbrot papers; not itself a physical claim.

Mainstream conflict: none (standard mathematics, presented as a reinterpretation)

Two-page results sheet (Dec 2018, 'The OM Particle' series). Redefines eps1 = 4 pi eps0 and mu1 = mu0/(4 pi), then defines capacitance C = (1/2)(c/omega) eps1 ... , inductance L, reactances X_C = X_L, voltage V = 2 omega q_pl / (c eps1), current I = omega q_pl, and a 'velocity of spin' omega^2 = 1/(LC). The impedance V/I = 59.958 ohm is said to be the 'correct' impedance of free space, i.e. Z0 / 2 pi (Z0 = 376.73 ohm), on the argument that only one 2 pi may appear and it belongs to omega. Two further 'quantum constants' are defined: quantum of momentum h/c = q_pl^2 mu1 = 3.5177e-43 and quantum of flow hbar c = q_pl^2/eps1 = 3.1615e-26. The equations are definitional rearrangements of Planck-unit and free-space constants; no measurement is predicted. Equations rendered in text layer, spot-checked: 376.73/2pi = 59.96.

Key claims

• Free space behaves as an LC circuit whose impedance is Z0/(2 pi) = 59.958 ohm.
• Placing all 2 pi factors in the angular frequency simplifies the equations of light.
• Planck's constant is a 'quantum of energy' per cycle and h/c is a 'quantum of momentum'.

Relevance: Compact statement of the 'LC model of the medium' that later feeds the OM particle model; relies on MUA.

Mainstream conflict: The 59.96 ohm 'correct' impedance disagrees with the SI value 376.73 ohm by a convention-driven factor 2 pi, with no new physics; per-cycle energy quantum conflicts with E = h f for a photon.

Preprint (Mar 2019, 5 pp). Worked example: force of a 0.516 W, 726 nm laser on a perfect reflector. Standard physics gives F = P/c = 1.7212e-9 N. The paper rederives the same number with 'Modified Unit Analysis' (MUA), which adds a base unit 'cycle' [Delta] and writes Planck's h as energy per cycle with a hidden 1-second 'measure time' t_m. Steps: power per frequency 'quantum of power' = h (numerically), a 'quantum of force' per cycle, a single-photon-per-second force F_s = 9.1268e-28 N (this equals h f / c at 726 nm, checkable), then an 'amplification factor' A = 0.516 / (h f) = 1.8859e18 and F = A F_s = 1.7212e-9 N. Since A is just P/(hf) and F_s is hf/c, the product is P/c algebraically, so the example agrees with the standard result by construction and cannot distinguish MUA from standard physics. Discusses 'it makes no sense' that quantum equations use momentum and energy while macro equations use force and power.

Key claims

• MUA reproduces the radiation force P/c of a laser from first principles using 'quantum of power' and 'quantum of force'.
• Planck's constant, as energy per cycle, attached a hidden per-second measure time to a per-cycle energy and so blurred the nature of light.
• Quantum mechanics is only statistical because of this unit confusion (suggested, not shown).

Relevance: Offered as corroboration of the Planck-constant paper's reinterpretation of h.

Mainstream conflict: Reinterprets h; for equal outputs it adds no testable difference. Statement that quantum mechanics is statistical because of units is unsupported.

Article (July/Aug 2020, 10 pp). Mostly Dinu's mechanical-aether theory with Gardi as co-author. Proposes that electric charge is not fundamental; electrostatic forces arise from vibration ('energy charge') of a new neutral chemical element, the 'electrigen', identified with Mendeleev's hypothetical element y of Group 0 (aether being element x). Electric current in a wire is a diffusion wave of electrigen, and the magnetic field of a current is the circular motion of aether in surface-wave fashion around the wire (water/air interface analogy). Supports: Crookes tubes, Richardson thermionic emission, thermoelectric effects and voltaic-cell thermodynamics (heat of reaction vs electrical work, i.e. Gibbs-Helmholtz) are read as showing 'electrification is molecular vibration'. The aether is a compressible inviscid liquid carrying only longitudinal waves. No equations or quantitative predictions appear in the text read.

Key claims

• Electric charge does not exist; electrostatic force results from vibration of matter ('energy charge') transmitted through the aether.
• A new neutral element, the 'electrigen', exists (Mendeleev's element y) and is what flows in metals as electric current.
• Electric current is a diffusion wave of electrigen, and its magnetic field is aether circulating around the wire like a water-surface wave.
• The aether is a compressible inviscid liquid propagating only longitudinal waves.

Relevance: The only non-Gardi-led document; shows the older mechanical-aether tradition Gardi collaborates in. Marginal to the Gardi-Yee line of work.

Mainstream conflict: Contradicts the electron (thermionic emission, J. J. Thomson, Millikan), charge conservation and quantisation, Maxwell's equations, and the periodic table (no Group 0 element 'electrigen'); a liquid with only longitudinal waves cannot support light polarization.

Conference essay (CNPS Vancouver 2017, 12 pp, ResearchGate preprint). Draws an analogy between the Mandelbrot set (iteration z := z^2 + c) and a Schwarzschild black hole: the set's singularity, photon sphere, event horizon, time, entropy and space-time curvature are mapped to features of the set, the atom is called a quasi-black hole, and chiral symmetry is discussed. The author labels the evidence 'circumstantial and highly speculative'. Prediction (section 15): the shadow/photon-sphere of a black hole should be oblate or slightly pear shaped, with the singularity at the (0,0) point of the Mandelbrot set. Evidence given: the M87 supermassive black hole sits 22 light years off the galaxy centre and a Hubble image of its bright region is pear shaped; a hand-aligned alpha-blended overlay of M87 on a 2-iteration Mandelbrot rendering shows the black hole at (0,0); quasar 3C 186 is displaced similarly; pear-shaped nuclei of Ra-224 and Ba-144 are cited as support for 'atoms as quasi-black holes'. No quantitative test or error analysis. The Event Horizon Telescope data (April 2017) were not yet released when written. Deep read: (1) The pear-shaped photon-ring 'prediction' is qualitative and hedged ('oblate or slightly pear shaped ... if at all'): no eccentricity, size or orientation is given, and the rule for registering a real image on the Mandelbrot set is not stated (done by eye). The author calls it 'highly speculative'. (2) The M87 '22 light-year offset' is quoted from Batcheldor et al., ApJ Letters 717 (2010) L6; the overlay uses a Mandelbrot rendering 'after only two iterations' (a free choice), with free scale, rotation and translation by alpha blending, no residual or uncertainty, and the pear is a feature of an optical HST image at kiloparsec to parsec scale, not the photon ring (tens of microarcseconds) [memory, high]. So the 'exactly where predicted' result is a post hoc fit. (3) For quasar 3C 186 (Chiaberge et al., A&A 600 (2017) A57, gravitational-wave recoil interpretation) no overlay, offset value or comparison is shown. (4) Pear-shaped nuclei (Ba-144, Ra-224) are offered as support for 'atoms are quasi-black holes' with only an analogy (nucleus = black hole, electron shells = photon sphere, weak-force range = event horizon). (5) The S-star orbit comparison (Appendix A, Fig. 12) and the Fermilab bubble-chamber comparison (Fig. 13) are visual similarities of curved trajectories with loose labels 'preliminary results'; no seed values, periods, masses or orbit elements are given, and the author says the model cannot give exact trajectories. (6) Other statements: it is 'just as hard to get into a black hole as to get out' (Chandra Sgr A* gas-inflow fraction cited); the 2D set is extended to 4D via quaternions with no derivation; entropy is handled by shrinking 'measuring sticks' (scale relativity) with accelerated expansion called 'an optical illusion', with no fit to redshift data; Einstein's cross is offered as an alternative to gravitational lensing; refs 9 and 11 are the same galaxy-chirality paper.

Key claims

• The Mandelbrot set is a mathematical model ('quasi-black hole') of the structure of real black holes, with matching singularity, photon sphere and event horizon.
• Black-hole photon rings should be slightly pear shaped rather than the circular ring of general relativity.
• The M87 and quasar 3C 186 black holes sit exactly where the Mandelbrot-set model predicts relative to their bright host regions.
• Atoms are quasi-black holes.
• Apparent cosmic acceleration is an optical illusion because measuring sticks shrink over time (scale relativity), and Einstein's cross shows a Mandelbrot-like structure that replaces gravitational lensing (asserted, no equations or data fits).
• Curved trajectory patterns in a Mandelbrot-set rendering resemble the orbits of the S-stars at Sgr A* and bubble-chamber tracks, so 'dynamics ... are encoded in the M-Set' (visual comparison only, labelled preliminary).

Relevance: A stand-alone speculative paper in the same author's 'fractal cosmology' interest; different in topic from the aether/Planck-lattice papers but shares the self-similarity theme (OM particle).

Mainstream conflict: General relativity predicts a near-circular photon ring for Schwarzschild/Kerr (EHT images of M87* and Sgr A* are consistent with that); a visual overlay is not a test. Atoms are not black holes (nuclear scales are far above their Schwarzschild radii).

Preprint (Jan 2019, rev 2 Feb 2019, 14 pp). Applies Ohm's law V = I R to the 'universe': the electric constant eps0 is cast as the voltage-like and mu0 the resistance-like property, the speed of light as the current. To make units agree, charge in coulombs is replaced by wave amplitude in metres (current becomes velocity, voltage a force). The authors then derive Coulomb's law, the electron rest energy / mass (at the classical radius r_e), and a 'strong force' via the Bohr radius, and offer an attractive/repulsive 'previously unknown repulsive force' that keeps electrons from collapsing into the nucleus. Credits the 'electric universe' movement as motivation. Deep read (equations read as page images): every equation is an algebraic rearrangement of textbook relations in which alpha, r_e and a0 are already tied by r_e = alpha^2 a0. (a) Electron mass: m_e = mu0 e^2/(4 pi r_e) (Eq. 2.9) is the definition of r_e solved for m_e. (b) 'Strong force' F_s = 42,127 N (Eq. 3.5): Coulomb's law at an assumed proton radius 8.663e-16 m (307.4 N) times 1/alpha = 137.036; the factor 137 is assumed (Eq. 3.1-3.2), and the radius has no stated source (CODATA 2014 gave about 8.751e-16 m, muonic hydrogen about 8.41e-16 m [memory, medium]; with 8.41e-16 m the formula gives about 44,700 N). QCD forces are not inverse-square with a factor 137 and quarks carry fractional charge. (c) The inverse-cube 'orbital force' F_o, a 'previously unknown repulsive force' active when the electron lies on a line through two or more quarks, has its prefactor (r_e/r)(1/alpha^2) chosen so that it crosses the Coulomb force exactly at r = r_e/alpha^2 = a0; the Bohr radius is therefore returned by construction, and alpha is then read off the result (Eq. 4.6), which is circular. (d) E_Ry = (1/2) F_o a0 reduces to e^2/(8 pi eps0 a0), and h = (1/2) mu0 c e^2/alpha (Eq. 4.20) is the definition of alpha solved for h. (e) Multi-electron atoms: the paper states that frequency 'is hiding another variable', a wave-interference factor Delta that depends on the number and configuration of protons and other electrons, enters as f = Delta alpha c/(4 pi r), and that frequencies from hydrogen to calcium 'are calculated with a similar methodology and are presented in a separate paper [12]' (not in the folder; it is most likely Yee's atomic-orbitals viXra paper, see the Spacetime entry). No Delta or r is given for any atom beyond hydrogen on pp.5-13, so with two free parameters per line any single photon energy can be matched. (f) The symbol Delta is overloaded (charge multiplicity, 1/alpha, alpha, many-body factor). Charge is relabelled as metres and voltage as a force (numerically nothing changes). No experiment, uncertainty estimate or falsifiable prediction appears: no number on pp.5-13 is a result that was not an input or a definition.

Key claims

• The universe obeys an Ohm's-law relation between eps0, mu0 and c.
• Charge is wave amplitude with units of metres, and current is a velocity.
• Coulomb's law and the electron's mass and energy follow from the wave-Ohm's-law energy equation at r = r_e (an identity: the definition of r_e solved for m_e).
• The strong force at the proton radius is 42,127 N, which is 137 times the Coulomb force (input 1/alpha times Coulomb's law at an assumed radius).
• An inverse-cube repulsive 'orbital force' keeps the electron at the Bohr radius a0 = r_e/alpha^2 (its prefactor is chosen to produce this).
• Planck's constant is h = (1/2) mu0 c e^2/alpha and the Rydberg energy and frequency follow (the definition of alpha rearranged).
• Photon energies of multi-electron atoms depend on a wave-interference factor Delta, which explains why they are hard to predict beyond hydrogen (no value of Delta is given; results deferred to an unseen separate paper).

Relevance: Step two in the Yee-Gardi chain: from wave electrons to charge-as-length, feeding the mass-charge paper and then the lattice papers.

Mainstream conflict: Redefines the SI unit of charge (coulomb) as a length; standard physics treats charge as an independent dimension. The 137-times 'strong force' with inverse-square dependence and a unit-charge pair of quarks is not QCD (fractional quark charges, colour, roughly constant string tension at hadron scale [memory, medium]). Multi-electron atoms are treated by Hartree-Fock, density functional and configuration-interaction methods in standard physics [memory, high]. 'Electric universe' is not accepted cosmology.

Earlier of two versions (uploaded 23 Dec 2018, 10 pp). Same main argument as V3 (see the V3 entry) with a different abstract ('a more classical definition of Planck's constant as the energy of one oscillation'). Deep read of pp.6-10 found two items the first pass missed. Appendix B ('displacement current'): the paper says Maxwell's equations are 'either incomplete or inherently flawed', citing a thought experiment of a circular wire as a series capacitor and inductor, credited to Robert Distinti and 'loosely transcribed' from his YouTube video 'The Great Displacement Current Caper', plus an unreferenced mention of an IBM 'camelback effect'. Its derivation (eqs. 36-42) starts from rho = div D, keeps only the x term, multiplies by dx/dt and 'cancels' the dx terms to obtain rho (dx/dt) = J = dD/dt, so Ampere-Maxwell (written 'nabla H = J + dD/dt', eq. 35) becomes '= 2 x J' (eq. 43) and then 'nabla H = J = dD/dt' (eq. 44): displacement current and current density are 'one and the same'. The hedge 'further investigation is highly recommended' is attached, but the displacement term is declared spurious. The paper also states that this calls Maxwell's plane-wave derivation into question and that the in-phase E and B of Fig. 4 is wrong versus the 90-degree sine/cosine of Fig. 3. Appendix A ('a proton force constant'): with the MUA quantum of momentum pq = h_q/c = 2.2102189e-42 kg m/s, the paper forms F_e = pq f_e = 2.7309e-22 and F_p = pq f_p = 5.01439e-19 (f_e, f_p the Compton frequencies c/lambda_C of electron and proton) and says F_p is absent from the NIST tables. Recomputed: both are exactly m_e c and m_p c (ratio 1.000000), i.e. momenta in kg m/s, not forces in newtons; the numbers are right but trivial. Also in V2 p.6: the MIT 500 pK figure is quoted by the author as 'one order of magnitude' above her floor. In sections 10-11 the paper says wt and kz 'cannot be added' in cos(wt - kz) because MUA units give [cycle-seconds] minus [cycle-metres], so 'any derivation using this expression, including Schroedinger's equation, is erroneous'; this is a notational objection (both are angles in radians).

Key claims

• The numerical value of h is the energy of one cycle, h_Delta [J/cycle], as in V3.
• Maxwell's displacement current is not a separate term: displacement current and current density are 'one in the same', so nabla x H = J = dD/dt (Appendix B, eq. 44; credited to Robert Distinti, unreferenced IBM 'camelback effect').
• The proton 'force' F_p = 5.01439e-19 N (= pq x f_p) is missing from the NIST tables (it equals m_p c in kg m/s, not a force).
• The expression cos(wt - kz) 'makes no logical or mathematical sense', so derivations using it, including the Schroedinger equation, are erroneous.

Relevance: Superseded by V3.

Mainstream conflict: Without the dD/dt term there are no electromagnetic waves in vacuum (rho = 0, J = 0 would give curl H = 0) and charge conservation fails: div(curl H) = 0 would force div J = 0 always, so a capacitor plate could never charge [memory, high; Griffiths ch. 7-9]. The 'cancel dx' step treats a spatial derivative as a ratio. Otherwise as V3 (contradicts E = hf at single-photon level).

Preprint (10 pp, DOI 10.13140/RG.2.2.29763.09767). The central text of Gardi's 'Modified Unit Analysis' (MUA). Claims that writing E = h f with units [J s][1/s] hides an unbalanced unit, because the '1' in 1/s means 'one cycle'. MUA adds a base unit 'cycle' [Delta]: h = h_Delta t_m, with h_Delta = 6.626e-34 J per cycle and a hidden 'measure time' t_m = 1 s. Thus E = h f is the energy collected in one second, not the energy of a photon, and each oscillation of light carries the same energy h_Delta regardless of frequency; the photon is 'an arbitrary accumulation of quanta over a 1-second interval'. Power is rewritten P = h_Delta f [J/s]. A section reinterprets Heisenberg's uncertainty principle: a smallest detectable energy change 6.626e-34 J removes the uncertainty. Also uses e^(i phi) = cos + i sin as the wave construct. Standard physics fact: a cycle is dimensionless, and E = h f for each photon is confirmed by the photoelectric effect (Millikan 1916), Compton scattering, and single-photon detectors; a constant energy per cycle would conflict with those. The 'per-cycle energy' number only equals h when an arbitrary 1 s interval is chosen.

Key claims

• The units of E = h f do not balance unless a base unit 'cycle' is added.
• The numerical value of Planck's constant is the energy of a single oscillation of light, the same at every frequency.
• A photon is not fundamental; it is an arbitrary one-second accumulation of per-cycle quanta.
• Light is better modelled with power P = h_Delta f than with photon energy.
• The Heisenberg uncertainty is removed because energy has a smallest detectable step of 6.626e-34 J.
• Maxwell's displacement current equals current density, so nabla x H = J = dD/dt (Appendix B, retained from V2, not softened).

Relevance: Foundational for later papers (LC circuit, Planck-unit lattice with h not hbar, OM particle).

Mainstream conflict: Contradicts photon energy E = h f at single-photon level (photoelectric threshold, Compton, photon counting), and the SI definition of h in J s. Rescaling a unit convention changes no measurement.

Preprint (Mar 2019, rev 2 May 2019, 6 pp). Extends the electric-universe paper: mass is standing longitudinal wave energy, charge is travelling longitudinal wave energy over distance. Granules (the substance filling space) collide and pass energy. The elementary charge is wave amplitude at the first wavelength (in metres). Mass of the electron is re-derived from the energy equation without the c^2 factor with r = r_e (m_e = mu0 e^2/(4 pi r_e), which is simply the standard definition of the classical electron radius rearranged); Coulomb's law is recovered with k = mu0 c^2/(4 pi). A units table renames C as metres, A as m/s, k as a force and mu0 as a linear density. All equation text is missing from the text layer.

Key claims

• Mass is standing-wave energy and charge is travelling-wave energy of the same longitudinal waves in a granular medium.
• The units of charge (coulomb) are 'incorrect' and should be metres.
• The electron's mass follows from the energy equation at r = r_e and Coulomb's law follows from the same equation with k = mu0 c^2/4pi.

Relevance: Bridge to the spacetime-lattice paper, which cites this as its baseline paper 1.

Mainstream conflict: Replaces independent charge dimension with length. m_e = mu0 e^2/(4 pi r_e) is the defining relation of the classical electron radius, so 'deriving' the mass from r_e is circular.

Preprint (May 2019). Paraphrases Lecture II of Steinmetz's 'Electric Discharges, Waves and Impulses' (1914): flux = L i for the magnetic field and Psi = C e for the dielectric field, inductance voltage e0 = L di/dt and capacity current i0 = C de/dt, stored energies L i^2/2 and C e^2/2. Lists dualities: dielectric lines of force end on conductors and are tension (N), magnetic lines are closed and are pressure (N/m^2); one stores potential energy, the other kinetic; attraction vs repulsion. Argues the notion of electrostatic charge on conductors 'destroys the analogy' and that dielectric energy lives in the space outside conductors. The equations given are standard circuit theory; the commentary about charge being obsolete is Steinmetz's (as quoted/paraphrased), not a new result.

Key claims

• The dielectric (electric) field is exactly analogous to the magnetic field: Psi = C e is to phi = L i as potential is to kinetic energy.
• The concept of electrostatic charge on conductors is a 'prehistoric notion' that obscures the electric/magnetic duality.
• Dielectric lines of force are tension and magnetic lines of force are pressure.

Relevance: Historical source for the 'capacitance/inductance' view of the vacuum used in the LC-circuit paper; also supports the charge-is-not-fundamental stance.

Mainstream conflict: Mostly none (standard 1914 circuit theory). Rejecting charge conflicts with the modern view and with Gauss's law, although the energy-in-the-field point is mainstream.

Preprint (Yee and Gardi, 2nd draft, 5 Oct 2019, 23 pp, DOI 10.13140/RG.2.2.14966.14401; 394 reads and 0 citations at download). Builds on the spacetime-lattice paper. Particles are standing-wave clusters around 'wave centers'; the neutrino is the fundamental unit. PDF page numbers are used below; the printed number is one lower. The model's one quantitative result (missed in the first pass): Eq. 4.10, E = E_nu K^5 Sum_{n=1..K} [n^3 - (n-1)^3]/n^4, where K is an integer wave-center count and E_nu = 2.38925 eV. E_nu is first 'derived' in Section 2: lambda = 2 q_P e^2 (e = Euler's number, q_P the Planck charge written in metres), r_e = 2 q_P (K_e e)^2/g_v with K_e = 10 and a 'g-factor' g_v = 0.983592 justified only as a Doppler effect, then E_nu = k q_v^2/r_v/g_v = 2.39 eV. The deep read shows this chain is an identity (Eq. 2.4 is the definition of r_e), a fitted constant (g_v is tuned to r_e to 2 ppm and then cancels exactly out of E_nu), unexplained exponent choices, and a K_e that is itself taken from the Section 4 plot that is calibrated on E_nu (circular). The closed form E_nu = hbar c/(2 K_e^6 e^10 q_P[m]) depends on a coulomb value reused as a length, and E_nu = m_e c^2/(alpha g_v K_e^4 e^8). For Table 5.1 the paper uses 'a refined value of 2.38925 eV ... resulting in the exact calculation of the electron's rest energy', so the E_nu used for every mass is fitted to the electron. Eq. 2.10 is cited on p.13 but does not exist. Fig. 4.2 plots ~30 particles, from the neutrino (K = 1) up to the Higgs (K = 117), by dividing each PDG energy by K^4 against 'the best fit' integer K; the dashed line is y = 2.39 K Sigma(K). Every K is chosen after the mass is known; clashing particles are moved to the next integer (Lambda/Sigma, D/D_s, B/B_s). Neighbouring integers differ in energy by a factor of about 1 + 5/K (1.63 at K = 10, 1.19 at K = 28, 1.12 at K = 44, 1.046 at K = 110), so any mass has an integer K within about 6 % (K ~ 44) or 2 % (K ~ 110): the fit has no predictive power, and no new particle, mass or K is predicted although the Conclusion says new particles 'may be predicted'. Table 5.1 (recomputed): K = 1 neutrino 2.389 eV vs '~2.20'; K = 8 muon neutrino 1.63e5 vs 1.70e5 eV; K = 10 electron 5.11e5 (fitted); K = 20 tau neutrino 1.73e7 vs 1.55e7; K = 28 muon 9.49e7 (printed 9.50e7) vs 1.06e8 eV (10.2 % low); K = 50 tau 1.756e9 vs 1.78e9 (1.2 % low). The three neutrino 'PDG values' are 1990s upper limits, not measurements, and are treated as values. K = 29 gives 113.25 MeV (7.2 % high), closer to the muon than K = 28, but K = 28 is chosen because 8 + 20 = 28 and 8, 20, 28, 50 are nuclear magic numbers (82, 126 and 2 are not used); the paper's own Fig. 4.2 plots the muon at x = 28 but its label y = 149.45 is the muon energy divided by 29^4 (dividing by 28^4 gives 171.9), which hides the misfit. Composite particles (Figs 5.6-5.11): the proton is 'likely four electrons and one positron' (a positron at the centre of a tetrahedron) and the neutron has 'an extra electron in its center' (six elementary particles); only the tau has a wave-center count (K = 50), yet Fig. 4.2 gives the proton K = 44. No charge, spin or mass is counted: simple counting gives -3e (proton) and -4e (neutron); the paper says only that constituents 'cease to be recognized either in charge or energy' by destructive interference. Five electron masses are 2.555 MeV versus 938.272 MeV (a factor 367); the gap is 'energy stored' in standing waves. The neutron is 6 particles in Figs 5.6, 5.9, 5.11 but 4 in Fig. 5.10. Quarks are relabelled (a quark is an electron with energy stored in its waves; a meson is an e-e+ pair; a baryon is three electrons after one pair annihilates; the pentaquark is the whole proton, citing LHCb 2015). Antiparticles are wave centers on the opposite node; annihilated pairs are 'dual tetrahedra' with no detectable charge until pair production (Fig. 3.4). Spin is attributed to the tetrahedron's centre-to-circumsphere distance sqrt(3/8) lambda 'not at perfect wavelengths' (Fig. 3.5), with no value derived. Decay: in beta decay a neutron 'may likely be triggered by something frequent on Earth, such as the bombardment of solar neutrinos'; 'A solar antineutrino collides with center electron and ejects it, becoming a proton', roughly every 15 minutes for a free neutron. No rate, cross-section, shielding or seasonal test is stated or proposed, so it is not stated as testable.

Key claims

• Particles are standing-wave clusters of 'wave centers' in a Planck-scale lattice, with the neutrino (E = 2.39 eV) as the fundamental unit.
• Particle energies follow E = E_nu K^5 Sum[n^3-(n-1)^3]/n^4 with integer K (neutrino 1, muon neutrino 8, electron 10, tau neutrino 20, muon 28, tau 50, proton 44, Higgs 117), and agree with measured masses (Table 5.1: muon 10.2 % low, tau 1.2 % low, electron fitted).
• The wave-center counts 8, 20, 28, 50 coincide with nuclear magic numbers (the choice K = 28 over the closer K = 29 for the muon rests on this).
• The proton is four electrons and one positron, and the neutron five electrons and one positron, with their constituents' charges 'ceasing to be recognized' through destructive interference.
• Beta decay of the free neutron is triggered by solar (anti)neutrinos knocking out the central electron.
• Plotting energy over K^4 versus K linearizes all known particle energies so that new particles may be predicted (no prediction is given).

Relevance: The only document in the folder with a quantitative particle-mass output, so it is the evidence base for claim 6; the first-pass review wrongly said it computes no masses.

Mainstream conflict: Conflicts with the Standard Model (quarks with fractional charge, gauge bosons, lepton-number conservation) and with proton structure from deep inelastic scattering. A 2.39 eV neutrino (and 0.16 MeV and 17 MeV muon and tau neutrinos) conflicts with direct limits (KATRIN m_nu < 0.45 eV, 90 % CL [web https://arxiv.org/abs/2406.13516]) and with oscillation plus cosmology, which put the summed masses well below 1 eV. Electrons inside nuclei were abandoned around 1929-32 on spin-statistics and magnetic-moment grounds (nitrogen-14) [memory, medium-high]. The Sun emits electron neutrinos, not antineutrinos [memory, high]; with a 880 s neutron lifetime a solar-flux trigger needs a cross-section near 1.7e-14 cm^2, about 10^29-10^30 times the known MeV-neutrino value, which would make the Earth opaque to solar neutrinos; free-proton beta-plus decay is forbidden because m_p < m_n [memory, high].

Second draft (5 Oct 2019, 33 pp). Same model as v2.3 but the lattice is a body-centred cubic (bcc) lattice, whereas v2.3 removed 'body-centred'. Otherwise the differences found in the diff were wording and metadata.

Key claims

• Same as v2.3; the lattice is body-centred cubic in this draft.

Relevance: Earlier draft of the main paper.

Mainstream conflict: Same as v2.3.

Principal technical paper (33 pp, DOI 10.13140/RG.2.2.23094.24642). Models spacetime as a cubic lattice of Planck-scale unit cells: a central 'granule' of Planck mass, radius Planck length and displacement Planck charge (treated as a length), cell separation 2 l_P e (e = Euler's number) and longitudinal wavelength 2 q_P e^2. A cell acts as a classical spring-mass system. Inputs are said to be five constants (Planck mass, length, time, Planck charge, and the electron classical radius r_e) from which 'more than a dozen' constants are 'derived' and found to match CODATA: Coulomb's constant, the fine-structure constant (as a geometric ratio of rectangle area to sphere+cone area equal to alpha when all lengths equal r_e), the Bohr radius and magneton, Avogadro's constant, and the gravitational constant G. Forces are attributed to geometry: electric = sphere, magnetic = sphere+cone, strong, and gravity from a 'shading' effect between two electrons. Page 28 (Eq. 5.8.1-5.8.7): the gravity derivation inserts alpha_e l_P^2 / r_e^2 into the electric-force form and cancels to F = (l_P c^2 / m_P) m^2 / r^2. Since l_P = sqrt(hbar G/c^3) and m_P = sqrt(hbar c/G), l_P c^2/m_P = G identically, so the derivation of G is an identity of the Planck units, not a prediction. Planck charge q_P = sqrt(4 pi eps0 hbar c) and e = sqrt(alpha) q_P likewise make the 'derived' electric constants rearrangements. Inputting r_e, which already contains alpha and m_e, means the electron quantities are not independent outputs. No new measurable prediction was found in the portions read. Deep read (pp.5-33). The paper's 'only five constants' (Planck length, mass, time, Planck charge q_P = 1.87555e-18 'm' and r_e) each already contain hbar, G, alpha, m_e and epsilon0, so any recombination can only return them: it is circular by construction. mu0 itself is an identity (4 pi m_P l_P/q_P^2 = 1/(eps0 c^2)). Classification of the 13 'derived' outputs [calc]: eleven are identities (mu0, k_e, e_e as the definition of alpha, m_e and E_e as the definition of r_e, alpha_Ge = G m_e^2/(hbar c)/alpha, G = l_P c^2/m_P, Bohr radius a0 = r_e/alpha^2 from an orbital force F_o = hbar^2/(m_e r^3) that is the Bohr centripetal term, Rydberg energy, Rydberg frequency and constant, Compton wavelength, Bohr magneton), three of them needing an unexplained factor chosen to fit (1/2 for h and E_Ry, r = r_e/2 for the Compton wavelength). Avogadro's constant N_A = a0/a with a = 2 l_P e (Euler's e) gives 6.02239e23, 37 ppm above the exact SI value, a one-factor fit (and N_A depends on the gram, so a ratio of lengths cannot equal it). The 'strong force' is F_s = hbar c/r^2, i.e. Coulomb's law times 1/alpha at all r, with no range cut-off; the 'magnetic monopole force' F_m = F_e/alpha^2 has no independent test. Geometric alpha (Eq. 2.2.4): alpha = 1/(4 pi^3 + pi^2 + pi) = 0.00729734 (1/alpha = 137.036304, relative difference -2.22e-6 from CODATA), built from hand-chosen lengths (cone slant l = pi r_e and sphere radius l = pi r_e); it is used as 'the' alpha in all later formulas, so it propagates to m_e (-2.2 ppm), a0 (+4.4 ppm), E_Ry and R_inf (-6.6 ppm), lambda_C, mu_B and N_A, but printing to 4-5 figures hides the shifts; taken literally R_inf is wrong by about 3 million standard deviations. The only output not fixed by the inputs is the 'fundamental wavelength' lambda_l = c/f_l = 2.7477e-17 m from a spring-mass cell (f_l = 1.09107e25 Hz); the paper says it matches 2 q_P e^2 = 2.7717e-17 m, but they differ by 0.87 %; its stated consequence, a lower limit on photon wavelength (energy hc/lambda = 45.1 GeV), is contradicted by Higgs-decay photons near 62.5 GeV and by PeV gamma rays [memory, high; web check failed]. Gravity as 'shading' between two particles is a Le Sage-type mechanism; the Conclusion's 'more than a dozen constants ... validating the equations' overstates identities. 'Validated from hydrogen to calcium' (p.27): the complete frequency equation f = Delta alpha c/(4 pi r) is said to be validated in 'a separate paper [15]'. Ref [15] is J. Yee, 'Atomic Orbitals: Explained and Derived with Energy Wave Equations' (viXra 1708.0146; v6 read by the deep reader; by Yee, Zhu and Zhou, 75 pp; Gardi is not an author; not in the folder). It models the proton as a pentaquark (four quarks plus a central anti-quark), fixes orbital distances per orbital with Mathcad and 'amplitude factors' by rule table, and compares first ionization energies H to Ne with NIST (H 1.31, He 2.30 vs 2.37, Be 0.93 vs 0.90, O 1.35 vs 1.31 MJ/mol). For one-electron ions He+ to Ca19+ the 'calculated' values equal Z^2 x 1.31275 MJ/mol, the 1913 Bohr formula, and fall short of NIST by 0.50 % at Ca19+, which is exactly the relativistic correction (Dirac formula within about 0.03 %). The paper itself contains no calculation for any atom beyond hydrogen.

Key claims

• Spacetime is a lattice of Planck-scale granules whose harmonic oscillation produces all particles and forces.
• The electromagnetic, strong and gravitational forces are one force expressed through different geometric shapes (sphere, cone, shading).
• The fine-structure constant is a geometric ratio of areas of a rectangle and a sphere+cone with 4 variables at r = r_e.
• The gravitational constant G, Coulomb's constant, Bohr radius and Avogadro's constant can be derived from five constants and match CODATA values.
• Charge is the displacement distance of a lattice granule, measured in metres.
• Eleven of the thirteen 'derived' constants are algebraic identities of the five inputs (found by recomputation, not claimed by the authors); Avogadro's constant matches only to 37 ppm.
• The geometric alpha 1/(4 pi^3 + pi^2 + pi) misses the measured value by 2.2e-6 (about 3 million standard deviations in R_inf when propagated).
• The fundamental wavelength 2.7e-17 m sets a lower limit on photon wavelength (equivalent to a 45.1 GeV photon-energy ceiling).
• The frequency equation with interference factor Delta has been validated from hydrogen to calcium in a separate paper [15] (Yee, viXra 1708.0146, not by Gardi).

Relevance: The central work of the project; all other Yee-Gardi papers lead to or extend it.

Mainstream conflict: Conflicts with Lorentz invariance of vacuum (a lattice picks out preferred directions; Planck-scale lattices strongly constrained by gamma-ray timing, Fermi GRB 090510) and with charge as an independent SI quantity; derivation of G is circular as shown from p.28.

Preprint (July 2023, 12 pp, DOI 10.13140/RG.2.2.31545.95842). Proposes 'A Universal Medium' (AUM) as the source of particles and forces. Particles are circular waves or solitons with tangential velocity c, localised and therefore massive; light is the non-localised propagating wave. Electron and proton use their Compton wavelengths; the medium consists of hypothetical quantum solitons with Planck wavelength, frequency and mass, using h rather than hbar (Planck units 'in terms of h') and cyclic frequency. Constants rewritten: Km = mu0/4pi = 1e-7 kg m/C^2, Ke = c^2 Km, Zi = sqrt(Ke Km) = 29.979 (impedance constant). Section 4 computes the 'anomalous magnetic moment' a_m = e^2/Q_p^2 = 0.00116141 (this is alpha/(2 pi) because Q_p uses h; it is the leading Schwinger term, whereas the measured electron value is 0.00115965, memory, confidence high). It claims the fine structure constant 'is anomalous and not required'. De Broglie waves are 'an artifact of wave interference'. The paper says its model is 'nearly identical' to John Macken's single-field model, differing only in using h and cycles. Gravity, electrostatic and magnetic forces are said to emerge as distortions of the medium; no quantitative test is given.

Key claims

• A universal medium of Planck-scale solitons forms all particles and forces and propagates waves at c.
• Particles are localised circular waves with tangential velocity c, and only localised waves have mass.
• Planck units should be defined using h rather than hbar, and frequency in cycles per second.
• The electron anomalous magnetic moment equals e^2/Q_p^2 = 0.0011614, with Q_p the Planck charge built from h.
• De Broglie waves are a wave-interference artifact.

Relevance: Latest and most compact statement of the Gardi's model; merges Planck-lattice papers with MUA and shows alignment with Macken.

Mainstream conflict: Conflicts with Lorentz invariance and with measured g-2 (the 0.0011614 is only the lowest-order QED term; higher-order terms bring theory and experiment to ~1 part in 10^12 per Standard Model). Rescaling Planck units by 2 pi is a convention, not new physics.