In 2010 we have shown  that the masses of large celestial bodies in the Solar system continue the scale-invariant sequence of fundamental particle rest masses (see table 1), corresponding with main attractor nodes of the fundamental fractal (1).
Table 1: Fundamental particle rest masses and the corresponding attractor nodes of F, with the electron mass as fundamental.
It could thus be put into doubt whether the theory by Higgs becomes necessary for explaining the particle rest masses
. In addition, the present theory leads to new results beyond those available from these and other so far established fundamental theories, as well as from the Standard Model in general.
A continuous slight increase of the charges and the rest masses
of the particles can explain the cosmological data.
In the cosmological data we observe the consequences of the real increase of the rest masses of the material particles, which takes place at an extremely slow rate.
the rest mass M0 of the generalized particle is equal to the sum of the rest masses of the material particle ([m.sub.0]) and the accompanying particle ([E.sub.0]/[c.sub.2]).
Based on (10) in the present paper we will calculate a list of model particle masses which correspond to the main spectral nodes and compare this list with rest masses
of well measured stable and fundamental particles--hadrons, leptons, gauge bosons and Higgs bosons.
* Steady electromagnetic states lead to rest masses
Consequently the quartet of intrinsic rest masses
0[m.sup.0.sub.0],0[m.sup.0.sub.0], -0[m.sup.0.sub.0] and -0[m.sup.0*.sub.0] of symmetry-partner particles or objects in the quartet of intrinsic metric spaces [phi][rho]', [phi][[rho].sup.0'], -[phi][rho]'* and -[phi][[rho].sup.0,*], are located at symmetry-partner points in their respective intrinsic spaces always, even when they are in intrinsic motions relative to symmetry-partner frames of reference in their respective Euclidean 3-spaces.
The equality of magnitudes of symmetry-partner rest masses
, [m.sub.0] = [absolute value of - [m.sup.*.sub.0]], that follows from the prescribed perfect symmetry of state between the positive (or our) universe and the negative universe and [m.sup.0.sub.0] = [absolute value of - [m.sup.0*.sub.0]] that follows from the prescribed symmetry of state between the positive time-universe and the negative time-universe, discussed in the foregoing paragraph, are possible of formal proof, as shall be presented elsewhere.
Nuclide ln m(nuclide)/m(H) multiples of e/2 [sup.1.sub.1]H 0.0 0.0 x e/2 [sup.4.sub.2]He 1.379 1.015 x e/2 [sup.16.sub.8]O 2.764 2.034 x e/2 [sup.56.sub.26]Fe 4.016 2.955 x e/2 [sup.208.sub.82]Pb 5.330 3.921 x e/2 Table 2: Selected particles with rest masses
and values on the logarithmic number line.