The bifurcation of subwaves in space and time
• Is the bifurcation of subwaves a process in space or in time, or both?
• How are elementary matter and force particles formed?
• What is the role of the potential well? 
In subwave / microvita theory, the bifurcation of subwaves in space and in time is closely interwoven, but each is treated differently.
The bifurcation in space, (B) subjective > (B) objective, constitutes a spectral analysis of the source wave numbers (cycles per unit of distance) and is initially manifested through the formation of matterwaves.
3 source subwaves 
4 bifurcated subwaves 
subwave # 
wave number 
angular
velocity 
1 
Phi^0 = 1 
1 
2 
Phi^1 = Phi 
1 
3 
Phi^2 
1 

subwave # 
wave number 
angular velocity 
0  electron 
Phi^2  Phi  1 = 0 
1  1  1 = 1 
1  photon 
Phi^2  Phi + 1 = 2 · 1 
1  1 + 1 = 1 
2  gluon 
Phi^2 + Phi  1 = 2 · Phi 
1 + 1  1 = 1 
3  quarks 
Phi^2 + Phi + 1 = 2 · Phi^2 
1 + 1 + 1 = 3 

Integral bifurcation table, with emphasis on spacial bifurcation. Only nonnegative wave numbers are considered.
Note the factor 2 each time  this is the wave number bifurcation, only occuring at Phi (1.618) synchronized scaling.
The common angular velocity (or phase or frequency) of the source subwaves bifurcates in time: (A) subjective > (A) objective. It manifests through the formation of a spherical potential well in which the matterwave or particle moves in a closed trajectory.
Increasing curvature of the matter wave, while spacetime is transformed into a potential well with a nucleus.
Note that unlike in philosophy, the straight flow ("nada") also has an inner oscillation  this is the subwave.
The matterwave is 1dimensional, implying a bound subwave with unit angular velocity (1 electron). The nucleus (incl. its surrounding medium), is 3dimensional, implying a bound subwave with triple angular velocity (3 quarks).
3 source subwaves 
4 bifurcated subwaves 
subwave # 
wave number 
angular velocity 
1 
Phi^0 = 1 
1 
2 
Phi^1 = Phi 
1 
3 
Phi^2 
1 

subwave # 
wave number 
angular velocity 
0  electron 
Phi^2  Phi  1 = 0 
1  1  1 = 1 
1  photon 
Phi^2  Phi + 1 = 2 · 1 
1  1 + 1 = 1 
2  gluon 
Phi^2 + Phi  1 = 2 · Phi 
1 + 1  1 = 1 
3  quarks 
Phi^2 + Phi + 1 = 2 · Phi^2 
1 + 1 + 1 = 3 

Integral bifurcation table, with emphasis on angular velocities.
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Electron and quark (Dirac) spinors, modeled as resp. (2, 1) and (2, 3) toruses.
The dashed tracks are the electric resp. accurate "color" charges, both a (2, 1) torus.
The white nodes show the interdigitation between the matter and force spinors.
In the current gauge the charge is cycling whereas the particles are still.
The potentialwell is 2dimensional, it is a topological or surface phenomenon which constitutes the charge. The associated particles are the photon resp. gluon, forcecarriers. The spherical potential well is nothing but the (space and time) bifurcation itself in dimensional form.
The spherical shell or surfacearea, in a general sense, accounts for the source subwaves' common phase cycle, bifurcating in selfinteractive, quadratic form, and therefore with dual angular velocity. The source phases and the topologically bifurcated phases together form a resonant potential well.
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Squaring a source subwave's phase angle (blue), bifurcates its angular velocity (red).
The two components together form a quadratic potential well based on selfinteraction,
relating the subwaves to a particle's mass (bifurcated wave's magnitude).
If the bifurcation is synchronized (which is the case for perceptual states and for harmonic entities), the quadratic part of a potential well is formed specifically by distinct, positively bifurcated subwave phase pairs of the resp. constituent waves. A phase pair couples the charge with a resp. Dirac spinor.
The temporal bifurcation is effectively a gauge phenomenon, indicating that the ever present, implicit (principal or axiomatic) bifurcation of the substratum (also, the "swabhava" in philosophy) is now explicitly being realized as a known resp. perceived state. This known state, in its most rudimental form, is a hydrogen atom.
3 source subwaves 
4 bifurcated subwaves, with potential wells and Dirac spinors 
subwave # 
wave number 
angular velocity 
1 
Phi^0 = 1 
1 
2 
Phi^1 = Phi 
1 
3 
Phi^2 
1 

subwave # 
wave number 
angular velocity 
0  electron 
Phi^2  Phi  1 = 0 
+1  1  1 = {1} 
1  photon 
(Phi^2)  Phi + (1) = 2 · 1 
(+1)  1 (+ 1) = [{2}  1] = 1 



2  gluon 
(Phi^2 + Phi)  1 = 2 · Phi 
(1 + 1)  1 = [{2}  1] = 1 
3  quarks 
Phi^2 + Phi + 1 = 2 · Phi^2 
1 + 1 + 1 = {3} 

Integral bifurcation table, with emphasis on temporal bifurcation and potential well. The paired subwaves
constituting the quadratic, charged sphere are in round brackets.
The factors 2 in the angular velocities
show
the
phase bifurcation. The potential wells are in square brackets, while
{2,3} and {2,1}
are the
resp. Dirac spinors.
The spherical potential well and bifurcation scheme (both simplified)
Note that it should not too literally be viewed as an atom model.
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Bifurcation tree, scaling to synchronization
In summary, it was shown that the bifurcation of subwaves consists of a spectrum analysis of the source wave numbers in space, and a topological analysis of the common phase cycle in time. The space and time bifurcation together constitutes a dimensional analysis, in the form of a spherical potential well.
