Dev:4th auric geometry

Auric: A term referring to 'golden' as used in the context of the geometry of a torus profile when major- and minor-radii are separated by four degrees of the golden ratio.

4th Auric Torus Profile

Major_Radius = Phi^4th = ~6.854

Minor_Radius = Major_Radius - Phi^0TH = ~6.854 - 1

Scaling the 4th Auric Torus Profile

The profile of a 4th auric tours is preserved when scaled by operating on the exponent in the radii term

Given a scaling operator = SO

Major_Radius = Phi^{SO + 4}

Minor_Radius = Major_Radius - Phi^{so + 0}

Where,

Phi = 5^0.5 X 0.5 + 0.5 = 1.618033...

Geometric magic in the 4th auric torus profile

The slope of the helix of a torus knot wound smooth/tight on a 4th auric torus profile will have a slope of the helix of the torus knot equivalent to the knot ratio.

Which means, the 13:8 torus knot windings, smooth and tight, for a slope on the helix of 13/8 = 1.6250

That means the 13:8 knot winding on a 4th auric torus profile is 0.0069... units error from Phi.
 
The error from a helical slope of Phi is the error of the approximation of 13/8 is to Phi.
 
Successive adjacent-pairs in the Fibonacci number sequence (1,1,2,3,5,8,13,21,33, ...) if used as a knot winding ratio on a 4th auric torus, create helical slopes that error from golden on alternate sides of a slope of Phi.
 
A knot with a slope of Phi is not a knot by definition, as by definition, a knot is an integral harmony of a winding path, such that it self-connects, continuing on the same path.  Integral path harmony.
 
As the golden ratio is very irrational, like Pi, a slope of Phi4:1 on a 4th auric torus would be an infinitely long line, never connectiing integrally with its beginning.
 
All of the Fibonacci adjacent pairs create a slope very near a golden slope.
 
 The nearness is exploited in the design of the bifurcated torus knot...
   ...because the bifurcated halves of a 13:8 | 3-group decompose to a 3:2 torus knot winding path —as a phase-sorted magnetic group-of-four-windings, which physical angle is a negative err from the golden helical slope — while the physical windings are at positive err to the golden slope.