D. Edward Mitchell 16:00, 14 April 2020 (UTC) Hello World!    groupKOS Developer Share —usually UNDER CONSTRUCTION

Pseudo-trefoil bifilar pattern in 13:8 3-group torus knots

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Tangential Magnetic Rotation of a Trefoil Dipole1 upon the surface of a Golden Orthogonal2 Electronic 3-Phase3 Geomagical4 13:8 Torus Knot Array5

Ring amp 3-phase orthogonal 13-8 torus knots 1024x768.png

An amateur concept development of reverse engineering a clandestine disclosure through life experiences.
1a   °   Continuous tangential trefoil dipolar magnetic vector rotation on a surface of a smooth 13:8 torus knot array
1b   °   Trans-diametric bifilar conduction of 3-phase current from six points —hexatronic
1c   °   13:8 3-Phase bifilar activation of pseudo-smooth magnetic trefoil array
2     °   Golden torus profile affording inner/outer knot winding orthogonality in Fibonacci knot ratios
3     °   Electronic 3-phase bi-segmented ring amplifier —the Hexatron
4a   °   Geomagical trefoil surface phase wave
4b   °   Geomagical 13:8 knot scalar length detanglement (electrical current age) affording flux density wave engineering

Dear Researcher!  Notice that the blue trefoil (3:2 knot) overlaps a 13:8 knot, shown as red and green chiral halves, only on the outer periphery of the abstract torus equator.  Notice again that inside the torus hole, the blue trefoil knot winding lays between the helices of the 13:8 knot.  This is a phase-difference between the trefoil and the 13:8 knot, generated as an square object of rotation!!! via the 'geomagic' of pattern-dissonance in a group of equally spaced smooth knots sharing a torus surface.

The phase difference arises from the difference between helical slopes on a torus surface of 'golden profile.'

On a golden profile torus (of a major radius that is four powers of the golden ratio larger than the hole radius) knot ratios of neighboring numbers from the Fibonacci number sequence will deviate from a slope of the golden ratio, and deviate on alternating slopes for successive Fibonacci neighbors. The alternation on the golden torus is eigher side of a golden slope. A golden slope does not produce a torus knot, which is by definition two integral harmonics for a knot ratio. The irrational knot ratio of Phi:1 would never find integer harmony, and would map solid the entire abstract torus surface at an infinity of helical windings, visiting all points on the surface at infinity.

Fibonacci neighbors as a knot ratio approximate the golden ratio, Phi, and differ from Phi on either side of Phi for successive pairs of neighbours as the knot ratio.

In principle, the golden ratio knot ratio on a golden torus will be non-harmonic, while a trefoil (3:2) and a 13:8 knot will have helical slopes on either side of the golden infinity slope.
!!! A square rotated three times on the plane of an axis while rotating around the axis two times (3:2) will trace one 13:8 knot by its four corners.  This solid of rotation formed by the square is a four-sided Moebius strip, with corners of the solid forming a 13:8 torus knot.  The 13:8 bifilar magnetic patterns must cohere at resonance with a trefoil knot's dipolar magnetic pattern of a differing slope.  Valence levels of the harmonic topology are anticipated.  Comments welcomed!  Don aght groupKOS doght cφm


Images above illustrate a single 13:8 torus knot in red and green chiral halves, with an overlaid blue trefoil (3:2 knot) showing the 'phase drift' of the respective knot ratios.

Below are shown a 13:8 torus knot 3-group, which displays the curious detanglement, or ordering of chirality and (red-handed helix, or green-handed helix) group-order.

The phase-drift begins centered between chiral hands at the outer periphery of the abstract torus. The drift ends centered at the opposite side again.
The drift wanders from between chiral groupings, from the hexagonal points (small spheres) to the center of a chiral-four-group in the center of the abstract torus.
The red and green chiral bands therefore are pseudo-trefoils in pattern only, while the slope of the banded knot helix remains as the ratio of the 13:8 host group.
Fascinating. Somehow.