Sunspot Amplitude, Butterfly Migration And Polarity Reversal

Series II Test 2A

Introduction

Series II shifts the investigation from spatial planetary geometry to temporal solar-cycle behavior. This test (Test 2A) examines whether several independent solar phenomena align within a consistent phase window of the solar activity cycle.

Specifically, this test compares the phase relationships between:
• Sunspot amplitude progression (solar cycle rise toward maximum)

• Butterfly diagram migration (latitudinal drift of sunspots)

• Magnetic polarity reversal timing of the Sun’s polar fields

If these signals cluster within a common cycle phase region, this would support the dynamic-recursion interpretation proposed in the Möbius Solar Constitution.

Datasets

The following observational datasets form the basis of this analysis:

Sunspot Number Record

Monthly mean total sunspot numbers from the SILSO (Sunspot Index and Long-term Solar Observations) database provide a continuous measure of solar activity.

Butterfly Diagram Data

Sunspot latitude distributions across successive Carrington rotations provide a record of hemispheric drift toward the solar equator over the course of each cycle.

Polarity Reversal Timing

Observations of the Sun’s polar magnetic fields provide approximate dates for polarity reversal in the northern and southern hemispheres.

Method

1. The solar cycle is normalized into a phase axis extending from cycle minimum (phase 0) to cycle maximum (phase 1).

2. Sunspot amplitude is plotted against this normalized phase.

3. The latitudinal center-of-mass of sunspot activity in each hemisphere is tracked across the same phase axis.

4. Observed polarity reversal dates are placed on the same timeline.

This approach allows the three independent solar signals to be compared directly in phase space.

Observational Pattern

Preliminary analysis shows that these signals cluster in a similar phase window during the rising portion of the solar cycle:
• Sunspot amplitude is increasing toward maximum

• Butterfly diagram bands are approaching the solar equator

• Polar magnetic fields approach and cross zero polarity

These events tend to occur before the peak of sunspot activity and frequently
exhibit a measurable north–south lag.

Interpretation

Within the Möbius Solar Constitution framework, this clustering is consistent with a recursive orientation process in which the solar magnetic system progresses through a structured phase region prior to polarity inversion.

The butterfly migration represents the latitudinal expression of this transition,
while the polarity reversal represents the orientation inversion event itself.

Test 2A therefore provides the first temporal examination of the Constitution.
While not conclusive, the phase alignment of these independent datasets supports the possibility that the solar magnetic system evolves within a structured recursion cycle rather than through purely stochastic reversal events.

Next Step

The next test (Test 2B) will introduce heliospheric current sheet tilt measurements to determine whether the geometry of the “ballerina skirt” participates in the same phase structure observed in this test.

Produced by The Lilborn Equation Team:

Michael Lilborn-Williams

Daniel Thomas Rouse

Thomas Jackson Barnard

Audrey Williams