…Of Solar
Phase Alignment

Series II Test 2C

Introduction

This test (Test 2C) completes this series of the testing program by examining whether the phase relationships identified in Tests 2A and 2B persist across multiple solar cycles. The objective is to determine whether the clustering of solar signals within a specific phase region represents a recurring feature of solar behavior rather than a coincidence within a single cycle.

Where Test 2A demonstrated that sunspot amplitude progression, butterfly diagram migration and magnetic polarity reversal timing cluster within a common phase window of the solar cycle and Test 2B extended this analysis to the heliospheric current sheet tilt, this test asks a broader question: does this phase alignment repeat when the analysis is applied to additional solar cycles?

Datasets

The following observational records form the basis for this multi‑cycle comparison:
• SILSO monthly sunspot number record spanning multiple solar cycles.

• Historical butterfly diagram datasets showing the latitudinal migration of sunspots.

• Polar magnetic field observations identifying polarity reversals in both hemispheres.

• Heliospheric current sheet tilt indices derived from global magnetic field models.

Method

1. Each solar cycle is normalized to a phase scale extending from minimum (phase 0) to maximum (phase 1).

2. Sunspot amplitude curves from multiple cycles are overlaid on this common phase axis.

3. Butterfly diagram migration patterns are compared across the same normalized cycles.

4. Polarity reversal timing and heliospheric current sheet tilt extrema are placed on the same phase axis.

This normalization allows cycles of different absolute durations to be compared within a common temporal framework.

Observed Pattern

Preliminary comparisons indicate that the clustering observed in Tests 2A and 2B is not unique to a single solar cycle.

Across multiple cycles several signals repeatedly appear within the late rising phase of the cycle:
• Sunspot amplitude approaches peak activity

• Butterfly diagram bands converge toward the solar equator

• Polar magnetic fields approach or cross zero polarity

• Heliospheric current sheet tilt increases toward maximum oscillation

This repetition suggests that the phase window identified in earlier tests may represent a recurring structural stage in the evolution of the solar magnetic system.

Interpretation

At this stage scientific restraint remains essential. The results presented here do not claim that the Möbius Solar Constitution has been proven as a physical law. However, the tests performed so far show that the proposed geometric framework remains compatible with several independent observational datasets.

What began as a geometric placement of planetary orientations has now been examined against planetary geometry, solar‑cycle timing, butterfly migration and heliospheric structure.

The framework has not collapsed under these tests; instead it continues to exhibit internal coherence across multiple scientific domains.

This outcome places the investigation in a promising position for continued testing. If the same structural relationships continue to appear under increasingly precise datasets, the possibility emerges that the solar system may exhibit an underlying geometric organization that has not yet been fully recognized.

Conclusion of Series II

Series II establishes that the temporal behavior of the solar magnetic cycle can be examined within the same geometric framework introduced in the Möbius Solar Constitution. The clustering of independent solar signals within a recurring phase window provides a compelling direction for continued investigation.

With the completion of this series, the Constitution has now been examined against both spatial planetary geometry and temporal solar‑cycle behavior. The next stage of testing extends the investigation outward into the heliosphere itself.

Next Series

The next series (Series III) will examine the geometry of the heliospheric current sheet directly, including spacecraft crossings of the sheet and the large‑scale structure of the Parker spiral. These tests will determine whether the heliospheric magnetic environment exhibits the same structural relationships suggested by the Constitution.

Produced by The Lilborn Equation Team:

Michael Lilborn-Williams

Daniel Thomas Rouse

Thomas Jackson Barnard

Audrey Williams