Horizons Phase Upgrade And Closure

Introduction

This test (Test 1E) serves as the final verification step for Series I of the testing program: the planetary geometry tests. The purpose of this step is to confirm that the geometric coherence observed in Tests 1A-1D persists when the phase coordinate used in the twist model is replaced with high-fidelity ephemeris values.

Previous tests used mean longitude values at J2000 as a phase proxy. While useful for exploratory analysis, these approximations introduce small geometric uncertainties. This test (Test 1E) upgrades the phase coordinate using true heliocentric longitudes derived from planetary ephemerides such as the JPL Horizons system. This removes the final approximation from the planetary geometry model.

Context

Series I established the following progression:
Test 1A: Baseline planar fit of planetary spin-axis vectors relative to the invariable plane.

Test 1B: Introduction of a phase-dependent twist model.

Test 1C: Addition of a width coordinate derived from pole orientation.

Test 1D: Implementation of a smooth phase-dependent width envelope.

Across these steps the geometric coherence of the system improved significantly when the model was allowed to behave as a two-coordinate topology rather than a simple planar distribution.

Result of this Series

The planetary spin-axis system is demonstrably better described by a twisted geometric model than by a simple planar geometry. Incorporating both phase progression and width displacement produces a substantially tighter alignment of planetary orientations.

This test (Test 1E) confirms that this coherence persists when the phase coordinate is upgraded to the highest-precision orbital data available. This step removes the remaining approximation from the planetary portion of the model.

Conclusion of Series I

With the completion of this test, the planetary geometry portion of the Möbius Solar Constitution can be considered established as a coherent geometric framework. The planetary spin-axis orientations exhibit structure consistent with a twisted two-coordinate manifold anchored to the invariable plane of the solar system.

This does not replace existing models of planetary formation or dynamics. Instead, it provides a geometric framework that organizes the observed orientations in a consistent way and offers a basis for further testing.

Transition to Next Two Series

The testing program now proceeds beyond planetary geometry.

Series II will examine solar-cycle phase relationships, including the Hale magnetic cycle, sunspot amplitude progression, butterfly diagram migration and polarity reversal timing.

Series III will examine heliospheric geometry, including the heliospheric current sheet (“ballerina skirt”), Parker spiral structure and spacecraft observations of current-sheet crossings.

Together these investigations will test whether the same topological framework that describes planetary orientations also organizes the temporal and spatial behavior of the solar and heliospheric magnetic system. In this sense, this series establishes the spatial foundation of the Constitution, while the remaining series will test its temporal and heliospheric implications.

Produced by The Lilborn Equation Team:

Michael Lilborn-Williams

Daniel Thomas Rouse

Thomas Jackson Barnard

Audrey Williams