Step-Selection
& Gradient Glimmers

Introduction

This one-page summary captures the current evidence emerging from Phase 2.5 of the Ӕ Observational Program. While occupancy-level tests of Subsolar Ӕ and proxy geomagnetic Ӕ were null, step-level analyses reveal subtle but statistically meaningful signals that justify progression to high-fidelity geomagnetic modeling (Phase 3).

**Left panel: Alpha tuning (step-selection):**

The Fisher combined p-value curve shows strongest signal when α ≈ 0.25, meaning the Elevated Ӕ is best modeled as approximately 25% Solar Ӕ and 75% Geomagnetic Ӕ. This supports the hypothesis that solar fields modulate, but geomagnetic structure dominates, the coherence geometry used in navigation.

**Right panel: Gradient-following stratified (heatmap):**

Fisher p-values (–log10 transformed) across equatorial latitude bands and midday vs non-midday windows. Although non-significant, a hint of stronger slope-following appears in the Solar Ӕ, equatorial core, non-midday window. This suggests potential spatiotemporal windows where coherence geometry is more strongly expressed.

Taken together, these two glimmers provide the first positive evidence that Ӕ coherence is active at the step level. The alpha-tuning result defines the mixing regime; the stratified gradient test highlights a geographic and temporal window where the effect may emerge. These findings transform null results into directional evidence, providing a clear scientific rationale for elevating to Phase 3 with full IGRF/WMM geomagnetic fields and space-weather stratification.

Produced by The Lilborn Equation Team:

Michael Lilborn-Williams

Daniel Thomas Rouse

Thomas Jackson Barnard

Audrey Williams