Topologically, these regions are connected spaces; a trajectory typically loops within the lower basin (Reckless ↔ Direct ↔ Specific), unable to escape.

On introducting a new mapping function: f : Compulsion → Surrender. This function permits traversal into higher regions of the manifold, where intent is refined, constructive, and ultimately pure.

The collapsed subspace of compulsion?

A state where paths circle endlessly?

The first homotopy—a deformation of the path-space—redirecting will from Reckless intent toward General openness.

Phase 2: The Great Divorce

Through inventory and admission (), the manifold is separated into clearer domains. Pathological loops are untangled. Intent shifts toward Oblique and Allusive zones, where foresight and openness replace rigidity.

Phase 3: Alignment and Transcendence

Through prayer, meditation, amends, and service (), the trajectory stabilizes in the higher regions: Constructive and Pure intent. These zones are topologically stable attractors—once reached, they guide action into coherence with transcendent principle.