Abstract

This white paper is exploring the fundamental topological archetypes—Sphere, Cube, and Torus—as they manifest across digital and physical systems. By examining these invariant forms in monetary systems (Bitcoin), architecture, and power structures, we reveal a unifying framework for understanding system resilience, value preservation, and social organization.

The 21 million Bitcoin supply cap represents a topological "hole" in the monetary manifold—an immutable property that cannot be altered without fundamentally transforming the system. Similarly, architectural forms and power structures exhibit topological invariants that determine their function and resilience.