Derivation IV: The Fiber Structure of Spacetime and the Origin of E=mc², The Geometry of Mass: Why Einstein's Equations Work

We reveal that Einstein's mass-energy equivalence and his field equations of General Relativity are not independent insights but dual aspects of a single geometric phenomenon: the fiber structure of spacetime. By extending the Update Bundle formalism (Derivations I-III), we show that: Mass is aliased frequency - matter arises when wave frequency exceeds the Nyquist limit (Action Phase Limit ) of foliation updates, causing the fiber to knot into a closed loop is computational equivalence - the equation describes conversion between storage (mass) and streaming (energy) in the geometric processor Curvature is processing lag - gravity emerges because high-density fibers create computational bottlenecks in the regulator's update flow This unifies quantum mechanics (fiber dynamics) with general relativity (base curvature) in a single geometric picture, revealing the hidden variable Einstein sought: the topology of the fiber itself.