Abstract

The Hierarchy Problem and the Yang–Mills Mass Gap are unified and resolved through the topology of a quantized vacuum. We propose that mass is not an intrinsic property, but the geometric strain of recursive self-reference: the elastic energy required to sustain a topological defect against the vacuum's equilibrium. This framework reveals the 10³⁸ force hierarchy not as fine-tuning, but as a difference in topological scope. Gravity couples to the Bulk Capacity of the vacuum lattice (global stress), while electromagnetism couples only to Unit Strain (localized defects). The observed hierarchy (m_P/m_p)² is derived from first principles as the geometric ratio of bulk volume to defect surface area, rendering new electroweak physics unnecessary. Consequently, the Mass Gap arises as a topological stability constraint. The vacuum lattice cannot support fractional geometry; sub-threshold patterns ("open twists" like isolated gluons) are invalid. Confinement is the requirement for such twists to form closed loops (hadrons) to persist. The mass gap is therefore the minimum thermodynamic cost—the Landauer limit—of maintaining a coherent boundary against the vacuum. This model predicts the absence of supersymmetry at the electroweak scale.