V74: The Hierarchy of Residues and the Σ-Cost of Existence

We present V74 as the explanatory companion to V73, applying the Σ-operator framework to the hierarchy problem and the origin of the particle mass spectrum. Building on the interpretation of forces as active Σ-operators and gravity as geometric residue, we argue that the extreme weakness of gravity can be understood as a categorical necessity rather than a tuning problem. Particle mass is interpreted as the minimal Σ-cost required to maintain a specific operator mode against the Σ-space background. Generations may correspond to recursion depths of a common operator structure, with shallow recursion producing low-cost, stable modes. Dark matter effects may originate from persistent Σ-structure without associated update operators—an ontological mismatch rather than missing particles. This reframing does not modify Standard Model predictions but offers a unified structural interpretation.