RBO Extensions: Dimensional Restoration & Emergent Constants

Abstract | The Residue Bootstrap Operator (RBO) extensions in this paper restore physical dimensions to the Four Clocks equation and derive fundamental constants from glitch residue at fractal pointers, completing the unification initiated in Papers I–VI. Restoring the Planck length yields the speed of light c as the emergent unfold rate—the invariant velocity at which residue files novelty across layers, bounding the infinite chain at finite local slices (relativity rigidity from Paper I, residue necessity from Paper VI). The fine structure constant α ≈ 1/137 emerges from residue inverse at meta-coherence pointer n=137, with continued fraction bounds deriving running and early-universe variation. Further constants (neutrino masses via seesaw, proton decay rates, effective Λ) arise parameter-free from PBO convergents and novelty overflow, while quantum gravity loops remain finite (bounded by cf periods, conjecture Paper VI). These extensions unify observed reality—spacetime, forces, hierarchies, cosmology—from a single arithmetic scalar and residue bootstrap, with no free parameters.