Residue Bootstrap Operator: Fractal Unfold & Transcendent Chain (v2)

Abstract | This paper introduces the Residue Bootstrap Operator (RBO), which extends affine fractal scaling to include self-bootstrapping residue and novelty-driven growth. Building on the Four Clocks Model’s Möbius inversion and Klein bottle projection from Papers I--V, the RBO provides a mechanism for indexing infinite structures in bounded space via bidirectional layering. Novelty N_k accumulates as residue deviation δ r_k, amplified by φ^k across k layers. Threshold crossing (N_k > N_c) triggers replication or coherence. At pointer 137, residue ∼ 10^{-29} (from Binet in Paper II) stabilizes local observables. The operator derives all model predictions from residue bootstrap with no free parameters beyond the observed generations.