Heterotic-Orbifold Embedding of the e-step Yukawa Ladder

This note presents a compact embedding of the e-step Yukawa ladder—a phenomenological framework for quark and lepton mass hierarchies—within heterotic orbifold compactifications, interpreted in the language of the Minimal Supersymmetric Standard Model (MSSM). The e-step ladder posits discrete exponential suppressions governed by a single parameter ε ≡ e^{-3} ≈ 0.05, anchoring masses to the strange quark node derived from charged lepton sums, with O(1) prefactors accounting for mixing and normalization effects. We demonstrate how standard orbifold mechanisms, including selection rules, higher-dimensional operators involving singlet VEVs, and geometric/worldsheet suppressions, naturally generate the required integer-exponent hierarchies without a full UV-complete model.