Relativistic limit on the $AdS_3 \times S^3 \times S^3 \times S^1$ string worldsheet

We study the relativistic limit of the worldsheet S matrix of $AdS_3 \times S^3 \times S^3 \times S^1$ strings in the presence of mixed Ramond-Ramond (RR) and Neveu-Schwarz-Neveu-Schwarz (NS-NS) flux, and complete the S-matrix bootstrap including the dressing factors for fundamental particles and bound states. Our results agree with the relativistic limit of the recent proposal arXiv:2512.07721.