A Saturn-Mass Planet in a Binary M-Dwarf System: Dynamical Architecture and Evolution in the Primary-Centric Framework (KMT-2016-BLG-1337L)

We present a dynamical and evolutionary interpretation of the microlensing event KMT-2016-BLG-1337L, which reveals a Saturn-mass planet in a binary system of two M-dwarf stars. The system exhibits a well-known microlensing degeneracy, yielding two distinct solutions for the planetary mass and orbital separation: a low-mass planet (~0.3 Jupiter masses) at ~4 AU and a high-mass planet (~7 Jupiter masses) at ~1.5 AU. Rather than treating this degeneracy as a purely observational ambiguity, we analyze both configurations within the framework of the Primary-Centric Framework (PCF), which characterizes orbital evolution through the dimensionless angular momentum ratio $\Lambda(a)$. we demostrate that the two solutions correspond to distinct dynamical regimes, representing different evolutionary states of the system. The inner solution is consistent with a dynamically stable, migrated configuration, while the outer solution lies near the boundary of binary-induced instability. This interpretation provides a physically motivated pathway for resolving microlensing degeneracies and offers new insight into planet formation and survival in binary environments. Our results suggest that planets in M-dwarf binaries can undergo significant orbital evolution while remaining dynamically stable, thereby expanding current understanding of planetary system architectures in multiple-star systems.