Predicted Partner States of $P_{cs}(4459)$

This archive contains the final PRL-format two-column preprint compiled with revtex4-2, studying excited partner states of the strange hidden-charm pentaquark $P_{cs}(4459)$ via an empirical mass recurrence scaling relation. Core research contents: 1. An exponential recurrence mass formula $m_n = m_0 \kappa^n$ calibrated on existing LHCb pentaquark measurements, with $\kappa=1.043\pm0.003$ for the $cs$ pentaquark flavor family; 2. Four low-lying predicted $P_{cs}$ states below 5.2 GeV, including the primary $3/2^-$ resonance at $4.662\pm0.068$ GeV with broad $\Xi_c\bar{D}^*$ decay width; 3. A unique narrow $1/2^+$ pentaquark candidate ($\Gamma<5$ MeV) proposed as a clear experimental discriminant for LHCb Run4 searches; 4. All predictions are fully falsifiable with upcoming high-luminosity proton-proton collision data. Supplementary machine-readable numerical tables with full mass uncertainty scans are uploaded alongside the PDF manuscript for complete reproducibility. No internal draft revision logs are attached to maintain clean preprint formatting.