Gudu: A Predicted Dwarf Planet at 31.4 AU from the Prime Orbital Distribution Law

We predict a yet-undetected dwarf planet-class object at ~31.4 AU (“Gudu”) as a mathematically required node (prime index p=127) of the newly discovered Prime Orbital Distribution Law: stable semi-major axes follow a_n = k·p_n with primes screened by resonance-avoidance function F(J,p)<0.35. In the Solar System (k_⊙=0.20 AU/prime), Neptune occupies p=113; skipping to p=131 or directly to Pluto (p≈197) violates the F<0.35 threshold. Inserting p=127 uniquely restores global stability. After applying the observed +23.5% outer migration correction, the predicted orbit is 31.4 AU. Using 2025 OSSOS constraints and LSST performance, the detection probability within 10 years exceeds 60% (conservative) to ~80% (optimistic). This prediction is fully falsifiable and constitutes a critical test of the prime orbital framework.