Ranking Prompt–Plateau Correlations in Gamma-Ray Bursts with Symbolic Regression

Gamma-ray burst (GRB) correlations probe central engines, relativistic outflows, and radiation processes. The Dainotti relation is an anticorrelation between the X-ray plateau luminosity L a and rest-frame plateau duration T a rest . We use symbolic regression to compare it with other low-dimensional correlations in 251 GRBs with Swift-XRT plateau properties and Swift-BAT prompt-emission parameters. We perform a Dainotti-guided search, in which log T a rest is always present, and an unrestricted search over subsets of at most three variables. The guided search recovers the Dainotti dependence; a D’Agostini fit gives log L a = ( 51.92 ± 0.30 ) − ( 1.31 ± 0.09 ) log T a rest , with intrinsic scatter σ int = 0.82 ± 0.05 dex. In the unrestricted ranking of 377 feature subsets, the classical Dainotti relation remains competitive, within the top ∼25% of the tested search spaces. The highest-ranked screened expression is log L a ≈ 0.855 log L peak − 0.782 log T a rest , with RMSE ≈ 0.46 and R 2 ≈ 0.88. The highest-ranked runs repeatedly reduce to this prompt–plateau structure, without retaining additional spectral, absorption, or afterglow-shape variables. A direct regression gives log L a = 4.718 + 0.776 log L peak − 0.805 log T a rest , with R P = 0.91 for 246 bursts. An errors-in-variables refit gives consistent coefficients. After removing shared luminosity–distance dependence, the relation retains nonnegligible explanatory power ( R 2 ≈ 0.62), consistent with a possible intrinsic component. Restricted Monte Carlo null tests give p ≈ 0.01. Plateau luminosity therefore shows a coupled dependence on prompt luminosity and plateau duration.