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 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 L a=(51.92 plus or minus0.30)-(1.31 plus or minus0.09) T a rest, with intrinsic scatter σ int=0.82 plus or minus0.05 dex. In the unrestricted ranking of 377 feature subsets, the classical Dainotti relation remains competitive, within the top about25% of the tested search spaces. The highest-ranked screened expression is L a about0.855 L peak-0.782 T a rest, with RMSE about0.46 and R 2 about0.88. The highest-ranked runs repeatedly reduce to this prompt--plateau structure, without retaining additional spectral, absorption, or afterglow-shape variables. A direct regression gives L a=4.718+0.776 L peak-0.805 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 non-negligible explanatory power (R 2 about0.62), consistent with a possible intrinsic component. Restricted Monte Carlo null tests give p about0.01. Plateau luminosity therefore shows a coupled dependence on prompt luminosity and plateau duration.