DiSCO-SR: Residual-Guided Symbolic Selection under Predictive-Risk Constraints

Predictively similar symbolic equations can imply different intervention responses. DiSCO-SR tests residual-guided equation selection within an explicit predictive-risk budget, separating equation choice from causal direction decisions. Separate data splits support fitting, selection, and direction decisions, with no refitting of the selected equations. We derive conditional guarantees for population risk and penalized finite-block residual dependence, and bound mean-intervention loss under correct orientation and bounded distribution shift. In independent confirmation on 1,920 synthetic cases from 240 mechanism clusters, the development-selected paired-stability rule achieves 95.21% direction accuracy and 0.1396 mean-intervention NRMSE, compared with 95.31% and 0.1385 for minimum-risk selection with the same direction rule. None of eight prespecified primary contrasts is significant after multiplicity correction. The stability rule changes 29.97% of directional equations, correcting four directions and corrupting six; its certificate counterpart always returns the minimum-risk reference across 2,916 confirmation cases. Matched regression controls attain stronger point estimates, and a separate bounded-score study exhibits large errors on measured physical interventions. These results provide an auditable framework for constrained symbolic selection, but do not establish an incremental mechanistic benefit from residual guidance.