When Scientific Constraints Improve Representational Discovery

Scientific constraints can reduce symbolic candidate spaces before empirical evaluation, but it is unclear whether their computational value reflects scientific information or merely generic search-space reduction. We compare scientifically constrained search (SCI) with target-preserving random reduction (RAND-T), matched in candidate count and complexity strata, across twelve scientific relations. At the frozen confirmatory operating point, eleven benchmarks showed identical perfect recovery. For Bernoulli's relation, SCI recovered the target in all 200 replicates whereas RAND-T recovered it in 73, a difference of 0.635 (95% confidence interval, 0.57–0.70) caused by ranking failures rather than target removal and robust across predefined noise conditions. However, the predefined cross-benchmark generalization criterion was not satisfied. A separately frozen post-confirmatory extension strengthened scientific constraints within three structural families. It produced a large additional SCI advantage in a Bernoulli-like additive family, no measurable change in a ceiling-limited monomial family, and essentially no strengthening in a reciprocal-additive family; the cross-family generalization criterion was again not satisfied. These results show that scientific constraints can improve representational discovery beyond matched reduction in particular candidate structures, while indicating that their value depends on which empirically competitive alternatives they remove rather than on reduction magnitude alone.