An automated evolutionary search designs dispersive positivity-bound functionals under one hard rule: the sole selection pressure is an exact-arithmetic certificate, not floating-point SDP up to tolerance. The pipeline reproduces the scalar EFT-hedron with all-spin exact certificates and yields spin-truncated certified bounds on the R⁴ coefficient of D=10 maximal supergravity. Framed as a certified-rigor methods demonstration rather than a new physics bound: a controlled ablation finds the language model gives no search advantage, and four independent routes converge on the same tangency wall near 3.0.