Physics-Constrained Conformal Screening: A Certified Machine Learning Framework for the Rational Design of Dual Glycoepitope-Imprinted Polymers Recognizing CA 19-9 and MUC1-Tn

The selectivity of a molecularly imprinted polymer (MIP) is decided the moment its functional monomer is chosen, yet that choice is still made largely by trial and error and without any statement of confidence, so a confident but wrong pick can commit months of synthesis before it fails. We recast the role of artificial intelligence in this problem: rather than predicting a binding value, which the scarce, noisy data of pre-synthetic screening cannot support, the learning layer issues a distribution-free certificate on the decision itself. We realize this as physics-constrained conformal screening, a fully in silico framework that returns not a ranked guess but a certified shortlist provably holding the best monomer. Site-directed monomer and template complexes are relaxed with the GFN2-xTB tight-binding Hamiltonian in implicit water; a competition-corrected score, Scomp, discounts monomer self-association and solvation; a best-of-k estimator measures how far the sampling has converged; and a distribution-free conformal bound turns the result into a candidate set guaranteed, with controlled probability, to contain the optimal monomer. We prove that the corrected estimator is one-sided exact, so only the lower bound needs calibration and the guarantee requires no correction for the size of the library, and we show that a single calibration transfers between targets. Applied to two pancreatic cancer glycoepitopes, sialyl-Lewisa, the carbohydrate antigen 19-9 (CA 19-9) determinant, and the mucin 1 (MUC1) Tn antigen (MUC1-Tn), the framework contracts a twenty-monomer library to two and five certified candidates at ninety-percent confidence while cutting compute by 35 to 67 percent, and it identifies 3,4-ethylenedioxythiophene (EDOT) and 3-aminophenylboronic acid (3-APBA) as certified affinity optima. The same multi-seed certificate then separates the selectivity claims it can support, EDOT reading the sialylation of sialyl-Lewisa and 4-aminophenylboronic acid (4-APBA) reading the Tn-glycosylation of MUC1, from the harder sialyl-Lewisx regioisomer discrimination, which it flags as under-determined rather than passing off an under-sampled gap as a decisive hit, a distinction an uncertified screen cannot make. Strikingly, no point prediction model beats a trivial baseline while certification succeeds, which locates the dependable value of machine learning, for cheap physics in a low-data regime, in a guarantee rather than a guess.