Truncated Multicomplex and Higher-Order Topological Models in ALS Drug Discovery

Polypharmacology in Amyotrophic lateral sclerosis (ALS) demands models that capture irreducible higher-order drug co-action. We introduce a categorical–topological pipeline that encodes regimens as truncated multicomplexes with a hypergraph–simplicial envelope; irreducible effects are identified by Möbius inversion, and CatMixNet predicts dose-response under monotone calibration while aligning multimodal omics via sheaf constraints. Under face-disjoint evaluation, omics fusion reduced RMSE from 0.164 to 0.149 (≈9%), increased PR-AUC from 0.38 to 0.44, and lowered calibration error to 2.6–3.1% with <10 dose-monotonicity violations per 103 surfaces. Triad-irreducible signal strengthened (95th percentile Δ★=0.151; antagonism retained at 24%). A risk-sensitive selector produced triads with toxicity headroom and projected ALSFRS-R slope gains of +0.04–0.05 points/month. Ablations confirmed the necessity of Möbius consistency, sheaf regularization, and monotone heads. Distilled monotone splines yielded compact titration charts with mean error 0.023. The framework supplies reproducible artifacts and actionable shortlists for iPSC and SOD1 validation.