Joint Syntactic ALIGN100- 1/7

This manuscript presents a mathematically rigorous and practically scalable frameworkfor aligning heterogeneous sentence representations — Universal Dependencies (UD), AbstractMeaning Representation (AMR), and Semantic Dependency Parsing (SDP). The approachintegrates three core contributions: (1) an Unbalanced Optimal Transport (UOT) alignment corethat formally handles null/extra nodes; (2) a differentiable low-rank Gromov–Wasserstein (GW)surrogate with provable approximation bounds that enables scalable structural regularization; and(3) a finite-precision analysis of log-domain Sinkhorn iterations with practical stability guarantees.In addition, the manuscript introduces structured calibration for transport plans, extendingcalibration theory to structured outputs and linking calibration error to downstream decisionrisk. Algorithms, theoretical results, proofs, and an experimental plan with ablation matrices areprovided. The work is presented in a hybrid style: it is focused and self-contained while formingthe first installment of a planned seven-paper program on robust syntactic–semantic governanceand adversarial resilience.