Traditional digital architectures process information via logic gate manipulation,requiring extensive redundancy to correct physically unstable microscopic states.In this manuscript, we present the paradigm of Topological Analog Computing,where hardware computes intrinsically through physics enforcing admissibility. By mapping the DSM-861 theoretical architectural framework onto recent experimental advances in programmable plasmonic Moiré superlattices, we demonstrate that computation can be executed as physical relaxation onto topologically protected macroscopic attractors. We introduce the Topological Correspondence Principle, utilizing π2(S2) homotopy classification to establish that plasmonic skyrmions function as exact physical emulators for hydrodynamic vortons. Crucially, we formalize the abstract DSM-861 idempotent projection operator (P) as a physical gradientdescent flow minimizing a specific Ginzburg-Landau free-energy functional. Finally, we translate the theoretical DSM-861 structural locking energy (Elock) into a mathematically rigorous, experimentally measurable topological transition barrier (∆Etop), providing a highly falsifiable, empirical foundation for scaling topological computing hardware.