O-DM Transformer: Geometric Transversality and Density Matrix Dynamics for O(1) Safe Swarm Intelligence

Real-time autonomous systems, such as drone swarms and self-driving vehicles, demand both macro-level contextual reasoning and micro-level safety guarantees against singularities. Traditional Model Predictive Control (MPC) incurs high latency due to iterative optimization, while large-scale Transformers lack verifiable geometric stability. We propose the O-DM Transformer, a hybrid architecture integrating a Transformer backbone with a Density Matrix Recurrent Neural Network (DM-RNN) constrained by the Orthogonal Equivalence Transversality Property (OETP). Leveraging Wishart eigenvalue repulsion for deterministic uncertainty collapse (average VNE drop ≈ 1.01 nats), our model achieves O(1) amortized inference latency per agent. By formulating Lanczos-based partial eigendecomposition within the OETP constraint, we establish a theoretical guarantee for near-O(1) latency even for large-scale swarms (d ≥ 100). Benchmarks show a 30× speedup over MPC. While stress tests yield 4 boundary contacts, the model strictly maintains a positive OETP gap (δ > 0) and full Jacobian rank, completely eliminating catastrophic control singularities and providing a provably secure framework for verifiable swarm intelligence.