Transformer-based architectures have dominated sequence modeling, largely due to the expressive power of attention mechanisms. However, for a class of deterministic state tracking tasks---such as parity checking, modular counting, and parenthesis matching---attention may be overkill. In this paper, we show that \textbf{state propagation alone is sufficient}. We propose the \textbf{Complex State Propagator (CSP)}, a minimalistic recurrent architecture that \textbf{only propagates hidden states} across layers without output projections at intermediate steps. The state is represented as a complex-valued vector, updated via input-dependent rotations in the complex domain. To enable deep propagation without gradient vanishing or degradation, we introduce a \textbf{block-level skip connection} alongside element-wise complex normalization and SiLU activation at sequence boundaries. Applied with Focal Loss, CSP achieves \textbf{100\% accuracy} with perfect F1 scores across canonical tasks.
Precise metric depth estimation is fundamental for autonomous robot navigation, yet monocular systems inherently suffer from scale ambiguity and scale drift. While recent recurrent flow-based SLAM systems have demonstrated state-of-the-art robustness, they remain scale-ambiguous. In this paper, we propose Metric-DROID, an end-to-end recurrent architecture that anchors visual SLAM to physical reality by integrating proprioceptive odometry. Our framework introduces the following innovations: (1) A LSTM Update Operator that encodes high-frequency odometry sequences into spatial feature maps, providing a persistent metric bias for iterative refinement. (2) An Uncertainty-Aware Metric Backend ($BA_{odom}$) that treats odometry as a geometric anchor with learned heteroscedastic covariance. By regressing a time-varying metric uncertainty $Σ_{o}$, our system intelligently balances visual re-projection and metric translation residuals, effectively mitigating the impact of wheel-slip and sensor noise. (3) We further propose a selective residual fine-tuning strategy to preserve pre-trained geometric priors while enabling zero-shot metric alignment.