The Branching Point: Threshold Theory for Discrepancy-Triggered Simulation in Autonomous Rover Digital Twins

This theoretical work introduces the Theory of Discrepancy-Triggered Branching (TDTB), a framework for autonomous rover digital twins that reframes simulation-to-real divergence: instead of overwriting deviations as errors, TDTB treats them as preserved branching data points to enable post-hoc analysis and model improvement. Building on prior Parallel Hypothesis Generation work, TDTB is governed by two sub-theories: (1) Adaptive Discrepancy Thresholding (TADT), which dynamically adjusts acceptable error margins to match terrain slip conditions (reducing false triggers in high-slip environments, improving sensitivity to micro-anomalies in predictable settings) via a covariance-weighted, environment-scaled threshold; and (2) Persistence Divergence Branching (TPDB), which only spawns parallel simulation branches when deviation exceeds the adaptive threshold across a sustained temporal window, preventing combinatorial explosion of branches from transient noise. The paper also presents a full real-time implementation architecture, covering state serialization, synchronized real-world data ingestion, confidence-based branch reconciliation, pruning/archiving controls, and formal framing as a Multi-Hypothesis POMDP. This framework captures the "near miss" and edge case data typically lost in standard localization filters, supporting improved predictive model and reinforcement learning agent training for unstructured autonomous navigation.