Anytime Estimation-Aware Certificate Checks for Serial Manipulators Supervised by Language Models

Preprint, interactive demo and simulation data for S. Yaqubi, "Anytime Estimation-Aware Certificate Checks for Serial Manipulators Supervised by Language Models", 2026. A language model that selects the controllers of a robot arm can be trusted with that choice only if the controllers' stability certificates hold for the true state, which the robot never observes. The preprint gives a test that a serial manipulator evaluates at every sample from its filter's estimate and covariance. For a conditionally Gaussian estimation error, the test bounds the probability that any sample passing it has the true state outside the certified set, over a run of any length, and the guarantee holds for any selector whose decisions depend only on the measurements, an adversarial one included. The preprint also shows that first-moment bounds of the form of Kushner's finite-time bound cannot reach a risk of 1% for entries of nominal stiffness at the filter accuracy of the test chain. In 1,400 simulated episodes per measurement variant on a three-joint chain, with language-model answers replayed from a published benchmark, the test certified 93.6% of 1,414,000 samples, and no certified sample had the true state outside the joint or speed limits. This also held with a biased elbow measurement that violates the Gaussian assumption. The record holds the preprint, an interactive page that evaluates the test at one sample (download it and open it in a browser), the per-sample logs of all simulated episodes and of the additional studies as MATLAB v7 files, and the numbers behind Fig. 2. README.md describes every file and field. The code that produced the results is not part of this record. The scenarios and the replayed language-model answers come from doi:10.5281/zenodo.24009073.