ARDENT: A Python package for fast dynamical detection limits with radial velocities

The architecture of planetary systems is a key piece of information to our understanding of their formation and evolution. This information also allows us to place the Solar System in the exoplanet context. An important example is the impact of outer giant planets on the formation of inner super-Earths and sub-Neptunes. Radial velocity (RV) surveys aim at drawing statistical insights into the (anti-)correlations between giants and inner small planets, which remain unclear. These surveys are limited by the completeness of the systems, namely, the sensitivity of the data to planet detections. Here, we show that we can improve the completeness by accounting for orbital stability. We introduce the Algorithm for the Refinement of DEtection limits via N-body stability Threshold (ARDENT), an open-source Python package for detection limits that include the stability constraint. The code computes the classic data-driven detection limits, along with the dynamical limits via both analytical and numerical stability criteria. We present the code strategy and illustrate its performance on TOI-1736 using published SOPHIE RVs. This system contains an eccentric cold giant on a 570-day orbit and an inner sub-Neptune on a 7-day orbit. We demonstrate that no additional planet can exist in this system beyond 150 days due to the gravitational influence of the giant. This outcome allows us to significantly refine the system completeness and also carries implications for RV follow-ups. ARDENT is user-friendly and can be employed across a wide variety of systems to refine our understanding of their architecture.