Acknowledgement

We gratefully acknowledge the support by The Scientific and Technological Research Council of Turkey (TÜBİTAK) with the project 122F358.

Scientific Heritage

This software implements and builds upon several key theoretical frameworks for modeling Observed‑minus‑Calculated (O–C) variations in close binary systems.

Light‑Time Effect (LiTE): For Keplerian orbital delay, the code utilizes the analytical formulations provided by Esmer 2021.

Newtonian Models: Modeling of Newtonian (N‑body) interactions is based on the integration procedures detailed in Esmer 2023, utilizing the REBOUND N‑body code.

Stellar Activity & Magnetic Effects: Period variations resulting from magnetic activity cycles are implemented following:

• The Applegate 1992 mechanism regarding quadrupole moment variations.

• The dynamo‑theory‑based models refined by Völschow 2018.

Software & Libraries

The development of this code relies heavily on the open‑source Python ecosystem. We particularly acknowledge the use of the following tools:

• arviz — for Bayesian posterior diagnostics (GitHub)

• corner — for visualizing multidimensional samples (GitHub)

• lmfit — for nonlinear least‑squares optimization (GitHub)

• matplotlib — for scientific plotting (GitHub)

• NumPy — for numerical computing and optimization (GitHub)

• pandas — for data structures and time series analysis (GitHub)

• PyMC — for Bayesian inference and MCMC sampling (GitHub)

• REBOUND — for high‑accuracy N‑body integrations (GitHub)

• SciPy — for scientific computing and optimization (GitHub)