Chronos: Towards a self-consistent and absolute stellar age scale. I. A Bayesian hierarchical lithium-age model: Validation on the Pleiades cluster

Context. Establishing a self-consistent age scale for stellar populations requires physically well-calibrated chronometers. Among these, lithium-based diagnostics, particularly the lithium depletion boundary (LDB), provide one of the most robust age constraints for stellar populations in the low-mass regime. However, their application is limited by heterogeneous temperature scales and astrophysical dispersion, especially among FGK stars, where rotation can significantly affect lithium abundances. Aims. As a first step towards a self-consistent age scale, our aim has been to formulate Chronos, the first version of a Bayesian hierarchical lithium-based age-dating model combined with a neural network trained on stellar evolutionary models. Methods. We implemented a Bayesian hierarchical model that jointly infers stellar effective temperatures, lithium abundances, and the global age of a stellar association. The theoretical LDB is provided by a pre-trained multilayer perceptron based on BT--Settl evolutionary models. The model incorporates a temperature-dependent transition between fully convective ultra-cool dwarfs (UCDs) and FGKM dwarf stars, together with a two-component FGK mixture to account for rotation-induced lithium enhancement. We applied the method to the Pleiades cluster and performed a validation using synthetic datasets. Results. For the Pleiades cluster, Chronos yields a posterior age distribution centred at $\mathrm{Age}=124.53_{-2.70}^{+3.34}$ Myr, consistent with classical LDB estimates, while simultaneously constraining both global and stellar-level rotation parameters. Conclusions. This work demonstrates that lithium-based stellar chronology can be recast as a coherent hierarchical inference problem, providing a flexible and statistically robust framework for making age determinations for young (1--600 Myr) stellar populations.