High-fidelity stellar extinction with Gaia and APOGEE -- I. The method and a new extinction curve

The scarcity of high-fidelity extinction measurements remains a bottleneck in deriving accurate stellar properties from Gaia parallaxes. In this work, we aim to derive precision extinction estimates for APOGEE DR19 stars, establishing a new benchmark for Galactic stellar population studies. We first determine reddening by comparing observed colorsr, etrieved from photometric surveys or standardized synthetic magnitudes from Gaia BP/RP spectra, to intrinsic colors predicted via an XGBoost model. The model is trained on minimally reddened stars to infer intrinsic colors and their associated uncertainties, using APOGEE stellar parameters (Teff, logg, [Fe/H], and [alpha/Fe]). The derived reddening values are then converted into extinctions using an anchor ratio of A_BP / A_RP = 1.694 +/- 0.004, derived from red-clump-like stars. Here, we provide extinction measurements in 39 filters across 10 photometric systems and introduce a new empirical extinction curve optimized for broadband passbands. Our extinction estimates (Av) outperform existing results (Bayestar19, StarHorse, SEDEX), achieving a typical precision of 0.03 mag in Av. Notably, we identify systematic deviations of up to 30% between monochromatic and passband-integrated extinction ratios at wavelengths greater than 700 nm. This result highlights the necessity of adopting passband-specific coefficients when correcting extinction to derive stellar parameters. As the foundation for a forthcoming series of papers, these benchmark measurements will be used to (1) revise asteroseismic scaling relations, (2) calibrate differential reddening in open clusters, and (3) reconcile heterogeneous dust maps into a unified, all-sky extinction scheme.