A self-consistent orbital architecture for GG Tau A. I. Simultaneous orbital fitting of the hierarchical triple

GG Tau A is a young triple system with the close pair, Ab 1 -- Ab 2, and Aa, surrounded by a massive circumtriple disk with a large inner cavity difficult to explain in a binary framework. We aim to determine the orbital architecture and individual stellar masses of GG Tau A and assess how the available astrometric and disk-based constraints restrict the range of admissible solutions. We performed a joint fit using Oracle, developed specifically for hierarchical stellar systems. All astrometric measurements were placed in a common reference frame, since the historical wide-orbit astrometry is given relative to the unresolved photocenter of the Ab subsystem. The fit included one new wide-orbit astrometric epoch and a prior on the total stellar mass derived from disk kinematics. We then applied, in post-processing, an additional geometrical constraint based on the observed center of the circumtriple disk. The fit yields orbital solutions compatible with the available astrometric and disk-based constraints and provides estimates of the individual stellar masses. The additional wide-orbit epoch only marginally reduces the range of admissible solutions. By contrast, the disk-center constraint leaves the favored orbital architectures largely unchanged but significantly tightens the stellar-mass partition. This yields posterior masses of 0.521+0.069-0.051, 0.106+0.017-0.013, and 0.79+0.10-0.10 M for Ab 1, Ab 2, and Aa, respectively. The reported values are posterior medians with 16th--84th percentile intervals. A joint treatment of the two orbital levels is required to recover a physically meaningful architecture and constrain the individual stellar masses. The resulting solutions provide a basis for future dynamical modeling of the circumtriple disk and for testing whether the observed cavity can further constrain the system architecture.