Tracing the galaxy-halo connection with galaxy clustering in COSMOS-Web from z = 0.1 to z ∼ 12

̊m deg ² of the COSMOS-Web survey, the largest contiguous JWST extragalactic survey. This study provides the first measurements of the mass-limited two-point correlation function at z 10 and a consistent analysis spanning 13. 4 Gyr of cosmic history, setting new benchmarks for future simulations and models. Using a halo occupation distribution (HOD) framework, we derived characteristic halo masses and the stellar-to-halo mass ratio (SHMR) across redshifts and stellar mass bins. Our results first indicate that HOD models fit data at z 2. 5 best when incorporating a nonlinear scale-dependent halo bias, boosting clustering at nonlinear scales (r = 10-100, kpc). We find that galaxies at z 10. 5 with łog (M_⋆ / M_⊙) 8. 85 are predominantly central galaxies in halos with M_ ̊m h ∼ 10^ M_⊙, achieving a star formation efficiency (SFE) of ɛ_ ̊m SF = M_⋆ / (f_ ̊m b M_ ̊m h) up to 1 higher than at z łe 1. The high galaxy bias at z 8 suggests that these galaxies reside in massive halos with an intrinsic high SFE, challenging stochastic SHMR scenarios. Our SHMR evolves significantly with redshift, starting very high at z 10. 5, decreasing until z ∼ 2 - 3, then increasing again until the present. Current hydrodynamical simulations fail to reproduce both massive high-z galaxies and this evolution, while semi-empirical models linking SFE to halo mass, accretion rates, and redshift align with our findings. We propose that early galaxies (z > 8) experience bursty star formation without significant feedback altering their growth, driving the rapid growth of massive galaxies observed by JWST. Over time, the increasing feedback efficiency and the exponential halo growth end up suppressing star formation. At z ∼ 2 - 3 and later, the halo growth slows down, while star formation continues, supported by gas reservoirs in halos.