z-independent theor. halo mass func.

Building on a generalised Press & Schechter model and triaxial collapse (GPS+), we predict the HMF in terms of the variance of the linear density field, with only a weak explicit dependence on halo mass and no explicit dependence on redshift.

The GPS+ model naturally provides the correct normalization and high-mass behaviour without requiring empirical fitting. We calibrate and validate the GPS+ model using the Uchuu N-body simulation suite, which combines large cosmological volume and high mass resolution under Planck cosmology. Using six simulations with up to 300 realizations, we obtain precision HMF measurements spanning halo masses in the range 6.5<=log(M200m/[h^-1^M_{sun}_])<=16 over 0<=z<=20, with reduced cosmic variance.