Evolution mapping III: A new recipe for the halo mass function
We present a new prescription for the halo mass function (HMF) built upon the Evolution Mapping framework. This approach provides a physical motivation to parametrise the non-universality of the HMF in terms of the recent history of structure formation and the local shape of the linear matter power spectrum. Our model was calibrated against measurements from N-body simulations, with halo samples defined by ten overdensity thresholds, $Δ$, ranging from 150 to 1600 times the mean background matter density. For our reference mass definition, $Δ=200$, the calibrated fitting function achieves per cent-level accuracy across a wide range of masses, redshifts, and structure formation histories, and maintains this performance when tested on cosmologies with different linear power spectrum shapes. This high level of accuracy is maintained across other mass definitions, degrading only slightly to the 5 per cent level at the highest values of $Δ$. We also provide fitting formulae to interpolate the parameters as a function of $Δ$, which allows for accurate modelling of HMFs defined by intermediate overdensities, with accuracy still well within 5 per cent when tested on halo catalogues defined by the virial overdensity threshold. Compared to other commonly used recipes, our prescription yields competitive or superior accuracy across all redshifts and cosmologies, successfully capturing the non-universal features of the HMF where other models exhibit systematic deviations. This work provides a high-precision modelling tool for cluster abundance analyses, and demonstrates the power of the evolution mapping framework for building accurate models of observables in the non-linear regime.