The MIP Timing Detector (MTD) of the CMS experiment, currently under construction for the High Luminosity phase of LHC, emerges as a key player in the pursuit of unrivaled temporal precision in particle physics.
The precise measurement of the time-of-arrival of charged particles provided by the MTD enables the implementation of a 4D vertex reconstruction and helps to discriminate interaction vertices within the same bunch crossing, aiming to recover the vertex cross-contamination levels of the current LHC conditions.

In this contribution, we explore the impact of the measured track momentum uncertainty in the time-of-flight determination and its use in the vertex reconstruction and mass hypothesis assignment, shedding light on its potential impact on event reconstruction and classification.
The results presented in this abstract demonstrate the efficacy of the MTD in advancing our understanding of particle dynamics in CMS, opening new avenues for an effective usage of precision timing in pileup mitigation and as a tool to probe signatures of new physics with characteristic time structures.