Revisiting the soft-hard separation in the transverse momentum spectra of $pp$ collisions

We study the separation of soft and hard components in the transverse momentum spectra of charged particles as measured by ALICE in proton-proton collisions at $\sqrt{s}= 2.76 TeV, 5.02 TeV and 13 TeV at the LHC. The soft component is described by a Boltzmann fit, while the residual spectra are identified as hard QCD-like fragmentation. After separation, the subtracted spectra show no evolution in the shape or peak position with multiplicity, supporting a two-component interpretation. Mean transverse momenta for both contributions remain nearly constant, while Pythia 8 Monte Carlo simulations confirm these trends. Our results support the two-component description as a robust alternative to hydrodynamical interpretations.