We present a multi-species analysis of identified-hadron transverse-momentum spectra in high-multiplicity p-Pb collisions at (sqrt{s_{NN}}=5.02~textrm{TeV}) within the Unified Statistical Thermal Freeze-out Model. The spectra are described through Cooper-Frye emission from an expanding freeze-out hypersurface, with resonance feed-down included. ALICE measurements of light mesons, protons, strange and multi-strange baryons, and the (K^{*}(892)) and (phi (1020)) channels are fitted in the soft-(p_T) region using a standard (chi ^2) minimization. To study the residual hadron-species dependence, we perform a constrained blast-wave analysis in which the spectral-shape differences are parametrized by the transverse-flow profile exponent (n_i) in (beta _T(r)=beta _{0T}(r/R)^{n_i}), where (r) is the transverse radial coordinate, (R) is the transverse geometric radius, (beta _{0T}) is the surface transverse velocity, and (n_i) is the species-dependent transverse-flow profile exponent. The common kinetic freeze-out condition is analyzed using the original (pi p) extraction, the conventional (pi Kp) bulk-hadron fit, and a global all-species constrained fit. The latter gives (T_textrm{com}=155pm 3~textrm{MeV}), (beta _{0T,textrm{com}}=0.85pm 0.03), and (chi ^2_textrm{tot}/textrm{dof}simeq 0.40), where (T_textrm{com}) denotes the common kinetic freeze-out temperature extracted from the global constrained fit and (T_textrm{kin}) denotes the kinetic freeze-out temperature used in the blast-wave description, with (T_textrm{kin}) and (beta _{0T}) common to all species and (n_i) fitted separately. A stable hierarchy is obtained: light mesons favor large (n_i), the proton lies in an intermediate region, and (phi ,Lambda ,Xi ,Omega ) occupy the small-(n_i) region. The hierarchy persists under variations of the common freeze-out condition and under fully free species-by-species correlation checks. We therefore interpret the extracted (n_i) pattern as a model-dependent spectral-shape signal compatible with species-dependent kinetic decoupling, rather than as a direct reconstruction of separate freeze-out hypersurfaces for different hadrons.


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