We have studied the higher-twist distributions of the proton, including T-even and T-odd transverse momentum-dependent parton distributions (TMDs). Under the umbrella of the light-front framework, we have chosen two distinctive approaches of quark-spectator systems for comparison, one inspired by the soft-wall AdS/QCD and another with a dipolar form factor at the nucleon-quark-diquark vertex. The comprehensive picture at higher-twist provided by both T-even and T-odd TMDs not only aids deeper insights into the internal structure of the proton in the quark sector but also provides an interpretation of different components of the energy-momentum tensor in quantum chromodynamics. Hence, using these standard parton distribution functions, further predictions regarding the physical insights of gravitational TMDs in momentum space are also provided.

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