Geometric effective modeling of proton pressure and shear forces

The internal pressure, shear force, and elastic response of the proton remain nontrivial emergent quantities in quantum chromodynamics (QCD). Recent lattice-QCD calculations and deeply virtual Compton scattering (DVCS) measurements have provided access to the gravitational form factors A(t), B(t), and C(t), yet a unified geometric interpretation of the proton’s stress–energy tensor is still lacking. In this work, we derive the proton’s mechanical structure within the Helix–LightVortex (HLV) framework, treated explicitly as an effective geometric model complementary to QCD. Within this approach, the proton is described as a confined helical excitation in a discretized quasicrystalline background, whose mechanical stability is governed by geometric torsion and spiral-phase modulation ψ(t) = t + iϕ(t) + jχ(t). Closed-form expressions are obtained for the isotropic pressure p(r), shear force s(r), confinement radius r∗, and an effective torsional stiffness parameter κHLV. The resulting stress distributions reproduce lattice-QCD pressure and shear profiles at the 5–10% level across the confinement region. The model further predicts a small geometric mass correction ∆m/mp ≈ (1.3±0.2)×10−3, consistent with existing precision constraints on the proton–electron mass ratio. Finally, we outline experimentally testable signatures in DVCS, polarized electronion collider (EIC) observables, and ultrafast laser–proton interactions. The HLV framework is not intended to replace QCD, but to provide a geometric realization of the same mechanical observables, enabling direct comparison with established experimental and lattice results.