A Refined Variational Framework for Proton Structure: Resolving Spin Dynamics, Calibration, and Deep QCD Observables

We present a refined variational framework for modeling the proton’s internal structure, integrating low-energy observables (mass, charge radius) with high-energy partonic distributions (GPDs, TMDs), spindependent interactions, and energy-momentum tensor diagnostics. The model uses a composite wavefunction with physically motivated basis functions, optimized via analytic gradients and JAX autodifferentiation. Unit calibration enables direct comparison to experimental data, while neutron and baryon extensions validate generalizability. We explicitly define the Hamiltonian, loss function, and regularization terms to avoid circular reasoning and ensure reproducibility. The model achieves 1–7% agreement with experimental values and offers a scalable alternative to lattice QCD.