Theoretical developments provide the foundation for understanding the dynamics of the strong interaction from first principles. Through renormalization we connect bare quantities computed on the lattice to physical observables, ensuring meaningful continuum predictions. Perturbation theory offers analytic control in the weak-coupling regime and guides the matching between lattice and continuum formulations. The gradient flow introduces a powerful framework to define renormalized observables and improve signal quality, bridging analytical insights and numerical precision. Our work combines these approaches to refine theoretical tools that strengthen the connection between Quantum Chromodynamics and measurable phenomena.