**4. Discussion**

By preserving nontrivial center regions, the full string tension can be recovered and extracted from the center degrees of freedom in SU(2) quantum chromodynamics. The choice of the free parameter *Tr*max based on the behavior of Creutz ratios does not give an unambiguous value, but merely an interval of good values of *Tr*max. This arbitrariness has to be investigated in further work. Preliminary data already hints at a way to eliminate it. The concept of identifying gauge-independent observables evaluating to the relevant degrees of freedom and using them to guide the gauge-fixing procedure reduces the number of free parameters of the gauge transformation. It forces all differing local maxima of the gauge functional to incorporate specific, gauge-invariant properties that are related to the relevant degrees of freedom. This might be a solution to the Gribov copy problem wherever the gauge-fixing procedure is based upon a specific gauge functional. The algorithms presented can be easily extended into higher symmetry groups or modified to capture different degrees of freedom. The procedures for identifying nontrivial center regions can also be used to reconstruct the thick vortices from P-plaquettes. This will allow further investigations of the color structure of vortices.

**Author Contributions:** Conceptualization, M.F.; Investigation, R.G.; Writing—original draft, R.G.; Writing—review editing, M.F.

**Funding:** This research received no external funding.

**Acknowledgments:** We thank Vitaly Bornyakov for the helpful discussions of the results.

**Conflicts of Interest:** The authors declare no conflict of interest.
