Unquenched Fermions, String Breaking, and Confinement Proxies in a Dynamical Graph Surrogate

We study whether a background-free graph surrogate can support nontrivial gauge-sector organization once matter backreaction is allowed to act on a fluctuating geometry. The main challenge is geometric stability: in many discrete gravity-inspired models, strong matter backreaction drives the graph into a crumpled or fragmented phase before any confinement-sensitive gauge observable becomes meaningful. In the QGEFT surrogate, we examine a stabilized matter-coupled branch, then probe confinement-sensitive observables on that background, and finally introduce unquenched pseudofermion dynamics to test whether the confinement proxy weakens under dynamical screening. Across the current benchmark program, we find three linked results. First, the scalar-coupled graph exhibits a sharp split between a crumpled branch and a stable weak-coupling or Goldilocks branch ; in the latter, the condensate reaches $\langle|\phi|^{2}\rangle\approx0.413$ while the graph remains largely connected and the diffusion-based dimensional signal survives several RG coarse-graining steps. Second, on a stabilized background the quenched gauge observables are compatible with a confinement-sensitive regime, with Wilson-loop behavior consistent with area-law-like organization and Polyakov-loop averages near zero. Third, once unquenched pseudofermions are introduced, the lowest modes delocalize at large hopping, the tuned HMC branch remains numerically controlled, and the Wilson-loop proxy weakens in a way consistent with a string-breaking surrogate. The narrow claim supported by the current data is not that continuum QCD has been derived on an emergent spacetime. It is that the QGEFT surrogate can avoid immediate geometric collapse, sustain confinement-sensitive gauge behavior on a nontrivial dynamical background, and then exhibit weakening of that proxy once dynamical fermionic screening is introduced.