Topological Chemistry and the Emergence of the Covalent Bond via Graph Annealing in QGEFT

The current Paper 34 benchmark does not claim that full continuum molecular chemistry has already been derived on a graph. It does show that a minimal annealed QGEFT diatomic surrogate can generate the defining geometry of a covalent potential curve in one reproducible run: a mild approach barrier, a locked minimum at topological distance `1.0` with total energy `9.5200`, and a sharp short-range exclusion wall that raises the energy to `14.9835` at `d = 0.8` and `52.0309` at `d = 0.6`. The corresponding binding depth relative to the isolated baseline is `2.1559`.