The Geometric Etching of Spacetime: Gravitational Waves as Topological Stress from Memory Channel Deviation in QGEFT

The current Paper 77 benchmark does not claim that continuum Einstein gravity or the full GW waveform has already been derived from first principles. It does show that the QGEFT repository now supports a concrete three-phase algorithmic mechanism: (1) a traversing particle etches a lowered-energy topological memory channel, (2) a second particle glides inertially through the channel with minimal resistance (passive gravity), and (3) forced deviation from the channel into virgin vacuum triggers a local optimization crisis whose radiated topological stress, when calibrated with $\beta/H_* = 30$, $\kappa_{\mathrm{stress}} = 22.0$, and $f_{\mathrm{sim}} \to f_{\mathrm{source}} = 0.01$, matches the NANOGrav 15-year stochastic background at $f_0 \approx 40.6\ \mathrm{nHz}$ and $\Omega_{\mathrm{GW}} h^2 \approx 1.00 \times 10^{-10}$.