The Leading Soft Graviton Theorem as Universal Bremsstrahlung of the Gravity Plexus

The leading soft graviton theorem states that the amplitude for emitting a graviton of vanishing momentum factorizes universally from any hard scattering process. In conventional quantum field theory this universality is derived from gauge invariance and asymptotic symmetries. In the Foam–Plexus framework, spacetime emerges as an ordered phase of a stochastic wormhole substrate. Persistent particles correspond to renewal eigenpatterns of this condensed phase. Each fermion possesses a Gravity face whose coherent circulation encodes stress–energy flux. Acceleration of this Gravity face produces free graviton emission as a renewal bremsstrahlung process. We give an explicit derivation of the leading soft factor. The 1/(p·q) pole arises from integrating a long-wavelength emission kernel along asymptotic worldline segments; factorization arises because soft modes cannot resolve the short-distance hard region. The numerator pµpν arises from universal coupling to stress–energy. The result reproduces the Weinberg soft graviton factor and reinterprets gravitational memory as a permanent large-scale rebiasing of the Gravity plexus.