Stochastic Rupture as a Non-Equilibrium Statistical Field Theory: Renormalization Group Analysis and Emergence of the Saturation Parameter η

The Stochastic Rupture (SR) framework for objective wave-function collapse is reformulated as a non-equilibrium statistical field theory using the Martin–Siggia–Rose–Janssen–De Domini- cis (MSRJD) path-integral formalism. The SR Langevin equation for the holographic saturation field χ admits an exact mapping to an MSRJD action with a cubic nonlinearity. Dimensional analysis yields an upper critical dimension dc = 4 and a dynamic exponent z = 2. In d = 3 a one-loop renormalization group (RG) analysis reveals a non-trivial infrared-stable fixed point at dimensionless coupling g ∗ = π (exact, of geometric origin). At this fixed point the satu- ration parameter η—previously phenomenological in SR v14–v15 with the empirical window 3 × 10−2 ≲ η ≲ 1—emerges as the expectation value ⟨χ⟩|g ∗ , not a free input. A specific prediction, contingent on the explicit evaluation of the source-renormalization diagram coefficient cS, is η = 2/3 (verified to machine precision under the stated condition). All assumptions are stated explicitly and open theoretical problems are listed