Explicit Decay Rate and Quantitative Threshold for the SND Gronwall Inequality: T2 Conditional Closure and GNC–Goldbach Bridge

We prove that the T2 inter-shell flux dispersal inequality closes conditionally on the Spectral Non-Dispersal (SND) condition, with explicit decay rate α = 2ν²·4^(1/ρ₀)·ρ₀ derived from the Shell-Spread Poincaré Inequality. Key results: (1) Lemma 1: The low-frequency inter-shell flux vanishes exactly by incompressibility — unconditional, no approximation. (2) Lemma 2: Under SND and the H^2.3 absorbing ball, |Φ_j(t)| ≤ C_φ·2^(-0.8j)·X(t)^(1/2)·D(t)^(1/2) with exponential shell decay. (3) Theorem 1: Explicit α = 2ν²·4^(1/ρ₀)·ρ₀ from viscous dissipation. (4) Theorem 2: T2 Gronwall closes conditionally on SND with η_N = 0.039 < 0.20 for threshold-class data. (5) Theorem 3: T2 ⇔ SND — the Gronwall inequality is SND expressed as a differential inequality. (6) Corollary: Explicit κ* for the Goldbach Non-Concentration (GNC) condition provides a computable bridge between NS regularity and Goldbach's conjecture via the Q_N(i,j) = 1/gcd(i,j) spectral operator. This paper is part of the Prime Field Technologies research program connecting Navier–Stokes regularity, the Riemann Hypothesis, and Goldbach's conjecture through the Universal Non-Concentration Principle (SND ≡ GNC ≡ Bridge).