Scale Graphs VI: Stochastic Forcing and Conditional Closure in Dissipative Scale Graphs

We extend the minimum-production scale-graph framework to externally forced and stochastically driven finite dissipative systems, and we separate the exact algebraic structure from the closures required to connect it to observed dynamics. For a shell-local additive noise we prove an Ito tail identity and a conservative expected-tail envelope with explicit finite noise tail. For linear slow-fast diffusions we show that minimum-production elimination and stochastic averaging select the same Schur-complement drift. Under standard mixing and Poisson-equation hypotheses we also record a covariance-response formula for stationary observables and a quantitative consequence of an approximately rank-one response operator. The paper then reports the frozen numerical programme carried out in campaigns v35, v35_bis, and v36. The stochastic solver, exact Ornstein-Uhlenbeck convolution, and linear-Gaussian Schur reduction pass their algebraic and numerical gates. By contrast, the passive noise-floor prediction is rejected: the measured shell-decay exponents lie between 0.68 and 0.96, rather than the predicted values 4 and 6, and the response is not consistently linear in the noise variance. A targeted v36 basis experiment finds locally low-rank finite-difference responses, but the preregistered linearity gate fails by factors between roughly 14 and 77, while the leading response mode changes strongly with the stochastic baseline. Thus no baseline-independent rank-one stationary-response mechanism is certified. The classical on-off T^-3/2 laminar-duration law is falsified, no universal alternative lifetime family is selected, and Freidlin-Wentzell scaling is not supported in the tested regime. Certificate-geometry variables carry a statistically nonzero but quantitatively small incremental out-of-sample signal, Delta R^2 = 2.43e-4. The physical edge trajectory is not certified as invariant under the observed RG map: none of four frozen phases passes the induced-map gate. Quotient projection substantially improves conditioning, but the transverse leakage remains approximately 0.918, so no closed edge cocycle or cocycle clock is constructed. Periodically forced ensembles show no certified pullback synchronization in the tested observable metric. Finally, a candidate Sabra adapter satisfies energy and telescoping identities at machine precision, but no theorem-level sum-of-squares proof record is yet available. The resulting conclusion is a three-level theory. Minimum-production, Prigogine completion, and Schur/Kron reduction form a robust universal algebraic layer. Realizability, edge/RG compatibility, stochastic response, and pullback or clock closures are system- and observation-specific. Lifetime laws, exponents, and observed classes belong to a regime-dependent phenomenological layer and do not follow automatically from the universal algebra.