Identification of the near-critical limit with the derivative-martingale measure

Let $M^{\gamma}$ be the subcritical chaos measures for $\gamma^2<2d$, and let $M^c$ be the positive random measure obtained in Proposition 3.1 as a limit $\lambda_n M^{\gamma_n}(dx)\stackrel{\mathrm{law}}{\to}M^c(dx)$ for sequences with $\gamma_n^2<2d$ and $\gamma_n^2\to2d$. Let $M'$ denote the derivative-martingale measure constructed earlier. Near-critical identification conjecture. The measure $M^c$ equals, up to a multiplicative constant, the derivative-martingale measure $M'$ described in the derivative construction. Moreover, the sequence may be chosen as

$$\lambda_n=\frac{1}{\sqrt{2d}-\gamma_n}.$$

This conjecture links the alternative near-critical construction to the derivative martingale and predicts the precise first-order normalization. The source presents it as a consequence of the preceding uniqueness conjecture, not as a proved result.