Effective reduced-density-matrix series conjecture

Let $\rho_N(x,t)$ be the finite-volume reduced density matrix. Set ${\mathcal B}_L=\{n\in\mathbb Z:-w_L<n<w_L\}$, ${\mathcal B}_L^{\mathrm{ext}}={\mathcal B}_L\setminus\{1,\ldots,N+1\}$, and ${\mathcal B}_L^{\mathrm{int}}=\{1,\ldots,N+1\}$. For particle and hole labels $p_a\in{\mathcal B}_L^{\mathrm{ext}}$ and $h_a\in{\mathcal B}_L^{\mathrm{int}}$, let $\rho_{N;\mathrm{eff}}(x,t)$ be the displayed effective form-factor series in the source. Effective reduced-density-matrix series conjecture. Its thermodynamic limit coincides with that of the reduced density matrix:

$$\lim_{N,L\to+\infty}\rho_N(x,t)=\lim_{N,L\to+\infty}\rho_{N;\mathrm{eff}}(x,t).$$

This conjecture is the explicit form of the simplifying hypothesis used to discard extensive-energy contributions and subleading finite-size corrections. It is proposed as the basis for the asymptotic analysis, and no proof is given.