Parametric fl-RDT algorithmic conjecture

Assume the setup of the paper's fl-RDT theorem, including the quantities $\psi_{rp}$, $\psi_{rd}$, $\hat{\mathbf p}$, $\hat{\mathbf q}$, and $\hat{\mathbf c}$. Define the algorithmically achievable value $\psi_{rp,a}$ by

$$\psi_{rp,a}=\max\left\{\psi_{rp}\ \middle|\ \lim_{n\to\infty}\mathbb{P}(\psi_{rp}\text{ can be achieved in polynomial time})=1\right\}.$$

Let $\psi_{rd}^{(r)}=\psi_{rd}$, with $\psi_{rd}$ as in the stated fl-RDT theorem. Parametric fl-RDT algorithmic conjecture. There is an $r$-sequence $\psi_{rd}^{(r)}$ with a decreasing sequence $\hat{\mathbf c}^{>}$ such that

$$\psi_{rp}=\lim_{r\to\infty}\psi_{rd}^{(r)}(\hat{\mathbf p},\hat{\mathbf q},\hat{\mathbf c}^{>} ).$$

If no subinterval of $[0,1]$ contains no elements of $\hat{\mathbf p}$ and $\hat{\mathbf q}$, then

$$\psi_{rp}=\lim_{r\to\infty}\psi_{rd}^{(r)}(\hat{\mathbf p},\hat{\mathbf q},\hat{\mathbf c}^{>} )=\psi_{rp,a},\qquad SCG=\psi_{rp}-\psi_{rp,a}=0.$$

Otherwise, there is an $r$-sequence with an arbitrarily ordered sequence $\hat{\mathbf c}^{\sim}$ such that

$$\psi_{rd}^{(r)}(\hat{\mathbf p},\hat{\mathbf q},\hat{\mathbf c}^{\sim})\geq\psi_{rp,a},\qquad \lim_{r\to\infty}\psi_{rd}^{(r)}(\hat{\mathbf p},\hat{\mathbf q},\hat{\mathbf c}^{\sim})=\hat{\psi}_{rd}=\psi_{rp,a},$$

and

$$SCG=\psi_{rp}-\psi_{rp,a}=\lim_{r\to\infty}\psi_{rd}^{(r)}(\hat{\mathbf p},\hat{\mathbf q},\hat{\mathbf c}^{>} )-\lim_{r\to\infty}\psi_{rd}^{(r)}(\hat{\mathbf p},\hat{\mathbf q},\hat{\mathbf c}^{\sim} ).$$

The conjecture proposes a general parametric fl-RDT mechanism relating computationally achievable values to limiting finite-parameter predictions; the source provides no resolution, so it remains open.