Haar-wavelet solvability conjecture for near-Tsirelson Bell-CHSH violations

Fix $\eta\in(\sqrt2-1,1)$. Let $N_0<N_1$ and $K>1$ determine a finite Haar-wavelet resolution, and define $\widetilde f,\widetilde f',\widetilde g,\widetilde g'$ by finite linear combinations of the Haar wavelets as in the paper. The coefficients are required to satisfy the normalization and inner-product equations

$$\begin{array}{l} \langle\widetilde f\mid\widetilde f\rangle=\langle\widetilde f'\mid\widetilde f'\rangle=\langle\widetilde g\mid\widetilde g\rangle=\langle\widetilde g'\mid\widetilde g'\rangle=1,\\ \langle\widetilde f\mid\widetilde g\rangle=\langle\widetilde f'\mid\widetilde g\rangle=\langle\widetilde f\mid\widetilde g'\rangle=-\langle\widetilde f'\mid\widetilde g'\rangle=-i\frac{\sqrt2\eta}{1+\eta^2}. \end{array}$$

Haar-wavelet solvability conjecture. For every $\eta\in(\sqrt2-1,1)$, a resolution $\{N_0,N_1,K\}$ can be found such that this finite system admits a solution of the prescribed Haar-wavelet expansion form.

If true, the conjecture would provide an exact finite-resolution construction of Bell-CHSH violations approaching Tsirelson's bound in the vacuum state of the free massless $(1+1)$-dimensional spinor field. The paper presents evidence for the claim, while no proof or disproof is supplied.