The corrected Gram-law conjecture for isolated bad Gram points

Let $g_n$ be an isolated bad Gram point, meaning the middle point of a Gram block whose adjacent boundary Gram points $g_{n-1}$ and $g_{n+1}$ are good. In the two-dimensional parameter space

$$Z_N(t;r_1,r_2)=Z_0(t)+r_1\sum_{k\in I_{\mathrm{shift}}}A_k(t)+r_2\sum_{k\in I_{\mathrm{descend}}}A_k(t),$$

where $A_k(t)=\frac{1}{\sqrt{k+1}}\cos(\theta(t)-\ln(k+1)t)$, let $\gamma(r)=(r_1(r),r_2(r))$. Two-dimensional corrected Gram-law conjecture. There exists such a curve with $\gamma(0)=(0,0)$ and $\gamma(1)=(1,1)$ for which

$$\Delta_n(r;\gamma):=Z_N\bigl(g_n(r_1(r),r_2(r));r_1(r),r_2(r)\bigr)>0$$

for every $0\leq r\leq1$. This conjecture proposes a collision-free two-parameter deformation for every isolated bad Gram point, extending the corrected Gram law beyond the linear deformation.