Nonvanishing Jacobian-minor conjecture for generalized constants

Let $n\in\mathbb{Z}_{\geq2}$ be fixed. For each $m\in\{2,3,\ldots,n\}$ and each $\theta\in\left(\mathcal{G}_{m}^{\left(\operatorname{U}\right)}\cup\{\gamma\}\right)$, let $\mathbf{J}_{m,\theta}^{\left(n\right)}$ be the Jacobian matrix defined in Lemma 5, and let $\boldsymbol{\gamma^{*}}$ denote the specified specialization of the generalized constants. Nonvanishing Jacobian-minor conjecture.

$$\det\left(\left.\mathbf{J}_{m,\theta}^{\left(n\right)}\right|_{\gamma^{*}}\right)\neq0$$

for all $m\in\{2,3,\ldots,n\}$ and $\theta\in\left(\mathcal{G}_{m}^{\left(\operatorname{U}\right)}\cup\{\gamma\}\right)$. The conjecture has been verified computationally for $n\in\{2,3,\ldots,26\}$ and is intended to support lower bounds on the density of transcendental terms in the generalized-constant sequences; its validity for all $n\geq2$ remains open.