The degree-sequence conjecture for non-trivial flow-critical tame canvases

Let $(\mathfrak{G},z)$ be a non-trivial flow-critical tame canvas, and let $C(\mathfrak{G},z)$ denote its associated degree sequence. If

$$\deg(z)\geq 8$$

and $\mathfrak{G}$ has a vertex of degree $\deg(z)-3$, then the degree-sequence conjecture says that

$$C(\mathfrak{G},z)\in\bigl\{\{\deg(z)-3,5\}, \{\deg(z)-3,5,5,5\}\bigr\}.$$

This removes the preceding corollary's assumption that a specified tip preflow exists. It is presented as a belief in the source, and no resolution is supplied.