Super vertex total local antimagic labeling existence conjecture

Let $G=(V,E)$ be a finite simple undirected graph without isolated vertices. A super vertex total local antimagic labeling is a bijection $f:V\cup E\to\{1,2,\dots,|V|+|E|\}$ satisfying $w(u)\ne w(v)$ for every edge $uv\in E$, where

$$w(v)=\sum_{x\in NT(v)}f(x),\qquad NT(v)=N(v)\cup\{uv:uv\in E\},$$

and additionally $f(V)=\{1,2,\dots,|V|\}$. The super vertex total local antimagic labeling conjecture. Every graph without isolated vertices admits a super vertex total local antimagic labeling. The paper presents this as an existence problem for a broad class of graph labelings; no resolution is supplied here.