Frohmader's localized clique-weight conjecture

Let $G$ be a graph, let $m$ be its number of edges, and let $\K(G)$ denote its collection of cliques. For $t\geq 2$ and each $T\in\K(G)$, define

$$\alpha_G(T)=\max\{k:T\subseteq V(S)\text{ for some }S\subseteq G\text{ such that }S\cong K_k\}$$

and

$$w'_G(T)=\frac{\binom{\alpha_G(T)}{2}^{t/2}}{\binom{\alpha_G(T)}{t}}.$$

Frohmader's localized clique-weight conjecture. For every $m$-edge graph $G$,

$$\sum_{T\in\K(G)}w'_G(T)\leq m^{t/2}.$$

This is a localized form of a theorem of Frohmader on maximizing the number of $t$-cliques in $m$-edge, $K_{r+1}$-free graphs. A generalization was announced by Aragão and Souza after the paper's preprint appeared, so the resolution of this exact formulation should be checked.