6 problems

Conjecture 6. There exists an exponent $\alpha$ with $0<\alpha<1$ such that

Conjecture 5. There are constants $C_1,C_2>0$ such that

Conjecture 4. There exists an edge-weight distribution $F$ with $F(0)=p_c$ and a constant $C$ such that

Conjecture 3. There is a constant $C$ such that

Conjecture 2. If $F_n\Rightarrow F$, then

Conjecture 1. If $F(0)>\vec{p}_c$, then $\vec{\mu}_F(\theta)$ has singularities at $\theta_p^-$ and $\theta_p^+$.