Large-loop log-Gamma distribution conjecture for phi-four periods

For each loop order $L$, consider the period Feynman integrals of $\phi^4$ theory and sample them with probability inversely proportional to the symmetry factor of their associated Feynman graph. A probability distribution is said to weakly converge if its integrals against bounded continuous test functions converge. Large-loop log-Gamma distribution conjecture. As $L\rightarrow\infty$, the distribution of these period Feynman integrals weakly converges to a $\log$-$\Gamma$ distribution. The observed convergence is based on finite-loop numerical data, particularly at 17 loops; the limiting parameters are fitted at each loop order, and their asymptotic laws remain to be determined.