The augmented acyclicity conjecture for the Collatz return graph

Let $G_M^+$ denote the augmented return graph at modular depth $M$, incorporating the mixed-state excursion, exit, and return dynamics, and let $K\ge1$ be the parameter indexing the net-positive regime. Augmented acyclicity conjecture. For every $M\ge13$ and every $K\ge1$, the graph $G_M^+$ is acyclic. The supplied text reports verification only for finite ranges of $M$ and treats all-$M$ acyclicity as the unresolved Layer-2 re-entry problem.