Weight bound for constructible graphical functions and periods

Let $G$ be a constructible graph in an even dimension $D\geq4$, and let $P_G$ be its associated period. The preceding reduction argument concerns the weight of graphical functions and periods under reductions (R1)–(R4). The weight-bound conjecture. Theorem (conthm) holds for all constructible graphs and periods in even dimensions $\geq4$. The statement is presented after a proof for the known cases and an expectation about the remaining edge-appending reduction. The supplied text gives no resolution, so the conjecture remains open.