Product structure conjecture for the generalized Somos-4 recurrence tree

Let $T$ be the recurrence tree generated by the recurrence referred to as (Som4Ord3), and let the generalized Somos-4 sequence be the sequence associated with that recurrence. Product structure conjecture. Every integer in $T$, and the numerator and denominator of every reduced non-integer rational number in $T$, are products of terms in the generalized Somos-4 sequence. The observation is motivated by the unexpectedly simple polynomial sequence found in the recurrence tree, whereas the closed form for the generalised Somos-4 sequence is expressed using elliptic theta functions. The source presents this broader product property as something observed rather than proved.