The 2-dimension series of the just-nonsolvable BSV group

I compute the structure of the restricted 2-algebra associated to a group first described by Andrew Brunner, Said Sidki and Ana Cristina Vieira, acting on the binary rooted tree. I show that its width is unbounded, growing logarithmically, and obeys a simple rule. As a consequence, the dimension of the successive quotients of powers of the augmentation ideal in the modular group algebra is p(0)+...+p(n), the count of partitions of numbers up to n.