Efficiently Inverting the L2-Invariant through Stability Theory

In [4], an efficient algorithm for inverting the L-invariant is presented, which amounts to a reduction to resolving a certain combinatorial-design problem, the so-called magic square. While elegant, this approach does not lend itself to generalization to greater numbers of variables. In this paper, I approach the L-canonization problem by explicitly seeking to exploit the well-behaved geometry of L-theories. Specifically, I present an algorithm to invert the L-invariant which relies on the fact that all complete L-theories are stable with “trivial” forking-dependence.