In the TGD framework, one ends up with both geometric and number theoretic analogs of the assembly theory. Algebraic complexity is a measure for the complexity determining the evolutionary level assignable to a space-time region, which would correspond to a polynomial P: roots of P determine the space-time region by providing a 3-surface to which holography assigns the space-time region as a 4-surface in M4×CP2.
The dimension of extension of rationals defined by its roots would serve as a measure for the complexity of quantum states obtained by Galois confinement, which serves as a universal mechanism for the formation of bound states. The algebraic complexity makes possible high information storage capacity, which is necessary for advanced life forms. Basic biomolecules serve as an example.
See for instance the article The TGD based view about dark matter at the level of molecular biology.