  We demonstrate that the assembly pathway method underlying Assembly Theory
(AT) is a dictionary-based encoding scheme for `counting copies', widely used
by popular statistical compression algorithms, some of which have been applied
to many areas, including systems biology, chemistry, and biosignature
classification. We show that AT performs similarly in all cases (synthetic or
natural) to other simple coding schemes and underperforms compared to
system-related indexes based upon algorithmic probability that take into
account the likelihood of related computable approximations of similar events.
Our results also demonstrate that simple (and tractably computable) modular
instructions can mislead AT, leading to failure in practice in capturing the
properties of physical systems. These theoretical and empirical results imply
that the assembly index, whose computable nature is not an advantage, does not
offer substantial improvements over existing methods. In contrast, other
resource-bounded (therefore also computable) indexes that approximate
algorithmic (Kolmogorov) complexity show the ability to separate organic from
inorganic molecules and even perform better on the mass spectral information
used by the authors of AT. We show the predictive power of these other
system-driven indexes based on their solid foundations and empirical results.
