  We present a novel, model-independent framework for studying the architecture
of an exoplanetary system at the system level. This framework allows us to
characterise, quantify, and classify the architecture of an individual
planetary system. Our aim in this endeavour is to generate a systematic method
to study the arrangement and distribution of various planetary quantities
within a single planetary system. We propose that the space of planetary system
architectures be partitioned into four classes: similar, mixed, anti-ordered,
and ordered. We applied our framework to observed and synthetic multi-planetary
systems, thereby studying their architectures of mass, radius, density, core
mass, and the core water mass fraction. We explored the relationships between a
system's (mass) architecture and other properties. Our work suggests that: (a)
similar architectures are the most common outcome of planet formation; (b)
internal structure and composition of planets shows a strong link with their
system architecture; (c) most systems inherit their mass architecture from
their core mass architecture; (d) most planets that started inside the ice line
and formed in-situ are found in systems with a similar architecture; and (e)
most anti-ordered systems are expected to be rich in wet planets, while most
observed mass ordered systems are expected to have many dry planets. We find,
in good agreement with theory, that observations are generally biased towards
the discovery of systems whose density architectures are similar, mixed, or
anti-ordered. This study probes novel questions and new parameter spaces for
understanding theory and observations. Future studies may utilise our framework
to not only constrain the knowledge of individual planets, but also the
multi-faceted architecture of an entire planetary system. We also speculate on
the role of system architectures in hosting habitable worlds.
