Origin Phase-Space Geometry

Systems originate when configuration space first contains a structure capable of sustaining admissible recursive continuation. Previous work within the Paton System identified this moment as an admissibility threshold: the point at which a minimal configuration becomes compatible with the governing constraints of the system. This paper examines the geometric structure of configuration space surrounding such thresholds. It shows that admissible configurations typically occupy small regions within a much larger space of unstable possibilities. System formation therefore occurs when evolving configurations enter these admissible regions. This geometric interpretation explains why most configurations fail to produce systems and why system formation often appears abrupt. Once configuration space contains an admissible region, structures entering that region can persist and evolve. The framework provides a unified structural interpretation of system origins across physics, biology, computation, and organisational systems by identifying admissible regions of configuration space as the geometric condition for system formation.