Basic physical fields are dynamic fields like our universe and the fields that are raised by electric charges. These fields are dynamic continuums. Most physical theories treat these fields by applying gravitational theories or by Maxwell equations. Mathematically these fields can be represented by quaternionic fields. Dedicated normal operators in quaternionic non-separable Hilbert spaces can represent these quaternionic fields in their continuum eigenspaces. Quaternionic functions can describe these fields. Quaternionic differential and integral calculus can describe the behavior of these fields and the interaction of these fields with countable sets of quaternions. All quaternionic fields obey the same quaternionic differential equations. The basic fields differ in their start and boundary conditions. The paper introduces the concept of the Hilbert repository. It is part of a hierarchy of structures that mark increasingly complicated realizations of a purely mathematical model that describes and explains most features of observable physical reality. That model is the Hilbert Book Model. The paper treats the mathematical and experimental underpinning of the Hilbert Book Model.