The Hilbert Book Model is a read-only repository for the dynamic geometric data that describe the live story of the elementary particles that exist in the universe. These data describe an ongoing hopping path that recurrently regenerates a coherent hop landing location swarm that characterizes the footprint of the elementary particle.

Elementary particles are elementary modules and together they constitute all other modules that exist in the universe. Some modules constitute modular systems. Some modular systems are intelligent.

Depending on the symmetry of the data, the hop landings can cause spherical shock responses of the embedding field. Spherical shock responses temporarily deform and persistently expand the embedding field.

Deformation of the embedding field corresponds to mass of the actuator. The initial deformation quickly fades away. The mechanism that generates the hop landing location must keep producing new hop landing locations to reach a significant persistent deformation by the footprint of the elementary particle.

The mechanism generates deformation and thus mass, but this mass is very transient. If the mechanism stops, then the mass vanishes. If the mechanism keeps producing, then the deformation bump travels with the particle to which the mechanism belongs.

Something must keep the mechanism going. The actuator is the ongoing embedding of the content of the eigenspace of the footprint operator, which resides in the quaternionic separable Hilbert that contains the life story of the elementary particle, The content is embedded step by step and controlled by the archived time-stamps into the field that represents the universe.

This field is archived in the eigenspace of a dedicated operator that resides in a quaternionic non-separable Hilbert space, That Hilbert space is the unique companion of a quaternionic separable Hilbert space that acts as a background platform.

All involved separable Hilbert spaces are applying the same vector space, but their inner product is defined by members of a privately selected version of the quaternionic number system. That version is managed in the eigenspace of a reference operator which resides in the private quaternionic separable Hilbert space of the particle that lives on this platform. The eigenspace of the reference operator provides a private parameter space. The platform floats with the geometric center of the private parameter space over the parameter space of the background platform.

The operator that manages the field of the universe resides in the non-separable Hilbert space, but owns an equivalent operator in the separable Hilbert space that manages the background platform.

Thus, embedding in the field of the universe is replicated in a mapping into the eigenspace of the equivalent operator in the separable Hilbert space of the background platform.

Thus embedding in the continuous field of the universe is replicated in an equivalent map into the countable eigenspace of the universe field operator in the background platform. The quaternionic function that describes this field must be equal to the quaternionic function that describes the field of the universe in the non-separable Hilbert space.