The Hilbert Book Model project produced this publication. The search for a reliable foundation of physical reality has had many setbacks and is slow. As a result, mainstream physics got at a sidetrack. Quantum Field Theory, Quantum Electro Dynamics, and Quantum Chromodynamics use the minimal action principle as their base. The Hilbert Book Model shows that continuums belong to the third phase of a special set and cannot work as a foundation of mathematical physics. This document shows how the three phases of the special set lead to a vector space and number systems, which apply to a system of Hilbert spaces in which the local universe and a parallel multiverse can pose. Also, the document shows that science must not consider the Higgs particle or the Higgs field as part of the Standard Model. Instead, the Standard Model of experimental particle physicists should restrict to elementary fermions. Most physicists interpret photons as excitations of the electric field. In contrast, the HBM interprets photons as chains of dark energy objects, and the dark energy objects are shock fronts that excite the field, representing the local universe. Hop landings of the state vectors of the fermions produce spherical shock fronts that move with light speed away from the location of this landing. This conflicts with the ideas of conservation laws that play in mainstream physics. According to the HBM, a big bang never occurred. The model considers two episodes, and at the beginning of the second episode, time starts running together with an ongoing creation of fermions.