This article is the sixth part of a scientific project under the general title "Geometrized vacuum physics based on the Algebra of signature" [1, 2, 3, 4, 5]. This article proposes a hierarchical cosmological model, which is developed based on the solution of the extended Einstein vacuum equation with an infinite number of lambda terms. The solution of a simplified vacuum equation with ten lambda terms is considered in more detail. As a result, a metric-dynamic model of a discrete hierarchical sequence of stable spherical vacuum formations ("corpuscles"), which are nested into each other like nesting dolls, was obtained. From this hierarchical sequence, the level of elementary par-ticles is isolated and examined in more detail. The use of methods and mathematical apparatus of Riemann differential geometry and the Algebra of signature allows us to obtain metric-dynamic models of all elements of the Standard Model of elementary particles: "quarks", "leptons", "nucleons", "mesons", "photons", "gluons" ", as well as the "at-om" of hydrogen and the "atom" of helium. It has been suggested that metric-dynamic models of stable vacuum for-mations ("corpuscles") of the "stellar-planetary" "galactic" and "universal" levels can be constructed in a similar way. The connection between the extended general theory of relativity and quantum mechanics is shown. At the end of the article, the advantages and disadvantages of the proposed hierarchical cosmological model are considered and the metaphysical prerequisites for resolving the problems that have arisen are outlined.