The efficiency of limiting quantities as a tool for describing physics at various spatio-temporal scales is shown. Due to its universality, limit values allow us to establish relationships between, at first glance, distant from each other's characteristics. The article discusses specific examples of the use of limit values to establish such relationships between quantities at different scales. Based on the principle of reaching the limiting values on the event horizons, a connection was obtained between the Planck values and the values of the Universe. The resulting relation can be attributed to relations of the Dirac type - the coincidence of large numbers that emerged from empirical observations. In the article, the relationships between large numbers of the Dirac type are established proceeding, in a certain sense, from physical principles - the existence of limiting values. It is shown that this ratio is observed throughout the evolution of the Universe. An alternative way of solving the problem of the cosmological constant using limiting values and its relation to the minimum spatial scale is discussed. In addition, a one-parameter family of masses was introduced, including the mass of the Universe, the Planck mass and the mass of the graviton, which also establish relationships between quantities differing by 120 orders of magnitude. It is shown that entropic forces also obey the same universal limiting constraints as ordinary forces. Thus, the existence of limiting values extends to informational limitations in the Universe. It is fundamentally important that on any event horizon, regardless of its scale (i.e., its gravitational radius), the universal value of limit force c4/4G is realized. This allows you to relate the characteristics of the Universe related to various stages of its evolution.
The Egorov theorem for transverse Dirac-type operators on foliated manifolds